Single-Photon Detection of 1.55 gm Entangled Light and Frequency
Upconversion in Periodically Poled Lithium
Niobate for Quantum Communication
by
Marius A. Albotd
B.S. Engineering Physics
Cornell University, 1997
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
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2002
@2002 Marius A. Albota. All rights reserved.
RARKER
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JUL 3 1 2002
LIBRARIES
The author hereby grants to MIT permission to reproduce and to distribute publicly paper
and electronic copies of this thesis documept in whple or in part.
A uthor......................
..............................
Department of Electrical Engineering and Computer Science
May 17, 2002
Certified by..............
Franco N. C. Wong
Principal Research Scientist, Rese rch Laboratory of Electronics
Thesis Supervisor
Accepted by.............
I A. C. Smith
Chairman, Department Committee on Graduate Theses
Single-Photon Detection of 1.55 pm Entangled Light and Frequency
Upconversion in Periodically Poled Lithium
Niobate for Quantum Communication
by
Marius A. Albota-
Submitted to the Department of Electrical Engineering and Computer Science
on May 17, 2002, in Partial Fulfillment of the
Requirements for the Degree of
Master of Science in Electrical Engineering and Computer Science
ABSTRACT
Entanglement generation, single-photon detection, and frequency upconversion are all
key ingredients of a proposed quantum communication scheme. We have demonstrated
single-photon detection at 1.55 jim with commercial indium gallium arsenide avalanche
photodiodes that were passively quenched, thermoelectrically cooled, and gated to
operate above breakdown voltage in Geiger mode. When cooled to -50'C we obtained
reliable photon-counting operation with quantum efficiencies of up to 20% at 1.55 gm,
dark count probabilities of 0.12% per 20 ns gate, and negligible afterpulses at repetition
rates of up to 200 kHz. The indium gallium arsenide single-photon detector was utilized
to demonstrate time entanglement of twin photons from a frequency-nondegenerate
quasi-phase-matched optical parametric downconverter with collinear and co-polarized
outputs at 808 nm and 1.56 gm.
We have designed and fabricated a 6-mm-long periodically poled lithium niobate crystal
with an 11.6 [tm grating period for first-order type-I quasi-phase-matched sum frequency
generation. Upconversion of 1.609 gm light with a strong pump at 1.064 pm resulted in a
sum-frequency signal at 640 nm near the peak silicon detection window. We achieved
single-pass conversion efficiency of up to 0.65% with 332 mW of pump power in good
agreement with theoretical predictions.
Thesis Supervisor: Franco N. C. Wong
Title: Principal Research Scientist, Research Laboratory of Electronics
2
ACKNOWLEDGEMENTS
First, I would like to thank Franco Wong for his patient advising. The door to his office
was always open for me and I enjoyed learning from him about nonlinear and quantum
optics. I thank Professor Jeffrey Shapiro for offering me the opportunity to join his team
and for providing invaluable theoretical insight into my experimental issues. I thank my
mentor and friend David Kocher for all his help, constant support, and encouragement
throughout this thesis. Dave also provided me with assistance on circuit designs, free
advice, and the excellent Lexington-variety honey for the teas and coffees that kept me
going through the writing of this thesis. I would like to acknowledge the backing and
encouragement that I received from the Group Leaders of the Optical Communication
group, Bill Keicher and Fred Walther during the course of my studies. I am grateful to
Rick Heinrichs, my former Group Leader in the Laser and Sensor Applications group,
who supported me in my initial decision to pursue graduate studies. Staff members Peg
Danek, Brian Player, and Jim Mooney deserve great thanks for their assistance with
numerous engineering issues. I thank MIT Lincoln Laboratory for their financial support
and for allowing me the opportunity pursue a higher degree through their Lincoln
Scholars Program.
On campus, I'd like to thank Elliott Mason for patiently teaching me the tricks of
periodic poling. I have learned quite a lot from him. The long nights we spent collecting
data in the laboratory, listening to Radio Contact, will not be forgotten. A big merci goes
to my friend and research colleague, post-doc Gaetan Messin, for his help with the
frequency upconversion experiments and for providing good insight into physics and
sometime politics through many lively discussions. I thank Chris Kuklewicz for always
helping out with issues related to computers, software (including LyX!), and data
analysis. I tremendously enjoyed working with former graduate student and friend Eser
Keskiner. His thesis was of great help to me. I thank our old and new team members
Shane Haas, Francois Impens, and Friedrich Koenig for stimulating conversations.
