Control of individual nuclear spins in diamond
L. Childress, B. Smeltzer, J. McIntyre
Bates College
QNLO 2010
Sensing nuclear spins
Ensemble NMR techniques
Measure ensembles of nuclear
spins with e.g. pickup coils,
micro-atomic magnetometers
NV centers
Electronic spin as sensitive
magnetometer
Coupled electron-nuclear spin
system
Ledbetter et al.
2008 PNAS
Sensitivity: ~ 1012 protons
MRFM
~103
protons
Atoms and ions
Mixed electronnuclear hyperfine
levels can be
precisely controlled
and measured
Nuclear spin environment of the NV
Can be viewed as a resource
Coherent interactions with proximal nuclear spins in the bath
Outline
• Hyperfine structure of the NV center
– A check on ab initio theory
• Controlling individual nuclear spins in diamond
– Polarization, manipulation, and readout of individual
nitrogen nuclear spins in diamond
• Multifrequency spin resonance
– Beyond the RWA: Multiphoton transitions and coherent
destruction of tunnelling
– Longitudinal excitation: another technique in the toolbox
The spin degree of freedom:
Hyperfine structure
Excited
state
?
Ground
state
ms = ±1
ms = 0
Always

 

H  S  gB S z  S  AN  I N  S  A1 3C  I 1 3C
2
z
Unlike atoms, F is not a
good quantum number
1.1% probability at
each lattice site
Weak (few MHz), anisotropic
hyperfine interactions
Experimental techniques:
wire
imaging
?
ms = ±1
ms = 0
~10 µm
532 nm
Single photon
counting module
N.A. 1.3
oil immersion
objective
fluorescence
Dichroic
20 m
copper
wire
Permanent
magnet
MW
Gruber, Science 1997
Experimental techniques:
?
wire
spin resonance
ms = ±1
ms = 0
MW or RF
…and repeat 10,000 times
MW or RF
excitation
Polarization and
fluorescence
detection of a
single NV
Experimental techniques:
?
ms = ±1
ms = 0
MW or RF
…and repeat 10,000 times
wire
spin resonance
Zoom in:
hyperfine lines
mI = -1/2
+1/2
-1 0 1
14
15N:
N:
2.2
MHzsplitting
splitting
3 MHz
Hyperfine interactions with proximal 13C spins
Measurement of possible hyperfine parameters
% change in fluorescence
different proximal 13C lattice sites have different hyperfine splittings
MW frequency (GHz)
Hyperfine interaction depends on 13C
lattice site and electronic spin density
Gali, PRB 80 241204R 2009
Hyperfine interactions with proximal 13C spins
Discrete hyperfine parameters correspond to individual lattice sites
observed values agree closely with predictions from ab initio theory
allows identification of individual nuclear spin lattice sites
+130 MHz
40 G
510 G
NV hyperfine interactions
Area of circles ~
hyperfine interaction
Nearestneighbor 13C:
130 MHz
6
NV
14N/15N:
14
MHz
2-3 MHz
9
4
How can we polarize, manipulate, and detect these nuclear spins?
…especially the nitrogen nuclear spin?
Polarization, control, and readout of nuclear spins
in diamond
Observation of
coherent oscillation
of a single nuclear
spin and realization
of a two-qubit
quantum gate,
F. Jelezko et al. 2004
Multipartite
Entanglement Among
Single Spins in
Diamond,
P. Neumann et al. 2008
Quantum Register Based on
Individual Electronic and Nuclear
Spin Qubits in Diamond
M. V. Gurudev Dutt, LC, et al 2007
Early techniques work for strongly-coupled 13C spins
Our work: Improve signal, extend to nitrogen nuclear spins
Polarization of nuclear spins in diamond
Use hyperfine flip-flops in
the excited state instead
The idea:
Fuchs 2008, Jacques 2009
NV
SWAP
Hard to do
precisely with
MW pulses
Especially for
weakly-coupled
nitrogen
nuclear spins
If we can swap the electron
and nuclear spin states
Laser excitation
We can polarize the
electron spin into a welldefined quantum state
And repolarize the
electron spin
Then we’ve prepared both
spins in a well-defined
quantum state
Dutt, LC Science 2007
Polarization of nuclear spins in diamond
The excited-state level anti-crossing (ESLAC)
The nitrogen hyperfine
interaction is about 20x
larger in the excited
state ~ 50 MHz
Fuchs et al. 2008
Robust polarization for many nuclear spin species
Nuclear magnetic resonance in diamond
B = 510G
polarization
MW to drive
electron spin
transitions
RF to drive
nuclear spin
transitions
Precise hyperfine parameters
Green light off during
pulses => working in the
electronic ground state
Fast NMR control
Strong signal
Smeltzer 2009
Also Stuttgart
Readout of single nuclear spins in diamond
Working at the ESLAC ~ 510 G we can
directly distinguish nuclear spin states!
ms  0, mI  1
already fully polarized bright
ms  0, mI  0
1 singlet pass to polarization  dark
ms  1, mI  0
2 singlet passes to polarization  darker
ms  1, mI  1
3 singlet passes to polarization  darkest
Steiner 2010
Simple, robust nuclear spin readout mechanism
Coherence properties of nuclear spins
14N
dephasing time can be close to the electron spin lifetime
14N
Electron spin decay
Dephasing times are widely variable, but can be extended with echo techniques
13C
lattice
sites A
Spin
echo
Millisecond dephasing times – long-lived quantum memory
Outlook: Scaling up with optical connections
Idea: encode and store qubits in nuclear spins
Entangle electrons
(probabilistically) without destroying nuclear qubits
Perform deterministic quantum gates between remote nuclei
via electron-nuclear coupling: “teleportation based gates”
Operations between any pairs at random locations can be performed
simultaneously: purely optical scaling possible
•quantum repeaters for long-distance communication
L.C., J.Taylor, A.Sorensen. M.D. Lukin PRL 06
•fault tolerant quantum computation
with very high error threshold
E.Knill,
Naure
(2004),
J.Taylor
et al, (07)
Can we
turn
on L.Jiang,
and off
hyperfine
flip-flops in the excited state?
Need nuclear spins to be unaffected by optical transitions!
What happens if you send in MW and RF simultaneously?
Weak MW to
drive electron
spin transitions
Strong RF to
drive nuclear
spin transitions
…a pineapple
Multifrequency excitation of the NV center in diamond
Low magnetic field data:
no nuclear spin
polarization
ESLAC data:
14N polarization
• Low frequency
splitting
• Multiphoton
transitions
• Missing resonances
Multifrequency excitation of the NV center in diamond
Low magnetic field data:
no nuclear spin
polarization
ESLAC data:
14N polarization
(also different,
stronger, RF
amplifier)
The major features have nothing to do with nuclear spins.
It’s purely a two-level system effect.
Numerical simulations
Features are characteristic of a twolevel system with:
• weak MW B field  NV axis
• strong RF B field || NV axis





