Microwave and Optical Control of Sub-Diffraction
Spin Qubits in Diamond at Cryogenic Temperatures
by
Michael P. Walsh
B.S., Massachusetts Institute of Technology (2013)
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
Massachusetts Institute of Technology 2015. All rights reserved.
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Department of Electrical Engineering and Computer Science
August 23, 2015
C ertified by .......................
Signature redacted
D rk R. Englund
Assi tant Professor
esis Supervisor
Accepted by ......................
Signature redacted
'ILeslI'AY Kolodziej ski
Chairman, Department Committee on Graduate Theses
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I
Microwave and Optical Control of Sub-Diffraction Spin Qubits
in Diamond at Cryogenic Temperatures
by
Michael P. Walsh
Submitted to the Department of Electrical Engineering and Computer Science
on August 23, 2015, in partial fulfillment of the
requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
Abstract
Efficient entanglement of negative nitrogen vacancy (NV) centers in diamond will
bring us significantly closer to realizing a large scale quantum network, including the
design and development of quantum computers. A central requirement for generating
large-scale entanglement is a system that can be entangled at a rate faster than it
decoheres. There are a variety of proposed protocols to implement entanglement,
however, thus far implementation of a system that performs efficiently enough in
practice to overcome decoherence has been unsuccessful. In this thesis, I laid the
ground work to entangle two NVs using a dipole coupling protocol, a protocol that
has the advantageous property of not requiring use of identical photons, making this
experimental approach highly feasible. The actual experiment will be done at cryogenic temperatures, a condition that provides an advantage over room temperature
realizations of the protocol by extending coherence time and improving readout speed
and fidelity. The ultimate goal of this work is to determine if this is achievable in a
scalable architecture that will establish a foundation for future experiments in this
research and development area.
Thesis Supervisor: Dirk R. Englund
Title: Assistant Professor
3
4
Acknowledgments
First and foremost, I would like to express my sincere appreciation for the exceptional
mentorship that Professor Dirk Englund, my supervisor throughout this project, has
provided. His guidance and enthusiastic support in each and every aspect of this
research effort was key to its success. Dr. Tim Schr6der, a postdoctoral fellow who
I had the good fortune of working closely with, not only made the lab atmosphere a
productive and fun place to work, but he provided amazing mentorship. The friendship and collegial support of other lab mates including Ed Chen, Sara Mouradian,
and Luozhou Li, who contributed significantly to this project is genuinely appreciated, especially Matt Trusheim who introduced me to pulsed measurements. I would
also like to acknowledge Sen Yang, a collaborator from the University of Stuttgart,
who provided the SIL sample that was critically important in this investigation.
The outcome of work conducted in support of this thesis is only a stepping stone
on the path to a much larger longer-term project that is occupying the time, effort
and vision of many other graduate students and postdoctoral fellows who are pushing
the envelope in the rush to build an NV quantum photonic network on chip. I would
like to acknowledge them for being there to discuss a myriad of wild and not so wild
ideas and providing technical support when it was needed.
Finally, I would like to thank my friends and family.
Their love and support
motivates me to do better, and I cannot thank them enough for being there through
good and difficult times. My parents, Ed Walsh and JoAnn McGee, are always a
phone call away, eager to advise and help in any way that they can, thank you!
5
6
Contents
1
2
3
Introduction
15
1.1
M otivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
1.2
The Q ubit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
1.3
The Negatively Charged NV Defect Center . . . . . . . . . . . . . . .
19
1.3.1
Energy States . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
1.3.2
State Transitions . . . . . . . . . . . . . . . . . . . . . . . . .
23
1.3.3
Room Temperature . . . . . . . . . . . . . . . . . . . . . . . .
25
1.3.4
Cryogenic Temperature . . . . . . . . . . . . . . . . . . . . . .
26
Previous Work on Entanglement
29
2.1
Flying Qubit Mediated Entanglement . . . . . . . . . . . . . . . . . .
31
2.2
Entanglement Through Dipole Interaction
. . . . . . . . . . . . . . .
35
2.3
New Concept
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
Experimental Setup
41
3.1
Sample Preparation Furnaces
. . . . . . . . . . . . . . . . . . . . . .
41
3.2
Qubit Control Apparatus . . . . . . . . . . . . . . . . . . . . . . . . .
46
4 Reference Sample
4.1
4.2
55
Spectral Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.1.1
Spectral Diffusion . . . . . . . . . . . . . . . . . . . . . . . . .
63
4.1.2
Linewidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
7
4.3
5
6
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
Engineered Sample
73
5.1
Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
5.2
Single NV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
5.3
Expanding to two NVs . . . . . . . . . . . . . . . . . . . . . . . . . .
79
Conclusion
81
6.1
Ongoing Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
6.2
Future Work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
8
List of Figures
1-1
The Bloch sphere represents the state of a qubit by plotting a vector
on the unit-sphere. A vector pointing perfectly up is in the state
A
pulse can be used to transfer this state to the axis coming out of
the page,
1-2
|0).
(10) + 1)). . . . . . . . . . . . . . . . . . . . . . . . . . .
18
The NV center is contained in a carbon lattice. The vacancy is shown
as transparent and the substitutional nitrogen is shown as brown. The
carbon atoms neighboring the vacancy are shown as black, and the
next-to-nearest carbon atoms are white. This Figure was taken from [141. 20
1-3
The molecular orbitals that will be used to construct the relevant energy states of the NV. This Figure was taken from [141. . . . . . . . .
1-4
21
Energy level diagram for the NV center. The left part of the Figure
shows the distribution of the 6 electrons in the defect center. Note that
the excited state could have the spin down electron populating e. or ey
orbitals which gives rise to the splitting in the NV states E. and Ey.
The light blue shaded regions indicate the phonon sidebands. Solid
lines correspond to transitions that require photons, while the dashed
orange line indicate phonon-aided transitions which are non-radiative.
From left to right, the first splitting is caused by a symmetry-breaking
strain in the lattice which shifts the e. and ey orbitals' energy. The
next splitting is the fine interaction of the electron spin . . . . . . . .
9
22
1-5
The energy spectrum described above has been replicated to the left
for convenience. The right plot shows the photoluminescence excitation
(PLE) spectrum of the NV showing all of the optical transitions. This
Figure has been adapted from Batalov et al.
2-1
[5].
. . . . . . . . . . . .
27
A diagram showing the entanglement steps for one of the NVs. On the
left, the full energy level diagram for the NV has been shown again.
The relevant states are maintained as we demonstrate the steps for
entanglement. The blue dot represents the state of the electron before
that step is applied.
The transparent dots represent the superposi-
tion achieved from the ! pulse. Finally, the resonant pulse is used to
conditionally excite the electron. . . . . . . . . . . . . . . . . . . . . .
2-2
32
A diagram showing the relevant combined system energy levels. The
solid colored arrows represent some of the possible MW transitions.
The Zeeman shift is responsible for unique addressing.
2-3
. . . . . . . .
A diagram showing the Bloch sphere representation of the entanglement protocol. Figure taken from Dolde [16. . . . . . . . . . . . . . .
3-1
36
37
Photograph showing the assembled furnace. All flanges are CF-100.
The foil has been removed from the main chamber to expose the heating
tape........
3-2
.....................................
Photograph (left) and schematic (right) of the heater stage. Images
taken from Tectra Physikalische Instrumente (www.tectra.de). ....
3-3
43
Magnified image of the thermocouple removed from the ceramic hole
(top) and secured in the hole (bottom). . . . . . . . . . . . . . . . . .
3-4
42
44
The thermocouple error relative to the infrared thermometer (noted
as "laser" in the Figure). Note the value read out is lower than the
infrared thermometer.
3-5
. . . . . . . . . . . . . . . . . . . . . . . . . .
44
Temperature of the cryostat as a function of time. . . . . . . . . . . .
46
10
3-6
Schematic of the main chamber inside the cryostat.
Note that the
faded end on the right continues to the closed-loop He pump and the
turbomolecular pump. The purple blocks represent piezo motors. The
bold X, Y, Z are the stepper piezo motors for coarse control. The italic
z above the objective is for fine control. . . . . . . . . . . . . . . . . .
3-7
Photographs of objective.
47
On the left image, notice the rectangu-
lar piezo block on the bottom left which secures the objective to the
chamber. The other images zoom in on the MW antenna across the
tip of the objective. The objective has a 300 pm working distance and
the wire is 50 pm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-8
48
Optical paths used in the experiment. All of the sources begin on the
right, and all collection is on the left. The inset plot shows an example
of an NV spectrum at room temperature (to emphasize the PSB). The
purple cutoff shows the spectral location of the 650 LP filter. A curved
line with an arrow at each end represents an element that can be moved.
The spatial filter represents a pair of balanced lenses focusing the light
onto a pinhole.
3-9
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
Schematic showing how a buffered count operation works when gated.
Note that the channel B rising edges that arrive when channel A is
low are ignored. On the rising edge of channel A, the counter stores
the current value (the number of rising edges that occurred in the
previous gate. In our particular case, channel A corresponds to the
gate provided by the PulseBlaster, and channel B corresponds to the
A P D clicks.
4-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SEM of a solid immersion lens (tilted at 52 *) fabricated into diamond
using a focused ion beam. Figure taken from Jamali [23]. . . . . . . .
4-2
52
56
Our SIL sample observed under a regular wide-field white light microscope.
For scaling reference, the SILs are about 10 pm in outer
diam eter.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
57
4-3
Our SIL sample examined with a wide-field fluorescent microscope (excited with 532 nm light and collected red fluorescence). The depth (z
axis) of the NV from the surface was estimated using the microscope's
stage. Again, for scaling reference, the SILs are about 10 pm in outer
diam eter.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
4-4 The top image is a confocal scan of the single NV in a SIL. The inset
is a zoomed out version.
The bottom plot shows the second order
autocorrelation of the arrival time of the photons. . . . . . . . . . . .
4-5
59
Spectrum of the NV center in the SIL with a grating of 300 grooves per
mm. The inset plot is taken with the highest resolution that we have of
1200 grooves per mm. Note the SIL only increases collection efficiency;
it does not alter the emission of the NV. The top plot is at room
temperature, while the bottom is at cryogenic temperature (18K). The
diamond Raman that can be seen very prominently is common for an
EG bulk diamond sample excited with 532 nm light. This NV has an
additional neutrally charged NV (NVO) element to it, as you can see
with the NVO ZPL near the Raman line. All of these lines at cryogenic
temperature are spectrometer-limited even with our highest grating of
1200 grooves per mm (you can see that it only has a full-width-halfmaximum of only 3 pixels).
4-6
. . . . . . . . . . . . . . . . . . . . . . .
61
Fast line scans of NV in SIL. Each pixel is acquired with a dwell time
of 2 ns a few hundred nW of excitation power. The bottom plot is a
vertical sum over all line scans showing the cumulative inhomogeneous
broadening with a linewidth of 447 MHz. . . . . . . . . . . . . . . . .
4-7
63
PLE scan of NV in a SIL. The top shows the pulse sequence used
for each pixel.
To acquire enough counts, the pixel's measurement
was repeated 10,000 times and averaged before advancing to the next
frequency point. The tall transitions (the two fitted on the left) are
the E_ and E. transitions. Approximately 20 nW of power was used.
12
65
4-8
The top Figure shows another PLE scan of the same NV as in the
previous Figure. The contrast of the two tallest peaks (E. and Ey) are
plotted below as a function of excitation polarization. . . . . . . . . .
4-9
66
Ionization time in the SIL. The top shows the pulse sequence used, and
the bottom is the plot of the averaged counts.
. . . . . . . . . . . . .
68
4-10 Ionization time in the SIL with increasing resonant excitation power.
As we would expect, the ionization time decreases as the power increases. 70
4-11 The top plot shows an ESR spectrum taken at five different temperatures. The bottom plot shows the linewidth of the four peaks as a
function of temperature. The linewidth was determined by fitting the
sum of 4 Lorentzians to the 4 peaks shown in the top plot at each
tem perature ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-1
72
Confocal scan of the engineered sample. This is the location where
the four quadrants intersect, near the center of the diamond. The top
right is the highest dosage of 10" and the sweep goes clockwise down
to the lowest dose of 108. . . . . . . . . . . . . . . . . . . . . . . . . .