Most of the fabrication work was done at Lincoln Laboratory where state-of-theart facilities enabled me do work that would have been difficult elsewhere. I would like
to acknowledge the help we have received from Lincoln Laboratory throughout my
3
involvement in this research and thank everybody there who contributed to the work
presented in this thesis.
I would not be where I am today if it wasn't for my great family who has always
supported me. My mother, Apriliana Virginia, deserves the credit for raising me during
the hard times of the Communist rule in Romania. My father, Mihail Gabriel, motivated
me through his own academic career and encouraged excellence form an early age. I
thank them both for believing in me. My uncle Mircea deserves a special multumesc for
always being there for me, morally and financially, throughout my undergraduate and
graduate career. I am indebted to the rest of my family, including aunts Gabriela, Ulpia,
and uncle Mircea James for their constant encouragement.
Last but not least, I thank my amazing girlfriend and partner in life Elizabeth for
all her patience, unwavering support, and unconditional love. Her constant belief in me
has been my guiding light throughout the many turbulent times.
Finally, I would like to apologize to everyone that helped me with this thesis and
whose contributions I forgot to acknowledge. My oversight belies my gratitude.
4
TABLE OF CONTENTS
CHAPTER 1. INTRODUCTION............................................................9
1.1.
Background and Motivation......................................................9
1.2.
A Review of Entanglement Sources............................................10
1.3.
An Entanglement Source for Quantum Communication .................... 11
1.4.
Key Technologies for Long-Haul Quantum Communication...............12
1.5.
Thesis Overview ...............................................................
12
CHAPTER 2. THEORETICAL CONSIDERATIONS.................................14
2.1.
Sum Frequency Generation......................................................14
2.2.
Quasi-Phase-Matching.........................................................18
CHAPTER 3. GENERATION AND DETECTION OF ENTANGLED LIGHT....22
3.1.
Motivation..........................................................................22
3.2.
Detectors for Single Photons................................................
3.3.
Low-Light-Level and Single-Photon Detection............................23
3.4.
Review of Photon Counting with InGaAs/InP APDs.....................25
3.5.
Geiger-Mode InGaAs APDs for Entangled-Photon Detection..............27
22
3.5.1. Theormoelectric Cooling.............................................28
3.5.2. Linear-Mode Operation.................................................31
3.5.3. Photon-Counting Operation.............................................33
3.6.
Results and Data Analysis.......................................................36
3.7.
Detection of Entangled Light................................................
3.7.1. Experimental Setup....................................................43
3.7.2. Entanglement Data....................................................46
CHAPTER 4. FREQUENCY UPCONVERSION IN PERIODICALLY POLED
LITHIUM NIOBATE.............................................................................48
4.1.
Introduction.....................................................................48
4.2.
PPLN Design and Fabrication................................................48
5
43
4.3.
Experimental Apparatus.......................................................53
4.4.
R esults and Analysis..............................................................58
4.4.1
Single-Pass Conversion Efficiency.................................62
4.4.2. Additional Observations.............................................63
4.4.3. Analysis of Cavity-Enhanced Frequency Upconversion....... 65
4.5.
Conclusion and Future Work..................................................66
CHAPTER 5. CONCLUSION..............................................................67
5.1.
Summary of Accomplishments..................................................67
5.2.
Concluding Remarks..............................................................67
BIBLIOGRAPHY...............................................................................70
6
LIST OF FIGURES
2.1.
Temperature-dependent Sellmeier equation for ne in LiNbO 3 .......
3.1.
Custom InGaAs APD cold box with cover off.........................................29
3.2.
Custom InGaAs APD cold box with cover on.........................................30
3.3.
Linear-mode APD bias circuit.........................................................31
3.4.
Linear-mode performance of InGaAs APD at 25'C and -55'C..................32-33
3.5.
Geiger-mode APD pre-amplifier circuit diagram......................................34
3.6.
Trace of Geiger-mode events recorded with JDS Uniphase APD................35
3.7.
Typical behavior of JDS Uniphase APDs gated in Geiger mode................36-37
3.8.
Dark-count histogram...................................................................38
3.9.
Light-count histogram...................................................................39
............ . .
21
3.10. Geiger-mode device performance.....................................................41
3.11. Schematic of PPLN-based frequency-nondegenerate parametric
downconversion experiment..............................................................44
3.12. Sample trace from Si SPCM recorded with Gage Scope..............................45
3.13. Histogram of conditional detection probability of an idler photon..................47
4.1.
Optimum PPLN grating period for SFG of 0.64 jim with 1.6 [tm and 1.06 pm
inputs versus temperature..............................................................49
4.2.