H  Sz  gB BMW cos(MW t )  BRF cos(RFt  )  S
1     RF cos(t )
 MW

H 






cos(

t
)
2
MW
RF

Quasistatic behavior
Observed effects:
• Low frequency splitting
• Multiphoton transitions
• Missing resonances
RF
MW
1     RF cos(t )
 MW

H 






cos(

t
)
2
MW
RF

Quasistatic regime: ω < t
Extremal detunings ±2ΩRF most likely
Multiphoton resonances
Observed effects:
• Low frequency splitting
• Multiphoton transitions
• Missing resonances
Floquet theory
2
1
0
-1
-2
3
2
RF
photons 1
0
-1
m=0
1     RF cos(t )
 MW

H 






cos(

t
)
2
MW
RF

m=-1
RF
MW
MW flips the spin; RF doesn’t
Intermediate state detuned only by ~ω
Explains dependence on
orientation of fields
Analytic approach
i(n  )t 
1    RF cos(
t )  An

0
e
MW
H   
t ) 
n





cos(

2
RF
Hint   MW i(n  )t
 
0
 An e

 n

Explains observed multiphoton
transitions and missing resonances –
“coherent destruction of tunneling”
Effective Rabi frequency
for n-RF photon transition
MW 2RF 
An 
Jn 

2

 RF 

Strong-field effects
in an easilyaccessible regime
Applications for longitudinal excitation?
Polarization and readout away from the ESLAC
Goal: drive hyperfine flipflops within the excited state when we
want them…and not when we don’t!
• “normal” MW excitation would
just flip the electron spin without
affecting the nuclear spin very much
• Longitudinal MW excitation has
the effect of bringing the states
into resonance without flipping
the spin
Proposed method: Use a microwave magnetic field oriented parallel to the
electron & nuclear spin quantization axis
Polarization and readout away from the ESLAC
Idea: Apply microwaves || NV axis: they cannot flip the spins directly, but
they can bring hyperfine flipflops into resonance
Floquet theory calculation incorporated
into a 3-level rate equation model to
predict equilibrium polarization
Polarization and readout away from the ESLAC:
Initial tests
Geometry: Microwave field 45 degrees from NV axis
=> compare theory & experiment
• Predict and observe a weak polarization effect
Is this useful?
Conclusion and outlook
Spin physics in diamond: preparation and detection of a single NMR molecule
What next?
• Higher-fidelity control over electron-nuclear spin registers using dynamically
decoupled gates Cappellaro et al. 2009 PRL
• Scaling up for QIS: NV-NV (Neumann 2010), NV-photon (Togan 2010)
can this be done in a manner that doesn’t entangle a nuclear spin?
• Magnetometry (Taylor 2008, Maze 2008, Balasubramanian 2008)
can this be used to look at single spins outside of diamond?
• Coupling to resonators and cavities for cavity QED and hybrid systems
(Kubo 2010)
• Other defect centers with similar or better properties?
Opportunities and challenges remain
Many thanks to
Bates NV Lab
Benjamin Smelzter `10
Jean McIntyre `10
Kyle Enman `09
Yuanyuan Jiang `09
Amrita Roy ‘11
Janith Rupasinghe ‘13
Gabe Ycas  UC Boulder
… and you for your attention!
Funding: Bates College, HHMI, Research Corporation