5-2
74
A Monte Carlo simulation (in SRIM) performed to determine the depth
of the ions implanted at 20 keV. The left shows the mean stopping range
of the ions, and the right shows damage to the lattice in the form of
vacancies caused by collisions with the ballistic nitrogen ions. ......
5-3
74
The top row shows confocal scans associated with the region of the
PLE scan (bottom). Note a very clear dependence of the linewidth on
the dosage. ........
5-4
75
................................
Fast line scans of the engineered NV. The NV is very stable for 5000 line
scans. The sum over all 5000 still yields a linewidth of approximately
100 M Hz.
5-5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ESR spectrum showing the m, = 0 to m, = -1
76
transition in the
ground state. This was measured wile continuously applying 532 nm
light and sweeping the MW frequency.
13
. . . . . . . . . . . . . . . . .
77
5-6
Rabi oscillation between the m, = 0 and m, = -1 ground states. The
data shown in the left plot is under green excitation, and in the right
is under resonant excitation. The pulse sequences are shown below
the plots. Note that there are two read-out times for the APD. In the
case of green excitation, this is used to normalize to. For the resonant
excitation it simply tells us that we can collect for a longer time since
the NV hasn't been ionized. . . . . . . . . . . . . . . . . . . . . . . .
5-7
78
A confocal-spectral scan of the second-lowest dosage region. The top
left image is a sum over all wavelenghts (equivalent to collection with
an APD). As expected, the majority of the NVs have ZPLs at around
637 nm (top right). The bottom left images show frames a two separate
wavelengths, where two NVs overlap spatially, but not spectrally. The
bottom right image shows one of the NVs as red, and the other as green. 80
6-1
An overnight PLE scan. Vertical lines have been added to help guide
the eye. The laser seems to have drift on the order of GHz, and what
appears to be a mode hop around scan number 10,000.
6-2
Sideband generation.
. . . . . . . .
82
The 637 nm light is amplitude-modulated at
3.3 GHz to produce sidebands. The plot shows an NV ZPL that is
originally at 0 GHz, but the
6-3
3.3 GHz sidebands also excite the ZPL.
83
QR code in diamond. The pillars in the center of the etched squares
are designed to improve the contrast between squares that are either
etched or not, a logical 1 and 0 respectively, under white light illumination. The circles and asterisk symbols are designed so that the
image recognition software can easily locate the corner of the design
with high precision. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
85
Chapter 1
Introduction
Interest in the concept of quantum communication and computation based on large
entangled networks has been on a steady rise for sometime now. It comes with the
promise of improved security protocols and immense computational power.
While
these expectations are based on theoretical models and first proof-of-principle experiments, actual implementation of such protocols has been challenging with regard to
the complexity and physical mechanisms of such systems that make their realization
extremely difficult. It turns out that engineering a scalable system at the quantum
scale that is decoupled from the environment, but can be controlled sufficiently to
perform computations has yet to be demonstrated.
One of the fundamental prob-
lems is that it is challenging to create quantum entanglement and such systems are
extremely fragile, in particular for atom-like defects in the solid state. This has so
far prevented entanglement rates that exceed decoherence rates.
The work in this
thesis is intended to advance the effort to engineer a system that will have an entanglement rate greater than the decoherence rate that is necessary to realize large-scale
entangled states.
The nitrogen-vacancy (NV) center in diamond has shown to be a promising solid
state qubit, exhibiting long spin coherence time, optical state preparation and readout. The dipole-dipole coupling of two neighboring NVs has been taken advantage
of to entangle the two spins 1161.
The state can be readout very efficiently and
with high fidelity at cryogenic temperatures using a single shot readout protocol
15
[42].
Specifically, we will prepare a system to implement a magnetic-dipole entanglement
protocols at cryogenic temperatures. This will allow us to take advantage of the long
coherence time of the negatively charged nitrogen vacancy center at low temperatures
and in particular allow resonant high-fidelity, single-shot state readout.
1.1
Motivation
While early versions of computing machines used mechanical representations of bits
as computational units, today's computers use extremely densely packed classical
states of matter that can be switched very rapidly; however, the basic principle of
computation remains the same: deterministic switching of a machine according to
classical rules. The computational power of classical machines scales roughly linearly
with the number of bits and transistors. Given n bits, an increase to 2n would result in
about twice the computational power. However, a quantum computer's performance
for certain known algorithms would increase roughly by a factor of 2n. To put this
in perspective, when considering even a small register with n on the order of 100
two-level quantum systems, the mere representation of the quantum state would be
impossible using every hard drive on Earth
[32].
For the past 30 years, exponential growth in the computer industry has been
observed.
Each year the number of transistors that can be loaded onto a chip is
doubled, as described by Moore's law
[441. Advancements in the nano-fabrication of
silicon have made this possible. The dimension of transistors inside many computers
today is on the order of ten nanometers. This is already a scale at which the classical
laws of physics begin to break down.
This manifests itself in quantum tunneling,
where electrons can tunnel through insulating materials causing excessive heating
and power consumption and limits further miniaturization of devices required for the
development of more powerful systems [43, 22].
It is only natural to begin investigating these quantum effects more thoroughly.
There are certainly solutions to this problem that will keep us in the classical regime,
and give us the opportunity to push Moore's law further.
16
However, is there a pos-
sibility to actually use the quantum effects in a highly advantageous way? Yes, by
applying the theoretical proposals of quantum information processing to the hardware of a classical computer, we can apply it to the information stored within the
computer, bringing us into the realm of quantum computation.
1.2
The Qubit
Instead of using classical bits that have a high and low state (binary systems), quantum computers take advantage of quantum mechanical phenomena, such as superposition and entanglement, to perform operations on certain computational problems
for which classical computers are inefficient' [38, 9j. This field promises to usher in a
new era of information technology that will greatly improve computational speed and
enhance the development of advanced security systems [45]. Development of quantum
systems will also seed the development of tools that will permit the achievement of
heretofore unachievable goals in other scientific and technology-based areas. Computational biology, engineering design optimization, and artificial intelligence are just a
few fields that will directly, and powerfully, benefit from the availability of quantum
processing systems [41, 271.
Similar to our classical binary machine that operates on bits, a quantum computer
can operate on qubits. Similar to bits, qubits can have two states, 0 and 1. However,
qubits can also exhibit the property of being in a superposition of 0 and 1. Most
generally, we can represent the state of a qubit as
| )
= a 0) + 3 1), commonly
visualized as a vector on the Bloch sphere, as seen in Figure 1-1.
There are many physical representations of a qubit that are being studied today.
Any quantum system that has an addressable two-level system is a candidate. Photon
polarization[8, 251, photon number[251, electron spin[17], nuclear spin[241, Josephson
junctions[33j are just a handful of candidate systems. It is possible to have a hybrid
system as well. We will not evaluate the relative merits of each possible system,
'Inefficient in computer science refers to computational time that scales worse than polynomially
with the size of the problem.
17
0)
0) + i 11)
Figure 1-1: The Bloch sphere represents the state of a qubit by plotting a vector on
the unit-sphere. A vector pointing perfectly up is in the state 0). A i pulse can be
used to transfer this state to the axis coming out of the page, T (10) + 1)).
but we can consider a few properties that are highly desirable. Ideally we want to
implement a system that is easily addressable (e.g., it has a well defined position)
and is isolated from the environment as much as possible, so that the system has a
long coherence time. Multiple qubits must also be able to interact so that conditional
operations, such as NAND and NOR gates, are available.
Among the various quantum-based architectures currently under investigation,
photonics is considered one of the most promising approaches. Spatial modes of photons - such as polarization - can be used to encode quantum states.
Their weak
interaction with matter implies a long coherence time, making them well suited for
fast and reliable quantum communication and networking applications [12, 3]. Unfortunately, it is difficult to get photons to interact with each other2 . Alternatively, an
atomic quantum system that readily interacts with nearby qubits through a dipole
interaction can be considered. A single charged atomic system can be isolated in
2
1t is not actually impossible for photons to interact with each other. There is a substantial
amount of research trying to prepare a quantum computer using linear optics [201.
18
an electromagnetic trap (e.g. Paul trap 1401) to isolate them from the environment.
These nodes can be constructed by placing ions in cavities to enhance their interaction with photons. This provides a stable stationary qubit that has great coherence
with photonic interconnects
[32].
The
Ions that are isolated in a trap constitute a very clean quantum system.
valence electrons can be manipulated optically to store information and exhibit coherence times of up to 50 seconds for the case of a hyperfine transition in
ions
4
3Ca+
[2]. However, with current technology, a serious limitation in the use of ion traps
has been encountered.
The electronics that go into trapping the ions are proving
to be very difficult to scale [47]. Electronic noise and the high voltage necessary to
create the trapping potential causes the ions to heat which decreases their coherence
times. It would be clearly beneficial if we could develop the same system without the
electronics required to trap ions.
One direction that might be taken is the use of solid-state systems, where a crystal
lattice behaves as the trap.
If this lattice has a point defect, like a substitution,
interstitial or vacancy, there is a good chance that it would produce a similar wave
function to that of a trapped ion
[14], as has been shown in various solid state matrices
like silicon, diamond, and SiC. This brings our discussion to a very special defect
center: the nitrogen-vacancy (NV) defect in diamond.
1.3
The Negatively Charged NV Defect Center
The negatively charged NV center, referred to as simply an "NV center" unless otherwise specified, shows great promise in quantum information
[49]
and metrology
[15].
The center has several qualities that make it an ideal system. It is capable of generating single photons, long coherence times
polarization and readout.
19
[3],
spin-spin coupling, and optical spin
4
9C
CC
to*ct
N
Figure 1-2: The NV center is contained in a carbon lattice. The vacancy is shown
as transparent and the substitutional nitrogen is shown as brown. The carbon atoms
neighboring the vacancy are shown as black, and the next-to-nearest carbon atoms
are white. This Figure was taken from 1141.
1.3.1
Energy States
The NV center has C3, symmetry in the diamond lattice. As shown in Figure 12, where we will define the axis of the defect to be along z.
This means that it
has the identity, C 3 (120* rotations) and three a-, planes (3 vertical reflections) as
its symmetries.
Using group theory and a linear combination of the dangling sP3
orbitals of the neighboring carbons, we can construct a set of molecular orbitals for
the NV. There are only three of these orbitals that exist in the bandgap of diamond:
Figure 1-3 shows the geometry of these orbitals and a schematic of their
energies. The a, orbital of the N-atom mixes with the a, of the C-atoms to form a,
{al, ex, e}.
and a'. The mixing pushes a' into the valence band, making it insignificant when
trying to understand the NV's observable properties. The logic of this explanation
can be found in work done by Doherty, et al. [141.
The energy diagram of the NV center is illustrated in Figure 1-4. The NV has
6 electrons associated with it. By filling orbitals, we produce a ground and excited
state that exist in the bandgap of diamond. The lowest molecular orbital (MO), a'
20
Conduction Band
0a,
14W *W
-I"PyO
a,
ey
ex
Valence Band
Figure 1-3: The molecular orbitals that will be used to construct the relevant energy
states of the NV. This Figure was taken from [141.
(in the valance band) is completely filled in both states:
Ground = a a2e2
Excited = a 2 a1 e 3
To simplify our discussion we will consider the NV center to be in the limit of high
non-axial strain. As a result, the excited state orbitals, Ex and E. are split in energy
due to their asymmetry. The last thing that is necessary to consider is the spin-spin
interactions of the electrons. Because there are 8 available states in the MOs and
only 6 electrons, we can think of the system as having two holes, which is much easier
to theoretically describe.
The two holes' spin interaction will split the remaining
states into triplets, each corresponding to a particular spin state, m. = {-1, 0, +11.
To summarize, the NV center has a spin triplet in the ground state, and an orbital
doublet in the excited state, each having a spin triplet.
These states can all be shifted by external magnetic and electric fields, variations
in temperature, and strain in the lattice, which is similar to an external electric field.
As we will see later, this can cause some significant issues using the NV as a qubit in
many quantum computing protocols.