Electric-field poling trace for the PPLN.............................................50
4.3.
Picture of PPLN crystal used for frequency upconversion.........................51
4.4.
Front-side photograph of a single PPLN channel......................................52
4.5.
Back-side picture of a PPLN channel................................................53
4.6.
Experimental setup for frequency upconversion....................................54
4.7.
Photograph of experimental setup for frequency upconversion.....................55
4.8.
Upconverted signal vs. pump power..................................................58
4.9.
Temperature phase-matching tuning curve...........................................60
4.10. Idler phase-matching bandwidth.........................................................61
4.11. Center idler wavelength vs. PPLN temperature........................................62
4.12. Photograph of output generated using PPLN........................................64
4.13. Measured SHG power vs. PPLN temperature......................................65
7
LIST OF TABLES
4.1.
Extraordinary indices of refraction of LiNbO 3 at selected wavelengths......56
8
CHAPTER 1. INTRODUCTION
1.1. Background and Motivation
Quantum communication exploits the laws of quantum physics in the rapidly advancing
field of optical communication. Over the past decade, with the arrival and growth of the
Internet, there has been tremendous interest in the development of secure high-data-rate
communication networks.
Today's fiberoptic links that span the globe to connect
continents and cultures are slowly but surely replacing clogged and obsolete copper
transmission lines. Scientists now envision ultra-secure communication links for voice
and data, and more capable and potentially faster computers based on quantum rather
than classical physical principles.
Entanglement is the key to the burgeoning field of quantum information
processing, including quantum cryptography and quantum computing.
In the early
1980s, Aspect's experiment [1] cleanly demonstrated the inconsistencies between
Einstein, Podolsky, and Rosen's (EPR) hidden-variable theory and physical observations
[2]. Since then, experimental violations of the inequalities derived by Bell [3] have been
confirmed using entangled pairs of photons [4]. High-flux sources of entangled light are
not only required for the real-world applications of tomorrow, but are also essential for
laboratory experiments that test the foundation of quantum mechanics.
Future
investigations in quantum information technology will be facilitated by the development
of new entanglement sources. These would include efficient, reliable, ultra-bright, and
narrow-bandwidth
sources
of
polarization-entangled
photons,
especially
at
telecommunication wavelengths. Many novel applications of entangled light have been
proposed, including quantum-enhanced positioning, clock synchronization, multi-particle
entangled states, and quantum cryptographic schemes of communication [5,6].
Spontaneous parametric downconversion via second-order processes in X
crystalline media is the most widely used scheme for generating entangled photon pairs
in an unfactorizable quantum state, as defined by one of the fathers of quantum physics,
E. Schr6dinger [7],
HIV )
ent
|y)12= 2
9
+ e |V 1H 2 )
Photon pairs can be entangled in time, frequency, and polarization. Polarization
entanglement is of particular interest to quantum communication schemes because the
two orthogonal polarizations of a photon can serve as the binary basis of a quantum bit or
qubit.
Light polarization can be readily manipulated in the laboratory using widely
available and highly accurate optical components such as polarizing beam splitters, wave
plates, and polarizers. One might also encode data onto the polarization of individual
photons instead of the thousands of photons required in today's classical optical
communication schemes.
The idea for long-distance quantum communication is simple. Out of each pair of
entangled photons produced by a source, one of the photons is sent to Alice's transmitter
station while the conjugate photon is sent to Bob's receiver node.
The polarization-
entangled photons are then loaded into local quantum memories for storage such that
polarization states can later be retrieved and used for teleporting the polarization states of
photons [8].
The polarization-entangled quantum bits (qubits) can also be utilized to
create a one-time secret key pad for applications in quantum cryptography and quantum
key distribution (QKD). Polarization entanglement of photons nevertheless is inherently
fragile and cannot be easily stored.
Atomic quantum memories are currently being
investigated as possible storage nodes for polarization entanglement.
1.2. A Review of Entanglement Sources
Several sources of polarization-entangled photons have been reported to date - such as
atomic cascade sources [1] and spontaneous parametric down converters (SPDC)
[9,10,11]. The rate of twin-photon generation in SPDCs that use crystal birefringence has
been relatively low due to the poor efficiency inherent in nonlinear processes. The SPDC
sources demonstrated to date are too low in intensity to be useful in most
implementations of practical quantum communication.
One of the most widely used
schemes employs type-II phase matching in a birefringent crystal. Pairs of orthogonally
polarized signal and idler photons are generated using an ultra-violet (UV) pump laser.
The output is emitted spatially along two conical manifolds with orthogonal relative
polarizations. Kwiat et al. [9,10] used type-II birefringent phase matching in parametric
downconversion from two identical crystals oriented at 90' to generate entangled photons
10
at a rate of 1.5 x 106 s-1 over a bandwidth of 5 nm centered at 702 nm when pumped with
150 mW.
1.3. An Entanglement Source for Quantum Communication
A future long-haul quantum communication scheme that uses polarization-entangled
photons and trapped-atom memories has been jointly proposed by research teams from
the Massachusetts Institute of Technology (MIT) and Northwestern University (NU)
[12].
The MIT/NU protocol utilizes a high-flux, narrowband, continuous-wave (cw)
source of polarization-entangled photon pairs [13] and a quantum atomic memory [8].
The quantum memory scheme was proposed by Lloyd et al. and uses ultra-cold rubidium
(Rb) atoms confined by a focused CO 2 laser beam at the center of a high-finesse cavity.
Rb is employed in this scheme because it has the right level structure to allow
measurements of all four Bell states and also for non-destructive determination of the
cavity-loading process [8]. The proposed entanglement source utilizes a doubly resonant
optical parametric amplifier that is resonant in both signal and idler fields and is capable
of a pair production rate of 1.5 x 106 s-1 per unit of pump power over a 30-MHz
bandwidth around 795 nm and 1.609 tm center wavelengths. The source is estimated to
have a photon generation rate that is five orders of magnitude brighter than the sources of
Kwiat et al. and Oberparleiter et al. [9,10,11] within the bandwidth of the cavity
containing the Rb atom. This source along with the quantum memory scheme proposed
by Lloyd et al. represent, if experimentally implemented, a complete scheme for the
production, storage, and transmission of entanglement and may form the basis of future
quantum communication systems. The MIT/NU singlet-based quantum communication
protocol for long-distance quantum teleportation may prove to be a feasible scheme and
could allow for secure communications. Pragmatic economic considerations will most
likely require any real-world implementation of a quantum communication scheme to
use existing fiberoptic infrastructure.
Thus it is preferable to generate the entangled
photons at wavelengths in the 1.5 THz-wide minimum-loss silica transmission window
centered around 1.55 pm. The MIT scheme addresses all these issues: it is designed to
operate with standard telecommunication fiber, and can achieve loss-limited throughput
11
as high as 200 entangled-pairs/sec with 97.5% fidelity over a 50 km path when there is
10 dB of fixed loss in the overall system and 0.2 dB/km fiber propagation loss [12].
1.4. Key Technologies for Long-Haul Quantum Communication
Entanglement
generation,
single-photon detection,
and quantum-state
frequency
upconversion are all key ingredients of a long-haul quantum communication project.
The proposed protocol requires a high-flux source of polarization entanglement at 795
nm and 1609 nm for loading of local and remote Rb-atom memories. Entangled light at
a wavelength near 1.6 Jtrm will have to be transmitted over fiberoptic cables and
upconverted to 795 nm prior to loading of the remote Rb quantum memory nodes. In
order to transfer polarization entanglement to remotely located atoms, we require
quantum-state upconversion to preserve the initial quantum state of the 1609 nm idler
photon and upconvert it to an identical state of polarization at 795 nm. The quantum
communication
protocol also requires
singe-photon detection
at the operating
wavelengths, including the visible and the low-loss fiberoptic transmission window near
1.55 gm where commercial detectors are not available.
1.5. Thesis Overview
The photonic polarization entanglement source and the transfer to Rb atoms are essential
parts of a proposed protocol for long-distance quantum teleportation. The purpose of this
thesis is to investigate several important issues related to this proposed quantum
communication scheme. Three key topics will be discussed in this thesis:
A) The design and construction of cooled and gated Geiger-mode single-photon
detectors at telecom wavelengths,
B) The use of these photon-counters to demonstrate entanglement from a frequencynondegenerate optical parametric downconverter, and
C) Theoretical calculations, device fabrication, and experimental implementation of a
frequency upconverter near 1.6 pm.
12
We discuss these three topics in Chapters 3 and 4. In Chapter 2, we present a brief
theoretical review of the nonlinear optical processes that govern the upconversion
experiments. In Chapter 5, we review our accomplishments, present concluding remarks,
and discuss our future research plans and the application of our results to quantum
communication.