Because the ground state is fairly important to many protocols since the qubit is
encoded in the spin degree of freedom, let us examine it a bit closer. The ground
21
+1
a
E
a'1
+1
-
ea
z
-
-
--
1
0
h
Metastable
State
-637 nm
e-
ex
/+1
--
--- ---
a'1
--
--
-2.8 GHz
0
Figure 1-4: Energy level diagram for the NV center. The left part of the Figure shows
the distribution of the 6 electrons in the defect center. Note that the excited state
could have the spin down electron populating e. or ey orbitals which gives rise to
the splitting in the NV states E_ and Ey. The light blue shaded regions indicate the
phonon sidebands. Solid lines correspond to transitions that require photons, while
the dashed orange line indicate phonon-aided transitions which are non-radiative.
From left to right, the first splitting is caused by a symmetry-breaking strain in the
lattice which shifts the e. and ey orbitals' energy. The next splitting is the fine
interaction of the electron spin.
22
state can be described by the spin Hamiltonian
(S
H = hD
-
[S(S + 1)]) + E(S.
-
Sj) + YpBB-S,
where S = 1 for the NV, g is the electron g-factor (g = 2), S is the spin operator
consisting of the S2, S. and Sz pauli matrices.
D and E describe the zero-field
splitting, PB is the Bohr magneton, h is Planck's constant, and B is the applied
magnetic field. The magnetic dipole interaction of the unpaired electrons sets the
splitting between m
symmetry of the m8
= 0 and m, =
=
1 to be around D = 2.88 MHz [191. The
1 levels makes them degenerate (E = 0) with no applied
magnetic field. An applied magnetic field will lift the degeneracy of these states
through the Zeeman effect.
The explanation has thus far ignored another very important state, the metastable state3 . This is a singlet state that has slightly less energy than the excited
states. We will touch on the properties of the meta-stable state in the next section
as we consider transitions.
1.3.2
State Transitions
This section will consider a simplified model that excludes phonon interactions.
All of the NV transitions, aside from a transition through the meta-stable state,
are spin conserving. If an NV is optically excited from m, = -1,
most likely 4 end up in the ms = -1,
0, or 1, it will
0, or 1 excited state, respectively. The average
fluorescence lifetime of these excited states is about 12 ns. The m, = 0 decays directly
back to the m, = 0 ground state 95% of the time, emitting a -637 nm photon5 . The
other 5% of the time, it decays to the meta-stable state. The m, =
directly to the m, =
1 will decay
1 ground state about 70% of the time, also emitting a ~637 nm
3
There are actually two states that comprise our simplified "meta-stable" state. This will not
have an impact on the physics discussed.
4There is a small chance that the NV will ionize or undergo a charge transfer. It is also very
possible that there are other transitions which are unknown preventing the NV from having an
internal quantum efficiency of one.
5
A -637 nm photon is only emitted around 3% of the time when considering phonons. However,
keep in mind, the model being used in this section is excluding phonon interactions.
23
photon. The remaining 30% of time, it decays to the meta-stable state as well 128].
Decaying into the meta-stable state requires phonon assistance and the transition
does not emit light. The meta-stable state has a lifetime of approximately 300 ns
after which it will most likely decay to the m, = 0 ground state, sometimes emitting
an IR photon. This process clearly is not spin conserving, in the case of ms =
1,
which provides the intersystem crossing. It is this mechanism that allows the NV to
be optically polarized and read out 1281.
If we optically pump an electron originally in the m, = 0 ground state, it will
be excited to the same spin sublevel and decay back to the ground ms = 0 sublevel
emitting a photon. This will continue with a high probability until we stop pumping
it. However, if the electron is originally in the m, = +1 ground state, there is a good
chance it will decay via the intersystem crossing and not release a visible photon.
Because this event is significantly more probable compared to the m = 0 case, it
will, on average, emit less light allowing us to determine if the NV was originally
in the m, =
1 state. After readout of mroe than a few 10 ns, the NV has been
polarized with high probability into the m. = 0 state, re-initializing it.
This leaves us to consider the last state transitions that will be discussed for this
thesis. All of the transitions discussed thus far, excluding the meta-stable state, are
processes involving the absorption or emission of a photon. Because photons can
only have spin
1, they can only contribute one quanta of angular momentum. If
the electron is pumped from the ground state to the excited state by absorbing a
photon with angular momentum, it gains orbital angular momentum, and remains
in the same spin state. However, if we are interested in inducing a transition in the
ground state, this angular momentum can be converted to a spin transition. If a
photon with spin 1 is absorbed, a transition between m, = 0 and m, = 1 can be
induced. Likewise, the opposite circularly polarized photon can induce the transition
to m, = -1
[1].
24
1.3.3
Room Temperature
The next element of a more complete description to consider are phonons. The NV is
buried in a diamond lattice at finite temperatures supporting phonon modes. Due to
the asymmetry of the NV wave function, the center couples to these phonons. This
has the effect of blurring the energy levels discussed previously with a continuum of
states. Furthermore, it increases the decoherence rate and probability of level-mixing
of the excited states which causes inhomogeneous broadening (to a few nanometers
in linewidth at room temperature).
As such, at room temperature, only a single
transition can be made - the zero-phonon line (ZPL) at 637 nm; all of the fine structure
discussed earlier has energy spacing of a few GHz, so they all heavily overlap now
making them indistinguishable.
The lattice interactions cause optical transitions
under creation and annihilation of phonons which can be observed experimentally in
a broad phonon sideband (PSB) that extends up to 800 nm.
Because a PSB exists in the excited state as well, we can excite the NV with an
off-resonant laser (-532 nm). A green laser can be used to excite the electrons from
the ground state to the excited state under the creation of phonons.
In addition to phonons, there are multiple sources of noise in the system that will
decohere the NV. Both come from paramagnetic impurities including other carbons in
the diamond lattice. Although diamond consists of 98.9%
12C
which has spin 0, and
therefore does not couple to the NV spin via spin-spin interaction, 13C (remaining
1.1%) is a spin 1 system. This creates a spin-bath that affects the NV, causing
decoherence. The longest coherence time at room temperature has been measured
to over 2 ms6
[35].
It is important to note that the coherence times that are being
discussed are those of the electron spin in the NV center. Besides the delecton spin,
als the nuclear spin of the N and nearby C atoms can be addressed and used, for
example performing a SWAP operation and storing the qubit in a near-by nuclear
spin, a system with coherence times approaching 1 second at room temperature
6
[29].
This approach uses a dynamical decoupling pulse sequence to further reduce the effect of noise
on the NV. Without this, the longest coherence time is approximately 400 ps (with a standard Hahn
echo sequence).
25
Nonetheless, the electron spin coherence is a useful metric to use when judging the
quality of the system and is the relevant spin-photon interface.
1.3.4
Cryogenic Temperature
At cryogenic temperatures, we are able to freeze out some phonon modes which
results in narrowing the ZPL transition. In principle, all of the six state transitions
are detectable optically and can be lifetime limited in spectral width
(~
14 MHz for
a 10 ns lifetime).
We gain an additional tool for optical state control and readout at cryogenic
temperatures because our transitions are considerably narrower. A resonant laser
can be used to excite the NV and this carries multiple benefits. Since we are on
resonance, significantly less power can be used and we take advantage of the fact
that the six transitions are unique. By applying a resonant pulse to one of m, = 0
transitions, we can determine if the NV is in that state by the brightness of emission.
If it is in that state, a photon will be emitted. If it was in a different state, it would
not have absorbed the excitation photon, thus would not have emitted a photon. This
has the added benefit of preserving the state since the m, = 0 transition will always
decay back to the same spin. In this way, single shot state readout can be performed.
Furthermore, because the transitions are so much narrower, we can use the technique described above to take an absorption spectrum of the optical transitions by
scanning the resonant laser across them, a photoluminescence excitation spectrum
(PLE). An example of this is shown in Figure 1-5 taken from Batalov et al. [5].
In this way, the spectral distribution and linewidth of the ZPLs can be determined
to gain knowledge about the optical properties of the NV and to find the relevant
transition energies.
The last advantage of working at cryogenic temperatures to consider is related
to coherence time. If we consider an isotropically pure diamond, with nearly all
"C and a very low defect concentration, our decoherence must be dominated by
phonon activity. Thus, maintaining a system at cryogenic temperatures will extend
coherence time up to almost 1 second
[31
by suppressing many phonon modes that
26
(a)
E excited state
2.6
E1
s~
2.3
Sz
E
E~Is(2)
S
(3)
(6)
()
L~~(6)
S,(
0.3
0.4
(b)
(5)
Ex
E
0d
-j
CL
(4)
(5)
(3) (2)
SV
SI"
3A 2j 2
5
z
10
15
Laser frequency (GHz)
M
S
Figure 1-5: The energy spectrum described above has been replicated to the left for
convenience. The right plot shows the photoluminescence excitation (PLE) spectrum
of the NV showing all of the optical transitions. This Figure has been adapted from
Batalov et al. [5].
27
would otherwise dephase our system.
28
Chapter 2
Previous Work on Entanglement
Now that we have considered the qubit, we can consider strategies for its manipulation. A qubit itself is a fascinating, but by itself it is not a very powerful tool in the
realm of quantum computing. It is the relationship, or correlation, of many qubits
that gives quantum computing its power and speed. These correlation events differ
slightly from classical dynamics. Classical correlations are common place in everyday
life. Take the case of coin flipping. For two coin tosses, the correlation of every possible coin toss outcome can be easily computed: "heads and heads", "heads and tails",
"tails and heads", and "tails and tails."
Quantum correlations are considerably more complicated. Based on the principal
of superposition, as discussed earlier, there are multiple ways to measure or observe
the qubit (e.g., if we consider the qubit in a black box, door 1 or door 2 can be
opened to make the observation, but not both1 ).
For example, a qubit encoded in
the polarization of light can be observed in a basis that detects horizontal or vertical
polarization (it can be one or the other). We can also measure in a basis that detects
450 and -45" polarization; again, it can be one or the other. Already, we can see that
the possible number of correlations becomes much richer. If we now consider the
case of two qubits, both can be observed by opening door 1 or door 2 and all of the
correlations can be written down. Opening door 1 of one qubit, and door 2 of the
'It is important to note that the operation of opening a door is equivalent to a measurement
on the system. The measurements being performed here are non-compatible, as in they do not
commute.
29
other does not contain any correlations since these observations are non-compatible.
After enumerating all of the possible options, it is clear that instead of having only
four options, as in the classical case, we now have 8; there are 2 ways to observe the
combined system and 4 outcomes for each. As the number of qubits increase, the
number of correlations grows exponentially.
There is a very special type of correlation in the quantum world that must be
considered: entanglement. When two qubits are described by some wavefunction, IT),
and this wavefunction can be decomposed into the single qubit wavefunctions, e.g.,
a product state,
RI) = 10i) 12),
then these qubits are not entangled. Alternatively,
when IT) cannot be decomposed, these qubits become entangled. The most common
example is probably the Bell states:
D+ )
(IO)A O)B +
=
IO)B - I1A I1)
=(10)A
<b-
X+)
1
=
1)A I1)B)
(IO)A
11)B + M)A O)B)
(O)A I1)B -
11)A IO)B)
where qubits A and B are represented in the basis {10), 1)}.
A spontaneous parametric down-conversion (SPDC) source is a good example of
entanglement generation.
A non-linear X( 2 ) crystal is pumped with an excitation
laser. Some of these excitation photon will be absorbed and two photons each with
half the energy of the pump photon will be emitted and exhibit entanglement in
their polarization.
Such entangled states are the resources that we want to use,
and although entanglement generation happens all of the time, it is challenging to
measure and use for quantum information processing. I will discuss two entanglementtechniques that are used in our physical NV implementation of the qubit.
30
2.1
Flying Qubit Mediated Entanglement
In the following protocols we consider 2 distance stationary NV electron qubits which
will be entangled via 2 flying qubits (photons) in a collision experiment. The measurement performed is a Bell-State measurement of the two photons which will entangle
the NV spins if successful. The NV systems must be at cryogenic temperatures so
that the optical transitions are narrow enough to be excited with a resonant photon.