13
CHAPTER 2. THEORETICAL CONSIDERATIONS
The experimental investigation of sum-frequency generation (SFG) of visible light in this
thesis is a feasibility study of near-100% upconversion efficiency that is needed for
achieving quantum-state frequency upconversion. In this chapter, we review briefly the
theory of second order nonlinear optical processes that underlie SFG.
We note that
spontaneous parametric downconversion (SPDC), used in the generation of entangled
photon pairs, can also be described by the same theory with the appropriate boundary
conditions. However, since SPDC is not the focus of this thesis, its theoretical review
will not be done here.
2.1. Sum Frequency Generation
The process of sum frequency generation, involves transfer of energy from two lower
frequency input fields to a higher frequency output field. In other words, two lower
energy photons combine into one higher energy photon. If one of the input fields has a
much higher intensity than the other, the strong field serves as the pump and the
nonlinear process that converts a weak input field to a higher-frequency output field is
often called frequency upconversion.
This nonlinear optical process occurs in a
noncentrosymmetric media characterized by a nonlinear susceptibility and nonlinear
polarization. X
is the nonvanishing second order susceptibility responsible for the
induced nonlinear polarization of the media, which in turn generates the output field. The
equations that describe this parametric process in the steady state are given by the
following system of coupled amplitude equations [14]
dE 3 = i, 3E E2 eiz
dz
dE2 = _iK 2E 3 E,*e-z
dz
dEd1-=
1
-irciE3
(2.1)
E2 *e-ik
dz
where K, =
(%deff
/njc (for j=1, 2, and 3) are the coupling coefficients written in terms of
the respective frequencies and indices of refraction, with the index 3 referring to the
14
highest frequency field. In deriving Eqs. (2.1) we invoke the standard slowly varying
envelope approximation (SVEA), plane-wave interactions with negligible absorption in a
conventional birefringent and purely non-magnetic crystalline media.
practice is to replace the three-dimensional tensor X
coefficient deff. Conservation of energy requires that
mismatch is Ak =
k3 -k2
0 3
It is standard
with the effective nonlinear
= co + o2 , and the wave vector
-ki . In the low conversion limit with an undepleted pump we
take the two input fields E1 (strong pump) and E2 (weak signal) to be constant and solve
for the amplitude E3 of the upconverted light as a function of interaction length.
Integrating the first equation in (2.1) from z = 0 to z = L, with E 3 (0) = 0 we obtain
E3 (wL)= -iK E, E 2L sinc(AkL / 2)eAkL/ 2 .
In terms of the field intensity, with I = -n
-EI
2 F'i00
2(0
13 (W3 , L)
d2
L2
3- ef
nin2n3c
,
(2.2)
we have
11 2 sinc 2(AkL /2),
(2.3)
0,
where
sinc(x) = sin(x)
x
is the familiar phase-matching function, a measure of phase synchronization or lack
thereof between the three propagating waves. The sinc 2 function is less than unity for
nonvanishing wave vector mismatch and, as energy is transferred between the fields, it
reduces the efficiency of the upconversion process. The plane wave results, relations
(2.2)-(2.3), have to be modified to take into consideration the Gaussian aspect of the
focused laser beams. The efficiency of the upconversion process is given by the ratio of
the upconverted power to the input power with P = IA, where the effective area for the
Gaussian beam of radius w in the near-field limit is A = (1/ 2)nTw 2 . Keeping the pump
15
power constant, and assuming perfect phase matching, Ak =0, we obtain an expression
for the single-pass conversion efficiency through a crystal of length L,
p3
=
-
_
w 212
16nd2P 1
P2
n1n2
0 2w
3CE03
3
(2.4)
2.
W1
2
The conversion efficiency is proportional to the square of the effective nonlinear
coefficient and crystal length, and it varies linearly with pump power. In the near-field
analysis, it was shown [15] that for optimum efficiency and in order to minimize the
parametric threshold of the interaction, the waist radii of the three beams have to be
related via
1- 2
W3
1
1
2
W1
(2.5)
2
W2
Substituting Eq. (2.5) into Eq. (2.4) and introducing the confocal parameter inside the
, where n3 is the wavelength-dependent refractive
crystal b1 = k w , with k1 = 2cn /j
index and Xj is the vacuum wavelength, we obtain
p
3
-
P2
=
16 df PL ~
CO!
, k
L
bI
nin2 ncE X, b3Ik1 +b
2
.
(2.6)
k2 _
We let the two confocal parameters be equal to the same constant and introduce the
efficiency reducing parameter L/b -> hn(B, ), [15,16].