Under perfect conditions 2 , emitted photons will also be spectrally identical, a condition that will be important for implementation of some of these protocols3 . Finally,
we will encode our qubit in the spin degree freedom. The m, = 0 will be defined as
It).
Arbitrarily, we will define
{) to be m,
= 1. By lifting the degeneracy of m, =
1
with an external magnetic field, we create an effective 2-level system in the ground
.
state, our spin qubit 4
In the first method, the first step is to entangle the NV center's electron spin with
an emitted photon. This spin-photon entanglement is quite readily available in the
system since there is spin-dependent fluorescence. A single NV can be initialized with
green laser pulse to
IT).
As with any two-level system, we can drive a rabi oscillation
between the two states, here IT) and
|4)
by applying a resonant field that couples the
states. In this system, the resonant field between the m, = 0 and ms = 1 ground
states is a MW field. By timing the duration of the MW pulse, we can generate a
2
pulse which puts our system in the superposition state,
IT) =
1(IT) + 4))
Figure 2-1 shows a simplified energy diagram that involves only the states nec2
No spectral-diffusion in the system so that all transitions are lifetime limited.
The condition that is actually important here is that the photons be spectrally indistinguishable
to the detector being used. The timing jitter of the detector sets the limit on how large the spectral
separation of the photons can be for them to be indistinguishable. Of course a perfect detector, one
that has no jitter and will click at an exact time will destroy all spectral information since they are
time and energy are a conjugate pair. When we add jitter, we lose timing precision and thus you
can imagine the environment can gain spectral information which will destroy our entanglement and
give us a mixed state 131].
4 In principal, this is not the only way to isolate the states. You could also exclusively use left or
right handed circularly polarized microwave radiation to uniquely address the m, = 1 states.
3
31
+1
EY
Ex{
-1
0
0
+1
-10
Ie)
le)
0
-X7
+1
-1
4)
It)2
it)
Figure 2-1: A diagram showing the entanglement steps for one of the NVs. On the
left, the full energy level diagram for the NV has been shown again. The relevant
states are maintained as we demonstrate the steps for entanglement. The blue dot
represents the state of the electron before that step is applied. The transparent dots
represent the superposition achieved from the ' pulse. Finally, the resonant pulse is
used to conditionally excite the electron.
32
essary for this protocol, along with the steps taken to achieve entanglement. The
ground states are as discussed previously, and the excited states that we choose will
be a state accessible by the m,
=
0 ground state, because we want a transition that
will be spin-conserving with high probability (avoiding the meta-stable state). This
leaves either the E, or E. state where m,
=
0, and we can arbitrarily choose one and
call it le).
Applying a laser pulse that is on resonance with
It)
up to
|e)
transition will
conditionally excite the electron. If the electron was in It) before the pulse, it will
have been excited to le) and emit a photon as it relaxes back to the ground state.
If the electron started in
resonant with
j4)
4),
nothing will happen because there is no excited state
and our laser pulse. Because we have prepared our NV to be in the
superposition state, IT), we can write out the full state of the combined NV-photon
system:
|T)
=
(it) |1) + 4)|0)),
where 10) and 11) correspond to the photon number emitted by the NV (more precisely,
it corresponds to the detection event of the photon). Since our wavefunction cannot be
separated into a spin portion and a photon-number portion, we achieve entanglement
between the electron spin and the photon number.
Our goal is to entangle two electron spins. So far, we have entangled one electron
spin to the photon number. Now, we must consider two separate NVs, A and B. We
will prepare both of them in a superposition state as described above, and perform
the same spin-photon entanglement scheme. The state of the joint system is:
-
2
(ITAtB) I1A1B) + 4AlB) IOAOB) IAB)
GA1B) + ITAIB) I1AOB))
This time the emitted photons will be overlapped on a beamsplitter before being
detected. This has the effect of erasing the information designating where the photon
originated. Assuming that these photons are indistinguishable and we have unity
33
detection efficiency, detection of precisely one photon would correspond to measuring:
} (IioB)
e-
OA1B))
This measurement projects the state into the maximally entangled state:
1F)(TA
B)
e4-AtB
A derivative of this experiment, theoretically proposed by Kok et al.
[4],
was per-
formed in Hanson's group by H. Bernien et al. [7]. Separate work has been done to
demonstrate the spin-photon entanglement, first demonstrated by Togan et al.
[46].
Despite this progress, one encounters many difficulties when actually performing the
experiment. Bernien et al. successfully generated these states, but each generation
took on the order of 10 minutes. Given that the NV coherence time is on the order of
seconds in the best case, it is impossible to scale to more than 2 qubits, a necessary
requirement for many quantum information applications.
Another technique that uses flying qubits is a cavity reflectivity measurement
[37]. In this scenario, the NV is placed in a cavity that is resonant with the 10)
to le) transition. Depending on the spin state, the cavity is either transmittive or
reflective for this state. By sending a resonant photon to a beamsplitter, we can
split its wavefunction so that it visits two of these cavities, just as in a Michelson
interferometer. The photon is conditionally reflected and passes back through the
beam splitter to erase the path information. The subsequent detection projects the
NVs into an entangled state.
The most significant problems encountered when considering techniques that involve spin-photon entanglement are photon loss and indistinguishablity. Naturally,
the NV emits only a few percent of the photons into the ZPL transition, the other
~97% into the PSB. The photons emitted into the PSB are not coherent transitions
and thus are not useful in the discussed quantum information application. A simplified way to think about this is that the phonon(s) involved in the transition can
be "measured" by the environment which destroys coherence. Consider a combined
34
Hilbert space of the system of interest and the environment: H, 0 He. If we assume
that the phonon that is in the environment is correlated to our system of interest, we
can write a general state as
Iq)= a Os0e) +
1isle)
If we write this as a density matrix we have,
p = 11F) (pi
P= la! 2 100e) (Os0el + 112 1isle) (1sle|+ a+ * !0s0e) (1sle + a*
ilsle) (OsOel
Because we are interested in the state of the system alone, we can trace out the
environment Hilbert space which will cause the cross terms to go to zero. This leaves
us with a statistical mixture instead of a maximally entangled state:
p
=
|c| 2 |Os0e) (OsOe +
12isle) (isle
Because only about 3% of the overall emission events allow for the intended entanglement generation, current systems are prevented from entangling at a higher rate
than the decoherence rate.
All of the issues preventing higher entanglement rates are related to the intermediate photonic portion of the system, which is obviously an important factor when
one step is entanglement of the spin and the photon.
2.2
Entanglement Through Dipole Interaction
A more direct approach to entangling the NVs is to use magnetic dipole coupling
properties [16]. Previously we examined how we could use state-dependent fluorescence or transmission to entangle two NVs, now we consider state-dependent phase
accumulation.
There is no requirement for identical photons in this protocol, meaning our re35
11A -
|0s-1
Zeeman
from B
-
1B)I IOA
Zeema
IOA
1B)
1B)AO
AO)
13)
*Zeeman
I-1AOB)I
IO3lB)-3B
from A
030OB)
Figure 2-2: A diagram showing the relevant combined system energy levels. The solid
colored arrows represent some of the possible MW transitions. The Zeeman shift is
responsible for unique addressing.
quirement of cryogenic temperatures no longer applies. Additionally, we can simply
apply an off-resonant excitation pulse at about 532 nm, reducing the experimental
requirements for optical control even more. Now, the main concern is the proximity of
the NVs relative to one another and the ability to address them individually, requiring individual MW transition energies. For a magnetic dipole coupling strength of
approximately 5 kHz, the NVs must be separated from one another by approximately
25 nm [16]. This is below the diffraction limit for visible light, making it impossible to
address the two uniquely with visible light. Instead, we can use a system in which the
two NV axis have different spatial orientations (given the diamond crystal structure,
there are four possible orientations). It is possible to apply an external magnetic field
that projects differently onto the two NVs which creates a different Zeeman shift in
each of them. The NVs can now be uniquely addressed by applying the appropriate
resonant MW fields. Figure 2-2 shows the combined energy diagram for the system
illustrating the important transitions.
We are only concerned about keeping track of the ground states when using this
protocol; there is no need to worry about excited states because their exact energy
isn't relevant because we are using the green off-resonant excitation and because the
spectrally broad emission at room temperature due to phonon coupling does not allow
36
Figure 2-3: A diagram showing the Bloch sphere representation of the entanglement
protocol. Figure taken from Dolde [16].
us to resolve them anyway. As such, it will be beneficial to change notation to labeling
the state by their spin: {mS
=
-1,0, 1} -+
{I-1) ,10),
1)}. Our goal is to entangle
10) and 1), however this protocol will allow for entanglement between any two spins.
The basic idea is to implement a Hahn echo sequence on both NVs, which can be
divided into a series of gate operations as detailed below [161.
Just as in the other protocols, we begin by initializing both NVs to 10) ground
state with a green laser pulse. Both NVs are projected into a superposition state
of 1-1) and 1) by applying a double quantum i rotation on both spins, as seen in
Figure 2-3. This gives us the following state,
1
2
Only the states that have the same spin will couple (the interaction term in the
Hamiltonian here is S- S) which will result in the state-dependent phase accumulation.
After some time of free evolution, the state becomes:
) =
where
#
(ei2
I-lA
-
1B)
-
hA
-
1B)
-
-AiB)
-- ei2o
I1A1B))
is the additional phase gained by the magnetic-dipole coupling. A double
quantum ir rotation followed by the same free evolution will cancel all quasi static
37
noise and double the phase accumulated by the dipolar coupling.
A final double
quantum i pulse will map the system onto
2 -"
-- 1)
|-1A
-
1B) + (e-i2# -
1+B)
If we allow the free evolution to occur for a certain amount of time, we can obtain the
maximally entangled Bell state,
(-1A
1B)
-
-- lAiB)). At this point application
of local (spectrally resolved) 7 pulses will put us in the entangled state we were trying
to achieve:
(IMAB)
-
Zi lAlB))
The most significant challenge associated with this scheme is the NV proximity.
NVs have to be approximately 20 nm from each other to realize this protocol which
is challenging to achieve in sample fabrication because the 2 NVs need to be in close
vicinity without any additional NV nearby[16j. The most common method to prepare
these systems is to artificially implant nitrogen by ion-implantation [6]. The yield
from nitrogen to nitrogen-vacancy suffers from more than an order of magnitude.
The extra nitrogen in the lattice diminish the NV coherence time because they are
spin 1/2 particles which contribute to the magnetic noise, and carry an additional
electron. However, we are presently preparing such samples as is discussed in chapter
5.
2.3
New Concept
The work in this thesis will advance the effort to adapt the existing dipole entanglement protocols to work at cryogenic temperatures. This can significantly improve the
existing room temperature application because cryogenic conditions allow for single
shot spin-state readout and extend the NV coherence time. Increased spin coherence
has a two-fold advantage. An extended coherence time means that the NV proximity
requirements can be relaxed [161, and will allow for more entanglement operations
within the coherence time. One can imagine cascading entangled systems to create
38
a large-scale entangled state. However, for this to work when considering 2 NVs, the
coherence time of each qubit must last throughout the entire period of the protocol.
The main advantage of operating at cryogenic temperatures that one gains is the
ability to read-out the state of an NV in a single-shot by using a resonant laser. This
allows us to measure the state faster and with a higher fidelity. At room temperature,
we have to take advantage of the meta-stable state to readout the NV spin state.
This is already a probabilistic measurement which will limit our readout fidelity.
At cryogenic temperatures we do not have to use the meta-stable state since the
ZPL transitions are sufficiently narrow to resolve all of them uniquely (fewer phonon
interactions). A resonant laser can be applied as described previously to determine if
the electron is in a particular state.
Furthermore, since each NV will experience a slightly different local environment,
the excited states will not necessarily overlap spectrally with those in other NVs.
This can be attributed to local strain in the lattice, which shifts the transition energy between ground and excited states. As stated earlier, identical photons are not
required when using this approach, so this is not problematical. In fact, we can use
this property to help screen for a well suited sample since we can perform a super
resolution technique by taking advantage of the ZPL frequency domain. This will be
covered in more detail when we discuss expanding our system to 2 NVs in chapter 5.
39
40
Chapter 3
Experimental Setup
This chapter will cover the devices that were built and used to prepare samples
and evaluate them. The diamonds that we use are grown at Element Six through a
chemical vapor deposition process (CVD). This technique is more favorable than highpressure, high-temperature (HPHT) techniques because it allows for a diamond with
fewer defects. CVD diamonds typically have a very low concentration of natural NV
centers, especially at the desired depth. Because of this, it is common to artificially
implant nitrogen atoms in the diamond using a focused ion beam.
3.1
Sample Preparation Furnaces
Once samples have been implanted with nitrogen, the diamond has to be annealed.
It has not been explicitly confirmed, but it is believed that the implantation process
creates vacancies in the lattice and interstitial nitrogen. Raising the temperature of
the diamond above 600 C promotes diffusion of the vacancies, a process that continues
until they reach a stable NV state
139].
However, it has been shown that annealing
at much higher temperatures (1200 C) will create a better environment for the NV
due to annealing out defects, allowing observation of lifetime-limited linewidths of
the ZPL [111.
It is clear that the annealing step must be scheduled after nitrogen has been
implanted in the diamond lattice. The ion-implantation is carried out at an energy
41
Figure 3-1: Photograph showing the assembled furnace. All flanges are CF-100. The
foil has been removed from the main chamber to expose the heating tape.
level necessary to create a mean depth of 30 nm, a subject that I will return to in
chapter 5. Atmospheric oxygen is sufficiently corrosive to begin etching diamond at
temperatures above 465 C. This condition requires one to remove as much residual
oxygen from the annealing chamber as possible to prevent etching of the diamond.
Therefore, we implemented a high vacuum furnace.
A photograph of the furnace components is shown in Figure 3-1. It was important
to make all connections ConFlat (CF) flanges to ensure that the chamber could support a high vacuum. The gaskets were chosen to be the standard oxygen-free copper,
enabling a base pressure below 10'3 mbar. When baking the chamber, by wrapping
heating tape around the it, materials should not anneal if the bakeout temperature
doesn't exceed 550 C for prolonged periods of time according to the standards specified by the manufacturer (Kurt J. Lesker).
42
The base pressure was verified using
364
Figure 3-2: Photograph (left) and schematic (right) of the heater stage. Images taken
from Tectra Physikalische Instrumente (www.tectra.de).
an active cold cathode transmitter from Pfeiffer vacuum (IKR 270). The pumping
station is a combination of a turbomolecular pump and a diaphragm backing pump
(Pfeiffer - the HiCube 300 Classic). The pump uses a dry and oil-free diaphragm
pump as a backing pump to a turbomolecular pump. The ultimate pressure that this
pumping station can achieve is 10-8 mbar. These pressures can be confirmed after
baking the system overnight at 200 *C (the temperature is limited by the pressure
gauge).
We chose to match the tube diameter to that of the chamber: CF-100.
This
decision was made partially because the pumping station could then pump at 260 1/s.
In addition we identified a heating element that is built on a CF-100 cap, as seen in
Figure 3-2. This AC Boralectric heater is theoretically capable of achieving 1200 'C,
and can be programmed to execute different heating stages with a PID controller.
It is important to make certain that the thermocouple is sufficiently accurate
in reporting chamber temperatures to allow for closed feedback control. Figure 3-3
shows a magnified view of the thermocouple. Once device was secured in the ceramic
hole, temperatures were measured when the heater was powered at 100% under the
maximum vacuum to avoid surface oxidation.
43
Figure 3-3: Magnified image of the thermocouple removed from the ceramic hole (top)
and secured in the hole (bottom).
0.146
ya
0.144
7.3A45x
+
0.13
0.142
0.130
I~i
0 134
0.132
0.13
0
120
140
160
Theioox~
(C)
180
200
220
Figure 3-4: The thermocouple error relative to the infrared thermometer (noted as
"laser" in the Figure). Note the value read out is lower than the infrared thermometer.
44
In an effort to ensure that our furnace operates at sufficiently high temperatures,
thermocouple acquired temperature values were compared with temperatures measured using a digital infrared thermometer as temperature was increased from room
temperature to 200 C. Although highly variable, measurements made using the thermometer consistently measured a higher value than the thermocouple, and the degree
of error increased as the temperature was increased, as seen in Figure 3-4. Assuming
that the operation in room pressure doesn't significantly influence the temperature
reached at a specified power, we estimate that projecting this error to high temperatures would reasonably approximate the reading from the thermocouple, leading to
the conclusion that the furnace was sufficiently hot when operating at full power.
Although we are able to reduce the pressure inside the chamber to ~ 10-8 mbar,
operating at such high temperature (T~ 1200 'C) still graphitizes the surface of the
diamond. To remove graphitic carbon from the surface, the sample is aerobically
baked at a much lower temperature; 465 C. It is generally held that oxygen environment at this temperatute removes sp 2-hybridized carbon at a much higher rate than
sp3 -hybridized carbon allowing for an oxygen terminated surface [11]. Surface termination is an important consideration when attempting to increase coherence times
and maintain the negatively charged NV center, as opposed to other charge states
that either don't have the spin characteristics necessary for quantum information or
simply do not fluoresce. An oxygen terminated surface is a convenient option because
it is easily achieved in the lab, and has shown to increase the probability of the NV
center to be in the negative charge state, where a hydrogen termination causes a
depletion layer favoring the NV 0 charge state 121]. This is not necessarily the best
surface treatment, other studies suggest that a fluorinated surface might be better,
in particular for spin coherence [131. This can be achieved using CF 4 or SF6 plasma.
To generate the oxygen termination, a NEY Centurion Q200 dental furnace (a
porcelain furnace capable of 1200 C) was used. In addition, either oxygen or nitrogen
can be delivered to the furnace through a gas input valve. The furnace is capable of
being programmed through the front panel and each stage of the program can control
the temperature, the ramp rate, and the gas flow. To achieve the desired oxygen
45
3001-Base Temperature
Sample Temperature
-
2W
5200k
cc
E
0
18.3K
-
10.7 K
0
1
2
Time (Hrs)
3
4
Figure 3-5: Temperature of the cryostat as a function of time.
anneal time, we program the furnace operation with the oxygen tank connected.
During the cooling phase, the nitrogen is swapped in for the oxygen so that the process
is terminated more rapidly than it would if the system was allowed to equilibrate back
to room temperature under oxygen. This protocol provides an enhanced degree of
system control, giving us better surface properties.
3.2
Qubit Control Apparatus
The system used to control and observe the qubit is, at its core, a confocal microscope.
The microscope is built around a closed-cycle Janis cryostat, with a base temperature
of approximately 11 K and a sample temperature around 18 K, as seen in Figure 3-5.
The temperature drop from the base to the sample is partially due to a 3-axis Attocube
stack' and additional thermal background radiation. The stack uses a piezo stepper
motor to allow for coarse movement of the sample up to many mm (Attocube).
Fine control of the excitation/ collection spot is achieved in the lateral direction
by a pair of galvanometer mirrors (galvos). The third axis, which is used for focus'There is a thermal link that bypasses the poor temperature-conducting stack.
46
Heaters,
Sensors,
Piezo Stack
Y
Cold Fingr
Figure 3-6: Schematic of the main chamber inside the cryostat. Note that the faded
end on the right continues to the closed-loop He pump and the turbomolecular pump.
The purple blocks represent piezo motors. The bold X, Y, Z are the stepper piezo
motors for coarse control. The italic z above the objective is for fine control.
ing, is controlled by a piezo focusing objective positioner. The cryostat was fitted
with a chamber extension to enable the objective to be placed inside the vacuum,
directly mounted above the sample, to increase collection efficiency. The objective
is maintained at room temperature, but is located in the same chamber that holds
the cold-finger, which is protected by a radiation shield. A schematic of the cryostat
chamber is shown in Figure 3-6.
A compact turbo pump (HiCube 80 Eco, Pfeiffer) is used to pump the chamber
to a pressure of 10-5 mbar before starting the cryostat. Once the cryo has reached its
base temperature, the additional effect of cryo pumping reduces the pressure to 10-6
mbar. Cryo pumping is the condensation of gases and vapours onto a cold surface.
For this reason, it is important that during the cool down process, heaters maintain
samples as close to room temperature as possible so that these particles condense on
the cold finger further from the sample.
Multiple feedthrough connectors allow access to DC electrical sources that are
47
Figure 3-7: Photographs of objective. On the left image, notice the rectangular piezo
block on the bottom left which secures the objective to the chamber. The other
images zoom in on the MW antenna across the tip of the objective. The objective
has a 300 pm working distance and the wire is 50 pm.
48
necessary for the attocube stack, the piezo on the objective, two heaters and two
temperature sensors; one at the base and one under the sample. Two additional
RF feedthroughs allow us to supply RF current to an antenna that is placed on the
objective as shown in Figure 3-7. The objective has an NA of 0.9, with a working
distance of only 300 pm. The antenna is not an optimized design, and has a limited
lifetime. However, it has been applied to a series of control experiments.
We are
presently developing alternative methods to supply MW radiation. A 50 [m-diameter
copper wire was carefully strung across the tip of the objective lens to provide the
near-field MW energy. Kapton tape, with an extremely low outgassing rate, was used
to electrically insulate the wire from the objective and to secure it. If too much of
the wire is in free space, and does not make contact with the objective, which acts as
a heat sink, the tendency to break was observed when driven with high MW power;
this occurs in the vacuum environment because there is no place for excess heat to
escape.
A signal generator with up to 3.3 GHz modulation frequency was used to drive
the electron between m, = 0 and m, =
1 in the ground state (SMIQ, Rohde and
Schwarz). The cycling rate of the generator does not permit sufficiently rapid pulse
sequence switching necessary to control the NV (see below). We run the MW through
a switch that can be gated with a rise time of 5 ns (ZASWA-2-50DR+ from MiniCircuits).
The confocal microscope setup used in this investigation was of standard design,
as illustreated in Figure 3-8. Excitation beams were delivered through a port for 532
nm light (a branch of a 5 W Verdi G-Series laser) and a tunable 637 nm source (New
Focus Velocity laser) that was used for resonant optical excitation. Each of these
sources is coupled to an acoustic-optic modulator (AOM) to provide on-off switching
capability on the order of tens of nanoseconds. The 637 nm laser is coupled to the 532
excitation path using a 90-10 beamsplitter, which will result in 10% loss of signal.
There is no way to avoid some loss of signal using resonant excitation techniques
since a dichroic mirror can't be used as part of the system since the excitation and
signal are identical in frequency. Finally, we take advantage of wide-field illumination
49
CCD
Spectrometer
A/2
PBS
Spatial Filter 550 LP
650 LP
Dichroic
PSB
T:
Q
90-10
Galvos
~APID
E "A
Wavelength
Figure 3-8: Optical paths used in the experiment. All of the sources begin on the right,
and all collection is on the left. The inset plot shows an example of an NV spectrum
at room temperature (to emphasize the PSB). The purple cutoff shows the spectral
location of the 650 LP filter. A curved line with an arrow at each end represents an
element that can be moved. The spatial filter represents a pair of balanced lenses
focusing the light onto a pinhole.
50
with white light to help locate the sample. In addition, the green laser port has a
short pass filter to block red fluorescence that is also emitted from the fiber when
illuminated with a few mW of 532 light. The red laser is sent through a 2 nm band
pass filter to provide additional spectral filtering from the diode.
The collected light can be routed to three devices. By default, it is coupled to an
Perkin Elmer avalanche photodiode (APD) through a single-mode fiber for confocal
spectroscopy. It is important that this is the default path since the coupling to the
fiber requires precise alignment, and a removable mirror will not maintain such a
configuration. A flip mirror allows us to direct all of the light to a free-space coupled
spectrometer and CCD. Since the spectrometer and CCD operate in free-space, the
flip mirror is sufficiently precise to allow for multiple tens of operations before realignment. Before splitting to the spectrometer and CCD, the signal light is focused
to a pinhole for spatial filtering. The pinhole is also mounted on a flip mount so it
can be removed when we are interested in looking at the whole field of view with our
white light illumination.