The expression for the
upconversion efficiency becomes,
fe
7 = -2 =
16)rd2 P L
hm(B,
1
nnnCe
2P3
16
_-1+k 2
(7
.kC
(2.7)
The efficiency reducing parameter depends on the double refraction (walk-off) parameter
B as well as on the focusing parameter
= L/b. The values of h.. can be computed
numerically for arbitrary focusing conditions. Optimum conversion requires
= L/b=
2.84 and B = 0, and results in a peak value for h,, of approximately 1.068. For non-ideal
focusing condition with L/b = 1, the efficiency factor is about 0.776 [16]. Contrasting
Eq. (2.7) with Eq. (2.4), we note the conversion efficiency is only proportional to L and
not L2 and that, typically, h,, < 1.
It has been shown that for quasi-phase-matched (QPM) interactions (see Section
2.2) in periodically poled media the effective nonlinear coefficient can be written as [17]
dm = -- sin(mnD)deff.
m71
(2.8)
In Eq. (2.8), D is the grating duty cycle defined as the width of the poled (or unpoled)
region divided by the period A and m is the order of the QPM grating. From Eq. (2.8) we
see that the maximum value for dm occurs for m = 1 and D = 0.5. Therefore, using a first
order grating with a perfect 50% duty cycle we would expect a nonlinear coefficient di
that is a factor of 2/n (63.7%) of deff. Hence, the upconversion efficiency 17 for an ideal
QPM device is at best 40.5% of the value given by (2.7). With this modification the
efficiency of upconversion with an undepleted pump, using QPM and focused Gaussian
beams is given by Eq. (2.7) with deff replaced by dm. Using the computations of Boyd and
Kleinman [16] and assuming negligible walk-off (B = 0), which is a very good
approximation for QPM, we find the following approximate numerical values for the
efficiency reduction factor: hm(0,1) = 0.776, hm(0,0.75) = 0.64, and hm(0,0.5) = 0.463.
Assuming optimal focusing with L = b, h, = 0.776, perfect phase matching, and a
perfectly poled first order 6-mm-long LiNbO 3 crystal with deff = d, = 16 pm/V, the
expected single-pass conversion efficiency is -2.7x10- 5 per mW of pump power.
If we allow for the possibility of complete (100%) upconversion and assuming
perfect phase matching with an undepleted pump, Eq. (2.1) is reduced to a pair of
coupled amplitude equations
17
d3 =-(ir'3Ej)E,
dE2
(2.9)
=-(ir, E,*)E3
dz
where the factors in the parentheses are taken to be constants. We look for solutions of
the form eliyz with no sum-frequency signal at the input, E3 (z=0) = 0, and with a weak
field fed into the crystal E2 (0). The solution relating the intensities of the upconverted
and input fields as a function of crystal length is
13 (L)= n3I
2 (0)sin 2(yL)
n2
1 2 (L)
where y 2 =
2
.
=
1 2 (0)cos
(2.10)
2
The solution shows that 100% of the input field at ")2 is
n2n3c
converted to the field at o> for yL = n/2. For longer interaction lengths or strong pump
powers energy will oscillate back and forth between the two fields. The required pump
power for 100% conversion efficiency using Gaussian optics is
n 1n3x1x2x3E0c
2
128di2Lhm(B,()
(.1
For a first-order, 5-cm-long PPLN crystal, with deff = d, = 16 pm/V, assuming optimal
focusing with B = 0, L = b, and hm = 0.776, the required pump power for 100% singlepass conversion efficiency is -1 1W.
2.2. Quasi-Phase-Matching
Conventional phase matching uses the intrinsic birefringence of the crystal to achieve
type-I or type-IL phase matching such that
18
n33___
(
n22)+
X3
X
n1()
)
X1
or, Ak = 0.
The indices of refraction are in general a function of both temperature and incident angle
relative to the crystal's principal axes. In angle phase matching, the dependence of the
refractive index on the direction of propagation is used to tune the phase matching
function. However the angular acceptance for critical-angle phase matching, propagation
not being along one of the principal axes, is limited to several mrad for crystal lengths on
the order of 1 cm, imposing tight tolerances on focusing and alignment. Type-I or type-II
phase matching refer to the lower frequency signal-idler relative polarization orientations
being parallel or orthogonal, regardless of the pump polarization. Birefringent crystals
such as potassium niobate (KNbO3 ), lithium niobate (LiNbO3 ), and potassium titanyl
phosphate (KTP) are readily available and have relatively large nonlinear coefficients.
However, exploiting these high nonlinear coefficients, if at all achievable, requires
inconvenient phase matching geometries or temperatures.