Now that we have covered all of the hardware in the setup, we will turn our attention to the control electronics. A PID temperature controller (Lake Shore Cryotronics) reads the temperature sensors and applies current to the heaters. The galvos,
objective piezo, and tunable laser require an analog signal. A NI-DAQ (USB NI-DAQ
6353, National Instruments) is used to provide these signals. Custom Matlab code
is used to program the NI-DAQ device using the NI-DAQmx dynamic link library
(dll). The two lasers and MW switch require a digital signal that acts as a gate.
This signal is provided by a PulseBlaster board (PulseBlaster ESR pro, SpinCore).
The board is an FPGA that has a clock speed of 500 MHz, providing 2 ns resolution in timing. Custom Matlab code, along with SpinCore.dll, were used to program
this device. Synchronization with the NI-DAQ is obtained by connecting a line from
the PulseBlaster to the NI-DAQ for gating purposes and installation of a counter is
required for the capturing clicks sent by the APD is the final component necessary
to generate an operational system. A digital input line on the NI-DAQ is used for
this purpose. All cables and optical paths were calibrated using the high resolution
51
Channel A
Channel B
Counter
Buffer
52
12
3
3
5
Figure 3-9: Schematic showing how a buffered count operation works when gated.
Note that the channel B rising edges that arrive when channel A is low are ignored.
On the rising edge of channel A, the counter stores the current value (the number
of rising edges that occurred in the previous gate. In our particular case, channel A
corresponds to the gate provided by the PulseBlaster, and channel B corresponds to
the APD clicks.
capability of the PulseBlaster to account for electrical, optical and switching delays.
At this point I would like to elaborate on two main functions. The first is a
confocal scan. The NI-DAQ is programmed to output a clock signal at a frequency,
f=
,
where
T
is the dwell time per pixel. A buffered write operation on the analog
lines to the galvos is programmed to be triggered off of the clock signal where the
values to be written are the ordered positions of each pixel in the scan. Finally, a
buffered counter, also programmed to trigger on the clock signal2 , counts the APD
clicks.
The second function of interest, gated photon detection, is required for pulsed
measurements. To carry out this operation, the lasers and the APD counter must be
gated. Since the clock of the NI-DAQ is limited 1 MHz, we took advantage of the
PulseBlaster's clock rate. The PulseBlaster is programmed for the appropriate pulse
sequence, which includes the detection gates. Before starting the PulseBlaster, the
NI-DAQ is programmed to execute another buffered read operation. However, this
2
Triggering the counter means to advance the buffer pointer, so when the computer reads the
buffer, it will be binned by clock cycle, which in this case is equivalent to a pixel.
52
time the operation is to return the "frequency"3 of channel A in units of rising edges
on channel B. Figure 3-9 shows a schematic of this process. The buffered operation
here returns the frequency of each high period in channel A (so channel A is behaving
like a gate). In this case channel A is the gate signal from the PulseBlaster and
channel B is the APD signal. This operation results in each buffer containing the
number of APD clicks in each gate interval given by the PulseBlaster.
3 Frequency is perhaps misleading here, however this is the description of the function being used
in the NI-DAQmx library.
53
Chapter 4
Reference Sample
Before preparing the sample for use in the experiment, we examined a sample with
properties that were similar to those expected theoretically. This sample was a high
quality CVD grown sample with a low concentration of 'natural' NVs, NVs that were
created during the CVD process. Due to the very low N concentration, the sample
had only a few NVs and very few defects. Such a sample has notably better spectral
properties because the NV is surrounded by a more pristine lattice that contains less
defects than implanted NVs.
The refractive index of diamond is 2.4, which makes it very difficult to couple light
from the diamond lattice to a free space mode because of high refraction and reflection
at the diamond-air interface. By carving the diamond in a way that emitted photons
intersect at right angles with the diamond-air interface, the amount of light that is
trapped by total internal reflection can be greatly reduced. This can be accomplished
using a solid immersion lens (SIL) that is integrated directly into the diamond, as can
be seen in a scanning electron microscope image (SEM) taken by Jamali in Figure
4-1. NVs are first located relative to alignment markers on the diamond surface, and
the SILs are carved into the diamond using a focused ion beam (FIB). The SIL is
large enough to avoid contamination or destruction of the diamond near the NV from
the FIB process (i.e., the NV spin and optical properties will not be diminished).
The SILs used in this investigation were fabricated by Sen Yang from the University of Stuttgart and the location of the SILs on the mm-sized bulk EG diamond is
55
Figure 4-1: SEM of a solid immersion lens (tilted at 52
using a focused ion beam. Figure taken from Jamali [23].
0)
fabricated into diamond
shown in Figure 4-2. As can be seen in these images, the sample's surface is quite
dirty. After these images were taken, the sample was sonicated in acetone, followed
by ethanol and finally blow dried with nitrogen to clean the surface.
The sample was then loaded into another microscope with wide-field fluorescent
spectroscopy capacity. This microscope is very similar to the white light instrument
used previously. However instead of exciting the sample with white light, a 532 nm
laser light is used. A filter is inserted into the system to block reflected excitation
light ensuring detection of the red NV fluorescence alone. Figure 4-3 shows the set
of SILs examined. Only one of these SILs (SIL 2 in Figure 4-3) revealed a promising
NV in the center; i.e., other SILs either didn't exhibit an NV or were dim relative to
SIL 2.
The next step was to load the sample into the confocal microscope integrated with
the cryostat as described in the previous chapter. The sample was initially examined
at room temperature. Figure 4-4 shows a confocal image of the SIL and the NV. A
second order autocorrelation (g( 2)(At)) measurement was performed to confirm that
the NV under consideration was indeed isolated. To perform a g( 2 ) (,At) measurement,
56
Figure 4-2: Our SIL sample observed under a regular wide-field white light microscope. For scaling reference, the SILs are about 10 pm in outer diameter.
57
Figure 4-3: Our SIL sample examined with a wide-field fluorescent microscope (excited with 532 nm light and collected red fluorescence). The depth (z axis) of the
NV from the surface was estimated using the microscope's stage. Again, for scaling
reference, the SILs are about 10 pim in outer diameter.
58
x 104
-10
1.5
2
2.5
3
3.5
-11 5
-10
-10.5
-11
2
Photon Autocorrelutlon (gh
~
g(2
Atocor
Photnaion
18
16
IIILIkI
I
1.
1.2
M
Cz
1
III
_0
M 08F
E
z
!''IIV
r
0.6b
04-
Wij
I
0,20
-200
-100
0
100
200
300
A t (ns)
400
500
600
700
Figure 4-4: The top image is a confocal scan of the single NV in a SIL. The inset is a
zoomed out version. The bottom plot shows the second order autocorrelation of the
arrival time of the photons.
59
the fluorescence from the confocal spot is divided by a 50-50 beamsplitter (in our case
this was accomplished using a 50-50 branched fiber) and sent to two APDs. The first
APD serves as a start signal and the second APD as the stop signal for a timecorrelator (PicoHarp, PicoQuant). The time-correlator stores all At's from photon
arrival times and plots those times in historgram form with 512 ps resolution. Because
the start and stop detectors will not be clicked simultaneously if the source is a single
photon (i.e., a single NV), the value of g( 2)(0) = 0. During experiments, background
noise always prevents g( 2)(0) = 0, but a measurement of g( 2 )(0) < 0.5 is considered
a single photon source. The minimum value the function can have at 0 At for n
emitters is g(2 ) (0) > 1 - I. We have confirmed with a high degree of confidence that
a single NV is present in the SIL with g( 2)(0) ~ 0.1.
Under confocal illumination, we made the observation that the angle of illumination had a substantial impact on the collection efficiency due to the specific geometry
of the lens refracting the wavefront non symmetrically for a non perpendicular angle
of incidence. It was necessary to realign the microscope to make certain that the
beam was perpendicular to the sample plane.
4.1
Spectral Properties
The spectrum of the NV was taken at cryogenic and room temperatures and, as
illustrated in Figure 4-5, it has a narrow and strong Raman line indicating that the
diamond lattice is well preserved in the SIL region. However, an NVO ZPL is also
apparent in the spectrum, which is not an ideal condition, but is acceptable for the
purposes of this investigation because the NVO content is considerably less than the
NV- content based on their spectral amplitudes. The contribution of NVO and NVis about 30% and 70% respectively, a value that has been reported for natural NVs
in a high quality sample [48].
The plot in Figure 4-5 shows that as the system cools down, a large fraction of
the phonon modes are frozen out of the system and the amplitude of the NV ZPL
transition is much higher than the PSB. This is primarily because the transitions are
60
3500
300 K
3000
NV- ZPL
-:2500
V
NVO ZPL
a,
Diamond Raman
2000[
015001.
1 000l
500
50
650
600
700
Wavelength (nm)
8
io
i
1800
1600-
$100
1400
800
750
/
1200
1000
0 600
0
6
WVWs~0~ (nM)
1 64 6e 838
400
200
0
-200-
550
600
650
700
Wavelength (nm)
750
800
850
Figure 4-5: Spectrum of the NV center in the SIL with a grating of 300 grooves
per mm. The inset plot is taken with the highest resolution that we have of 1200
grooves per mm. Note the SIL only increases collection efficiency; it does not alter
the emission of the NV. The top plot is at room temperature, while the bottom is at
cryogenic temperature (18K). The diamond Raman that can be seen very prominently
is common for an EG bulk diamond sample excited with 532 nm light. This NV has
an additional neutrally charged NV (NVO) element to it, as you can see with the
NVO ZPL near the Raman line. All of these lines at cryogenic temperature are
spectrometer-limited even with our highest grating of 1200 grooves per mm (you can
see that it only has a full-width-half-maximum of only 3 pixels).
61
much narrower since the ZPL is less homogeneously broadened by phonon-induced
dephasing, although it still accounts for only approximately 3% of the emission. The
spectrums presented here are taken with a grating of 300 lines per mm, giving a
resolution of approximately one half of a nm. The six ZPL lines cannot be resolved
by our highest grating, 1200 lines per mm, with a resolution of 0.028 nm (20 GHz at
637 nm).
To further resolve the lines, we employed a resonant excitation protocol, commonly
referred to as a photoluminescence excitation (PLE) measurement.
This involves
scanning the tunable laser across the resonance of interest. In such a measurement,
the NV is excited resonantly and we collect the PSB emission. It is important that
the linewidth of the laser is narrower than the spectral width of the optical transitions
being probed since it is the convolution of the laser profile and the transition that will
be our signal. We assume that the laser linewidth is substantially smaller than the
linewidth of the transition; the laser should be on the order of 30 kHz in width, while
the best linewidth we can theoretically achieve in the NV is -14 MHz, as discussed
above. Much like the NI-DAQ controls the galvo scanning angle with a DC voltage,
during a confocal scan, the NI-DAQ controls the laser frequency through an analog
channel. Just as it does during a confocal scan, it bins the counts at each step in the
wavelength scan.
In the case of this sample, we implemented a protocol that we refer to as a "fast"
line scan, primarily because the implementation is technically straightforward and it
is not necessary to synchronize the NI-DAQ and PulseBlaster; note that after the
initialization pulse, which is very roughly timed by the computer, the red laser is
always on. The NV is initialized by delivering a pulse of green light of approximately
10 ms, and the NI-DAQ subsequently sweeps over a selected frequency range using
the resonant laser, while binning the counts. The dwell times per scan step were
on the order of ms, making each individual line scan approximately one second in
duration, giving us time-resolved information on the resonance's spectral position.
From this measurement, we can determine the single scan linewidth and the overall
inhomogeneous linewidth accumulated over many scans.
62
10
20
30
)40
50
U 0~
70
80
- -
100
-7
-6
-5
-4
-3
-2
-1
0
-
90
1
250
3200
j
(-150
-
100
E50
0
-8-6
-202
-4
Detuning (GHz)
Figure 4-6: Fast line scans of NV in SIL. Each pixel is acquired with a dwell time of
2 ns a few hundred nW of excitation power. The bottom plot is a vertical sum over
all line scans showing the cumulative inhomogeneous broadening with a linewidth of
447 MHz.
4.1.1
Spectral Diffusion
Spectral diffusion is the spectral wandering of a ZPL transition frequency with time
and is caused by local fluctuations of the NV's electrostatic environment, an especially
problematic state of affairs when there are defects such as extra nitrogen ions in the
sample that can act as electron donors and acceptors. However, spectral diffusion in
this sample should be minimal since it is a natural NV in EG diamond with very low
defect concentration.