At temperatures below the Curie temperature a ferroelectric material can show
spontaneous polarization that can be reversed by applying a sufficiently large electric
field to the bulk nonlinear crystal. In recent years the techniques of ferroelectric domain
inversion of nonlinear optical materials via periodic poling has allowed for the design and
fabrication of QPM structures. The idea of a layered media to compensate for the wave
vector mismatch dates back to Armstrong et al. [18]. QPM permits temperature-tunable
non-critical-angle phase matching at any wavelength within the transparency window of
the crystal, thus greatly expanding the operating wavelengths of many nonlinear materials
[19,20,21]. Moreover, the acceptance angle for 90'-phase matching is over an order of
magnitude larger than with critical (angle-tuned) phase matching.
Another clear
advantage of QPM is the engineered access to the largest nonlinear coefficient (for
example d33 in LiNbO3 ), normally not available for birefringent phase matching.
QPM is achieved by introducing a compensating grating vector, Km = 2am/A,
such that Ak vanishes. Perfect phase matching is achieved when k3 = k2 + k1
19
2am/A,
where A is the period of a domain-reversed unit cell and m is the order of the grating. If
we consider the specific case of type-I phase matching, with E1 , E2 , and E3 being
collinearly polarized and oriented along the extraordinary crystal axis, phase matching is
achieved entirely through the contribution of the Km vector. The quasi-phase-matching
condition becomes
n,(X
3 ,T)
X3
n,(X
2 ,T)
=+
X2
ne
(X-,T) + M
-,(2.12)
ki
A
where ne is the extraordinary refractive index of the material.
The material of choice for this thesis, one of the optical materials that exhibits
some of the largest nonlinearities of all known inorganic media, is LiNbO3. We have
also chosen LiNbO 3 because it is relatively inexpensive and widely available, has a wide
transparency range (from -0.35 pm to 5 pm), and because the periodic poling techniques
are mature [22]. Sellmeier equations that give the values of the extraordinary index of
refraction in congruently grown lithium niobate and include thermal expansion effects
have been published [23,24]. In Figure 2.1 we plot the extraordinary index of LiNbO 3 as
a function of wavelength using the Sellmeier coefficients from Jundt [24] at two
temperatures of interest.
20
2.35
T = 191.6C
T = 211C
2.3-
-
2.25 -
---
-
-
.........
-.-.-
-
-
P 2.2 -
-
2.15
0.4
0.6
0.8
1
1.2
1.4
Wavelength (microns)
1.6
1.8
2
2.2
Figure 2.1. Temperature-dependent Sellmeier equation for
ne in congruent LiNbO 3.
The largest nonlinear coefficient for LiNbO 3 is d33 with a value of -25.2 pm/V [25].
However, birefringent phase matching only allows for the utilization of d31 , which is
approximately a factor of 6 smaller than d33 . Although first-order QPM reduces the
theoretical value of the nonlinear coefficient by approximately 40% to -16 pm/V, this is
still approximately 4 times larger than d31 , and thus allows for more efficient nonlinear
optical interactions. Some details related to the use and fabrication of PPLN crystals are
described in Chapters 3 and 4.
21
CHAPTER 3. GENERATION AND DETECTION OF ENTANGLED LIGHT
3.1. Motivation
Direct single-photon detection at 808 nm and 1.56 jim is required for the PPLN-based
entangled-light source recently developed at MIT [26].
Our ultimate goal was to
demonstrate the intrinsic nonclassical features of our entanglement source, such as time
and polarization entanglement and also to investigate quantum interference of twinphoton pairs.
Detectors that work near 1.55 ptm are essential components in QKD
systems and are also critical for the experimental evaluation of future quantum
communication schemes that use standard telecommunication fiber for transmission. In
this chapter we demonstrate excellent gated Geiger-mode performance with selected
indium gallium arsenide (InGaAs) avalanche photodiodes that were passively quenched
and thermoelectrically (TE) cooled. We have also utilized the detectors to demonstrate
high-flux
time-bin
entanglement
from
a
frequency-nondegenerate
parametric
downconverter. These results are presented in Section 3.7.
3.2. Detectors for Single Photons
The task of counting the 800-nm signal and 1.6-pim idler photons from our PPLN
entanglement source was made difficult because of the lack of commercially available
single-photon detectors at the longer wavelength. Silicon-based single-photon counting
modules (SPCMs), such as PerkinElmer's model SPCM-AQR-14, are commonplace.