The experiment described above was performed with a variety of different dwell
63
times and laser powers at a temperature of about 18 K. The goal was to maximize
the SNR. Nonetheless, the maximum counts per bin occurred when approximately
100 nW of red excitation power was delivered for 2 ms. This trial is plotted in Figure
4-6. The linewidth of the transition appears to be approximately 1 GHz and the
center frequency remains very stable over the course of 100 line scans, which requires
a couple of minutes of data acquisition. It is possible that spectral diffusion occurs at
faster rates, meaning that our resolution of system dynamics is limited to the order
of seconds.
Analysis of future spectral diffusion data led us to conclude that maximizing
counts was not the best approach in this case. This optimization resulted in the use
of substantial amounts of red power which itself may have caused spectral diffusion
and power broadening in each scan. We adjusted for this and lowered the power
considerably resulting in much narrower lines for the same NV.
4.1.2
Linewidth
After completing these first experiments, we improved our measurement techniques
significantly. The two most significant changes affecting system performance were to
use the PulseBlaster for timing purposes, and reducing the excitation power of the
resonant laser. These changes gave us finer control over the initialization pulse and
the pulse sequence used to acquire each pixel. This also allowed us to make faster
measurements with more precise timing. Previously, it was necessary to power the red
laser continuously, but the added control achieved by making these changes allowed
us to implement a short initialization using the green laser at each frequency value, a
system modification that gave us more signal because recovery from ionization events
is now possible, as discussed in the next section.
These changes also have a potential downside.
For example, greater spectral
diffusion should occur as a result of applying the green repump for initialization.
Each time high-energy green photons impact the diamond, electrons bound by nearby
defects will be reconFigured and cause a slightly different local environment for the
NV. This problem is enhanced when many defects are found in the diamond in the
64
Red Laser
1
I
Green Laser
APD Gate
Time (us)
2
12
0.025
E,
0.02200
30 MHz (Lorentzian Fit)
0.015-
-
0.01
Ey
0.005
0
-8
-6
-4
2
0
-2
Detuning (GHz)
4
6
8
Figure 4-7: PLE scan of NV in a SIL. The top shows the pulse sequence used for each
pixel. To acquire enough counts, the pixel's measurement was repeated 10,000 times
and averaged before advancing to the next frequency point. The tall transitions (the
two fitted on the left) are the E., and Ey transitions. Approximately 20 nW of power
was used.
vicinity of the NV that can act as acceptors or donors for electrons.
While this
consideration must be addressed for other samples, it does not apply to this specific
sample, as we are working with a natural NV and the appearance of large numbers
of "extra" nitrogen atoms from implantation is unlikely. Thus we are not anticipating
significant data acquisition problems.
Figure 4-7 shows an example of what we refer to as a "slow" scan. As described
previously for the fast scan protocol, each line scan took approximately 1 second to
execute, and scans were repeated multiple times.
In this protocol, each frequency
is repeated many times to acquire statistics before incrementing frequency.
Use of
this protocol is only possible because the initialization pulse is controlled by the
PulseBlaster in our upgraded operating scheme. That measurement strategy should
yields a result that is similar to that observed when the sum of the fast line scans
65
0.05
0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0-8
-4
-6
-2
0
6
2
Detuning (GHz)
4
8
\
0.3
-
.
025
21 1*
0.15
w
w
0.1
0.051
01
0
50
100
150
200
Polarization
250
300
350
400
Figure 4-8: The top Figure shows another PLE scan of the same NV as in the
previous Figure. The contrast of the two tallest peaks (E, and E.) are plotted below
as a function of excitation polarization.
66
is considered.
In fact, it turns out that a linewidth almost 5 times smaller than
observed in the fast scans is acquired. We attribute this to the lower power used in
these experiments compared to the original fast scans that were performed.
The two fitted peaks on the left part of the scan, in Figure 4-7, are the E. and
Ey transitions with m,
=
0. We conclude that is due to their intensity relative to the
other peaks and their polarization relative to each other. Without MW radiation,
the other peaks should only be accessible due to phonon-induced mixing, since we
automatically initialize to m,
=
0 with our 532 nm excitation. Furthermore, the two
orthogonal orbitals of e, and ey should respond differently to a given polarization
of the excitation beam. By adding a linear polarizer and a half-wave plate, we can
control the polarization of the red excitation laser. Figure 4-8 shows the contrast of
the peak value of the E. and Ey transitions. It is clearly polarization dependent, with
a maximum at 90 degrees indicating their orthogonal polarization.
4.2
Ionization
As discussed in chapter 1, the NV's energy levels are energetically located within the
bandgap of diamond. Because of its proximity to the conduction band, ionization of
electrons into the conduction band induces a charge state conversion to NVO. The
charge state can be recovered by exciting the electron from the valence band, which
corresponds to the wavelength lower than 575 nm (yellow) light1 . This does not occur
when the system is pumped using a green laser. The green photons have sufficient
energy to ionize and repopulate the center in a two-photon absorption process, while
two resonant red photons only have enough energy to ionize the center.
Once the NV has been ionized, it cannot absorb any resonant excitation light and
thus will not generate any signal until it has been restored. We can measure the time
constant that it takes the NV to ionize by running the pulse sequence shown in Figure
'The mechanism is not quite as simple as this because there are multiple electrons in the model,
and the NVO is also a stable charge state. The NVO has a set of energy levels of its own, but what
is important is that we can pump an electron back into the defect center, restoring the NV- charge
state.
67
Red Laser
Green Laser
I I I I I I
APD Gate
0
5
10
15
20
30
25
35
40
45
I
50
5 x1O4
4.5
20 nW resonant power
4.
3.5
3
-
Co
-
2.5
-
2
1.5
1-
0.5
0
0
2
s
Time (s)
5
10-
Figure 4-9: Ionization time in the SIL. The top shows the pulse sequence used, and
the bottom is the plot of the averaged counts.
68
4-9. First the NV is initialized into the negative charge state, and then illuminated on
resonance with the tunable laser. During continuous excitation, photons are collected
in 60 ns long bins (limited by the temporal resolution) that are exponentially placed
in time to 60 ps. This sequence is repeated hundreds of thousands of times with the
PulseBlaster, a process requiring several minutes and the results are plotted in Figure
4-9.
Before pressing on, it is important to address issues related to the measurement
scheme used in this experiment.
It is well understood that the ionization rate is
heavily dependent on the spatial and spectral overlap of the laser mode and the NV
center. Taking extended measurements is challenging as the laser emission is not
frequency-stabilized, but drifts on the order of a few MHz/s.
That said, our goal was to qualitatively understand the dependence of the system
on power. To accomplish this, we repeated the same measurement described above
using 10,000 averages, a condition that makes the process 10 times faster, for 20 nW,
200 nW and 2 pW of the resonant excitation power, as shown in Figure 4-10.2 As
expected, the ionization time decreases with increasing power.
However, there is more to the story. Changing the power over such a large range
might push us into different NV driving regimes. Considering the fact that count
rates at the beginning of the ionization curves for each power value are roughly constant, it is reasonable to conclude that we are driving the NV at saturation. Because
background fluorescence grows linearly with excitation power [261, we concluded that
the best data acquisition protocol was to use the lowest power with an integration
time of around 10 ps.
4.3
Temperature
The linewidth measured for this NV was broader than expected. When using a natural
NV, we expected the linewidth to to be closer to the lifetime limited linewidth, but
2
1f one compares the 20 nW case to the averaged one in 4-9, one will notice the ionization time
is shorter. This suggests that during the long averaging, the laser spectrally drifted.
69
6
5-
20 nW
4LI,
3
0
-
2
10
6
5
200 nW
40
3
2
0
10-4
6
5
2 uW
4
(3
2
0
.
1
0
1
2
3
Time (s)
4
5
6
X 10 -5
Figure 4-10: Ionization time in the SIL with increasing resonant excitation power. As
we would expect, the ionization time decreases as the power increases.
70
our measurement was nearly an order of magnitude larger. Because the linewidth is
highly temperature dependent, (T5 ), due to the phonon-induced dephasing, the real
sample temperature and resulting linewidth is a significant parameter to consider [181.
The dependence of linewidth on system temperature is plotted in Figure 4-11 and
it is clear that all of the transitions exhibit a T' dependence on temperature. The
relationship between linewidth and temperature was estimated by fitting the sum
of 4 Lorentzians to the four transitions indicated in the top plot of Figure 4-11, in
each ESR measurement. An accurate initial condition was required to successfully
fit all of the peaks, otherwise the the algorithm would get stuck in an incorrect local
maximum. A curve showing a T' behavior is added to emphasize the trend in the
data.
In the absence of a more extended study, it is difficult to extrapolate the linewidth
at lower temperatures. All we can say is that at 18 K, there is a good chance that the
linewidth is homogeneously broadened due to temperature. This will be a limiting
factor for the remainder of the experiments.
71
0.12
0. 11
-
38.7 K
0.1
30.1 K
0.09
0.08
27.7 K
0.07
0.06
0.05
23 K
0.04
0.03
0.02
3
2
-8
-4
-6
18 K
4
2
0
-2
Detuning (GHz)
4
6
8
3
2
2.51
4
N
2
1.5
-3
1
0.5
A
15
20
30
25
Temperature (K)
35
40
Figure 4-11: The top plot shows an ESR spectrum taken at five different temperatures.
The bottom plot shows the linewidth of the four peaks as a function of temperature.
The linewidth was determined by fitting the sum of 4 Lorentzians to the 4 peaks
shown in the top plot at each temperature.
72
Chapter 5
Engineered Sample
When considering scalable systems, natural NVs are not sufficiently abundant to
reasonably expect to find two NVs within a diffraction limited region. As such, an
appropriate sample must be engineered. Implanted NVs represent a desirable solution
to the problem because controlling the density over a single chip is easily managed.
There is also the additional advantage that in future experiments, implantation of NVs
through a mask to precisely position them (e.g., in a cavity or waveguide structure). In
this chapter, we will concentrate on preparation and characterization of an engineered
sample.
5.1
Sample Preparation
An EG diamond from Element 6 (E6) was divided into four regions with an implantation dose of 108, 109, 1010 and 1011 ions/cm 2 respectively, as seen in Figure 5-1.
They were implanted approximately 30 pm below the surface of the sample, using an
implantation energy of 20 keV. Figure 5-2 shows the result of a SRIM (The Stopping
and Range of Ions in Matter) simulation to approximate the depth and damage to
the lattice.
The natural isotope of nitrogen is 14N, which has an odd number of both protons
and neutrons (7 each), each contributing a spin of t
giving the nitrogen a total
magnetic spin of 1. This is detectable in electron spin resonance (ESR) measurement,
73
K 0 1
-50
2.5
2
1.5
0
1,
1
0.5
50
-50
0
0
Distance (um)
50
.
Figure 5-1: Confocal scan of the engineered sample. This is the location where the
four quadrants intersect, near the center of the diamond. The top right is the highest
dosage of 10" and the sweep goes clockwise down to the lowest dose of 108
COLLISION EVENTS
ION RANGES
Ion Range =
Saggie
275A
a 85A
Skewness
= 4.2415
Kurbois
a 2.A=
Vacancies Produced (K-P)
0
45(10 4
S
.21
0
35x1] 4
.24
~J2
CV2
30r0
E
.20
25x10
.16
1,
.12
S
IE
IWO0 4
-
TarLt Deth
-04
0
i
A
Lrget Depib -
_b
L-
-L
-L-
--
L
_----.--
0
10W0A
Figure 5-2: A Monte Carlo simulation (in SRIM) performed to determine the depth
of the ions implanted at 20 keV. The left shows the mean stopping range of the ions,
and the right shows damage to the lattice in the form of vacancies caused by collisions
with the ballistic nitrogen ions.
74
Positions in um
-5
35
3
2.0
4
4
-3
3.5
I
3
3~
-2
2,5
5
6f
-6
-2
-4
0
0
14
-1
12
1
8
1
2
6
3
1
3
4
4
0.5
4
5
-6
46
-2
2
15
10
-3
56
2
10
6
0
50
5
0
6
-100 MHz!
40I
40
. . 'I
G0
f)
De120ng 12z1
X rs
Gm
Figure 5-3: The top row shows confocal scans associated with the region of the PLE
scan (bottom). Note a very clear dependence of the linewidth on the dosage.
where the MW frequency is swept over the zero-field splitting in the ground state
(around 2.8 GHz) while optical pumping distinguishes the m,
=
0 and m, =
1.
As mentioned earlier, the implantation dosage will have an impact on the dephasing of the NV center, which has a direct impact on the linewidth. To verify this, we
cooled the sample down and performed PLE scans on the three region with the lowest
dose (the highest dosage region had indistinguishable NVs, resembling a Ila diamond
from E6). Figure 5-3 shows these data with neighboring confocal scans. The results
agree with results from [111. A direct comparison is difficult to make because the NVs
were implanted with different energies, thus implanting different distances from the
surface.
After implantation, the sample was annealed at high temperatures (~1200 -C)
to turn the implanted nitrogen ions into NV centers. We have no hard data on the
benefit of high temperature annealing, but findings from other groups suggest that
high temperature annealing does extend coherence times 111, 50, 30, 36J.
75
100
200
300
400
500
600
-30
-20
-10
0
Linewidth (GHz)
10
20
30
Figure 5-4: Fast line scans of the engineered NV. The NV is very stable for 5000 line
scans. The sum over all 5000 still yields a linewidth of approximately 100 MHz.
5.2
Single NV
A single NV was found in the lowest dose region, with a linewidth of approximately
100 MHz (the same from Figure 5-3). This was promising because it has the lowest
spectral diffusion of all NVs we have thus far observed; even beyond this sample.
Figure 5-4 shows the individual line scans as well to emphasize the spectral stability
of the systen. Approximately five NVs were investigated in this region that did not
exhibit any signal when resonantly excited. It is unclear why this is the case, although
it could be that they ionize too quickly or that their charge state is unstable.
We made an ESR measurement to determine the resonant frequency between the
rn = 0 and r. = --1 states, as seen in Figure 5-5. The dip in fluorescence is caused
by the meta-stable state. When the MW field is on resonance with the transition, the
electron is transferred to m, = -1 Imore frequently which has a higher probability of
decaying through the non-radiative meta-stable state.
We can show Rabi oscillations between n, = 0 and to,
-1 by applying ini-
tializing into m, = 0 and then driving the system with the resonant MW field and
76
CW ESR
260
--
1
+--APD
255
250
(0
1=
245
C
0
240
-I
I
-
235
230
225
2. 7
2.72
2.74
2.76
2.82
2.8
2.78
Frequency (Hz)
2.84
2.86
2.88
x
2.9
109
Figure 5-5: ESR spectrum showing the m, = 0 to m, = -1 transition in the ground
state. This was measured wile continuously applying 532 nm light and sweeping the
MW frequency.
77
XI10*,
3.5
14
13
12
09
2
0.8
071
0
01
02
03
07
06
0.5
04
Rabi Pulse Duration (s)
08
09
15
1
0
01
02
03
04
05
07
06
Rabi Pulse Duration
t)
08
1
09
10
Rabi
Pulse
Rabi
Pulse
Figure 5-6: Rabi oscillation between the m, = 0 and m. = -1 ground states. The
data shown in the left plot is under green excitation, and in the right is under resonant
excitation. The pulse sequences are shown below the plots. Note that there are two
read-out times for the APD. In the case of green excitation, this is used to normalize
to. For the resonant excitation it simply tells us that we can collect for a longer time
since the NV hasn't been ionized.
reading out. By sweeping the length of the MW field (the Rabi pulse) we can map
out the Rabi oscillation, as seen in Figure 5-6, on the left.
If two NVs were located in this same diffraction-limited spot, we would be unable
to distinguish them using this measurement strategy because they both will absorb
the green excitation equally. If it was desirable to preserve the state of one NV while
the other was read out, we would have to excited the NV resonantly, assuming the
centers had different ZPL spectral positions.
The right plot of Figure 5-6 shows the result of reading out resonantly and it is
clear than that the contrast is significantly better. Reading out with green excitation
requires the probabilistic transition into the meta-stable state which limits the contrast we can expect to see. Resonant excitation does not depend on the meta-stable
state. If we are in m,
=
0, when the resonant laser is on, we are pumping that state,
thus we should get photons (as you can see at time 0 in the Rabi oscillation). On the
78
other hand, when we are in m, = -1, we are not pumping that state, so we expect 0
photons, as you see around 100 ns, which is a wr pulse (of course there is always some
amount of background).
5.3
Expanding to two NVs
As stated earlier, one long term goal of this experiment is to expand the system to
include two NVs that can be entangled through their dipole coupling. Although such
a condition has not been observed in screening efforts thus far, we have developed an
effective screening method using a super-resolution approach.
Super-resolution is not a new idea when it comes to imaging emitters, but it is
useful. Because of the state-dependent fluorescence, we can turn an NV 'on' and 'off'
by preparing the electron spin and take a picture of each state. If there are two NVs
within a diffraction limited spot, and they have unique MW resonances, one can be
switched. By subtracting the images, the switched NV can be localized with arbitrary
precision. This technique was developed by Ed Chen, from our group [101.
A similar approach can be implemented in our system. Because our ZPL transitions are so narrow at cryogenic temperature, and the local strain will vary from NV
to NV, we can distinguish the NVs by their ZPL spectral locations. To do this, we
set up our confocal scan to acquire light using the spectrometer instead of the APD
so we can resolve the frequency domain. These scans take significantly longer than
APD collection, since each pixel has to dwell for a couple seconds. This also limits
the area in which we can scan because the stage drifts with long periods of time.
The result is a 3 dimensional image that has 2 spatial dimensions and a spectral
dimension. By fitting 2D a Gaussian to a spot in space and frequency, we can pinpoint
the center to arbitrary precision. Figure 5-7 shows an example of such a scan. Of
course only a few slices in frequency could be shown.
79
Figure 5-7: A confocal-spectral scan of the second-lowest dosage region. The top
left image is a sum over all wavelenghts (equivalent to collection with an APD). As
expected, the majority of the NVs have ZPLs at around 637 nm (top right). The
bottom left images show frames a two separate wavelengths, where two NVs overlap
spatially, but not spectrally. The bottom right image shows one of the NVs as red,
and the other as green.
80
Chapter 6
Conclusion
The work in this thesis has advanced our effort to entangle two NVs via their dipolar
interaction at cryogenic temperature. Our system was tested with an ideal natural
NV, giving us insight into the NV dynamics. We measured the spectral diffusion over
extended periods of time, and the homogeneously broadened ZPL linewidth, and the
effect temperature had on the linewidth.
A sample was prepared with dosage regions to confirm a previous result on the
effect of implantation dosage and the NV ZPL linewidth, and to provide us with a
region that will hopefully contain two NVs that are within 40 nm and have distinct
transitions. A single NV was measured in this sample that exhibited ideal spectral
properties.
Although significant progress has been made in the effort to reach the next level,
to achieve entanglement, more work is required to achieve that goal. For example,
at the moment, multiple resonances cannot be simultaneously excited, which is an
important step to realize coherent manipulation of two NVs.
6.1
Ongoing Work
The immediate goal of ongoing work is to complete hardware and software development necessary to drive both NV resonances.
After dissembling the cryostat to
rearrange wires, we achieved a base temperature as low as 13 K, a benchmark that
81
Binned arouos of 10
500
E 1500
M
2000
2500
3000
-30
-20
10
0
-10
Detuning (GHz)
20
30
Figure 6-1: An overnight PLE scan. Vertical lines have been added to help guide the
eye. The laser seems to have drift on the order of GHz, and what appears to be a
mode hop around scan number 10,000.
is important in the effort to approach the lifetime limited transitions.
An additional ongoing sub-project is the preparation of a second signal generator.
This is necessary because the signal generator currently being used is not fast enough
to switch between two different frequencies.
To overcome this limitation, a second
signal generator that is connected with a second switch so that our PulseBlaster can
gate them independently is being prepared.
Our current resonant excitation system is also undergoing an upgrade. The tunable laser uses a grating attached to a piezo to tune the cavity length (thus the laser
frequency). This method doesn't allow us to stabilize the laser output frequency with
a PID feedback controller. Over the course of some long experiments, laser drift and
mode-hopping was observed, as shown in Figure 6-1. Our solution to this problem
is to branch off a small portion of the laser output to frequency-stabilize the system
with a WS 7 wavenmeter from Toptica.
We also plan to adopt sideband generation, a method that is familiar to the atomic,
molecular and optical (AMO) physics community for sometime now. A fiber-coupled
82
0.025
-
0.02
-
0 015
0
001
-10.5
-7
-3.5
0
3.5
Detuning (GHz)
Figure 6-2: Sideband generation. The 637 nm light is amplitude-modulated at 3.3
GHz to produce sidebands. The plot shows an NV ZPL that is originally at 0 GHz,
but the 3.3 GHz sidebands also excite the ZPL.
EOM is modulated by way of a third signal generator. Figure 6-2 shows an example
of a PLE scan with 3.3 GHz amplitude-modulated sidebands. As would be expected,
the transition appears three times, one for each sideband, and one for the signal
frequency. If our EOM visibility was 100%, we would expect the signal frequency to
completely disappear, but that is not a problem because the sidebands can be driven
far enough detuned from any NV resonance of interest. The sideband method will
allow us to switch between ZPL frequencies significantly faster than possible when
using a piezo, and with significantly more precision. The limiting factor regarding
how far the frequency can be modulated is the signal generator. Using our current
model, we aren't able to exceed
3.3 GHz, giving us a 6.6 GHz window for the
distance between the two ZPL transitions.
To summarize, a colder base temperature in the cryostat will further lower homogeneous broadening. A second signal generator will allow addressing of a second
NV with timing resolution of nanoseconds. The sideband generation on the resonant
laser will provide an excitation beam that is much more frequency-stable and allow for
faster switching between frequencies. These enhancements will provide the necessary
control architecture to entangle two NVs via their dipolar interaction.
83
6.2
Future Work
Findings reported here have established a foundation for future work that will almost certainly take many different directions.
One notable outcome of the work
completed as part of this thesis, the work that was focused on minimizing spectral
diffusion through low implantation dosage and high temperature annealing, was the
development of a sample that is well suited for executing the flying qubit protocol for
entanglement, as described in Chapter 2.
Independent of specific future experiments, the next logical step is to begin engineering the diamond surface. We have already developed and begun revising a
scalable approach to design nano-photonic structures in the diamond
[34].
Guiding
fluorescence emitted by the NV using waveguides and enhancing NV emission using
cavities will greatly improve overall system efficiency.
To begin realizing diamond nano-fabrication, a great deal of effort has been invested into the design of an automated approach to characterize samples. Customized
"QR" codes are initially patterned onto the surface of the diamond in a grid with 50
prm spacing so that a robotic microscope (RoMi) will be able to navigate the chip
without human assistance. Figure 6-3 is an SEM image of one of these QR codes
that has been etched into the diamond surface. RoMi can first examine the chip's
fluorescence to register the location of NV centers. Nano-photonic devices can be
positioned around the NV centers and etched into diamond to enhance emission and
collection of NV fluorescence.
While the ultimate goal of engineering a large scale, practical quantum computer
isn't within striking distance today, we are making progress and it is my hope that the
work reported here will help move the effort forward in a meaningful and measurable
way.
84
IJm
EHT
5.00 kV
WD = 7 1 mm
Signal A = HE-SE2
Column Mode = High Resolution
Mag= 1303KX
I Probe =
135 pA
Date 17 Aug 2O15
*
u
CMSE
Figure 6-3: QR code in diamond. The pillars in the center of the etched squares are
designed to improve the contrast between squares that are either etched or not, a
logical 1 and 0 respectively, under white light illumination. The circles and asterisk
symbols are designed so that the image recognition software can easily locate the
corner of the design with high precision.
85
86
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