They offer turn-key, reliable, continuous Geiger-mode operation at up to 5 Mc/s, dark
counts of less than 100/s, quantum efficiencies (QE) on the order of 50% at 795 nm, 300
ps timing resolution, and less than 50 ns dead times. The photon-counting technology
using Si is well established. Two-dimensional photon-counting Si APD arrays are being
designed and fabricated [27] for use in a variety of imaging and laser radar applications
[28]. A Hamamatsu photomultiplier tube (PMT), model H7421, is also commercially
available. It puts out positive-logic, 30 ns long, TTL pulses in response to single photons
with QEs on the order of 15% at 800 nm, has a large 5 mm diameter active area, and
performs well with dark counts of less than 200/s and gains on the order of 106. Hence,
detecting the 808 nm photons generated in the frequency-nondegenerate parametric
downconversion experiment does not represent a problem.
22
Although single-photon
detection with silicon photon-counting modules has been achieved as far as 1.064 pim,
where QEs on the order of 1% have been reported by members of our research group
[29], the band gap of the Si strictly limits their detection range to wavelengths below 1.1
gm. For low-light level operation at longer IR wavelengths near 1.55 gm, including
those in the third telecom window ranging from 1.1 to 1.6 pm, germanium (Ge) and
indium gallium arsenide/indium phosphide (InGaAs/InP) APDs, and PMTs are the only
choices.
Germanium APDs are extremely noisy and require cooling to cryogenic
temperatures for decent performance.
Their energy band gap however shrinks with
lowering temperature and at liquid nitrogen (LN) temperature (77K) they do not work
well for wavelengths beyond 1.45 jim [30]. A Hamamatsu near-infrared PMT (R550972) is functional as a photon-counter up to 1.7 jm but only barely - it has a QE of
-
0.4%
at 1.6 jim at a temperature of -80'C; it is large (17 kg) and expensive ($25k), requires
kV-level DC voltages, and up to two-hours of LN cooling with an "exclusive" cooling
unit prior to operation. For single-photon detection at telecom wavelengths the only
convenient and reasonable "choice" is InGaAs/InP APDs [31].
3.3. Low-Light-Level and Single-Photon Detection
With the advent of broadband telecommunications,
optical receivers are being
manufactured for the rapidly expanding fields of fiber optic communication and optical
networking, where high-sensitivity and high-bandwidth performance are compulsory. In
current optical telecommunication applications p-i-n (PIN) photodiodes (p-n junctions
sandwiching intrinsic regions) are widely used. Although they have no intrinsic gain,
when used in conjunction with low-noise transimpedance amplifiers (TIA), they can be
used for low-light detection down to approximately 2000 photons/bit.
Detecting
extremely dim light pulses of less than several hundreds of photons with commercial
PIN/TIA modules is currently impossible due to noise limitations in the amplifiers.
While structurally not very different from PIN photodiodes, APDs provide
internal gain in response to photoelectrons.
APD-type optical receivers for long-haul
SONET and DWDM at 2.5 and 10 Gb/s are commercially available for the low-loss
telecom windows. However, these APD modules are designed for low-light detection
with multiplication factors (M) of up to 100 or more.
23
In this linear regime they
substantially increase the sensitivity of optical receivers providing clear advantages over
PIN photodiodes with TIAs. Photon-countingoperation (at very large values of M) with
today's commercial APDs is difficult, if not impossible, because of the high dark counts,
tremendous afterpulsing contribution, and very low QEs exhibited by the material of
choice, InGaAs/InP. This should not be entirely surprising, as these devices were not
originally designed with photon-counting operation in mind.
Reasons for these
undesirable features in Geiger mode include lattice mismatch between the absorption and
multiplication regions at the InGaAs/InP interface, trapping and subsequent release of
carriers.
Several groups are working on developing APDs specifically tailored for
Geiger-mode operation. While research into III-V compound semiconductor materials
for photon-counting detectors is very active, as of the writing of this thesis we are not
aware of the existence of any commercially available photon-counting APDs at 1.55 jim.
Recent work shows however that Geiger-mode operation with some commercial InGaAs
APDs designed for linear-mode operation is in fact possible but only with carefully
selected devices operating under very specific conditions.
The techniques for device operation in Geiger-mode and several photon-counting
circuit designs are available in the literature for applications requiring both active and
passive quenching [27,28,32,33,34]. For photon-counting applications, the APDs have to
be reverse-biased above breakdown to operate in Geiger mode. When in Geiger mode,
an electron-hole pair generated by the absorption of a single photon initiates an avalanche
process, which causes the APD to break down. Geiger-mode devices are advantageous
because, in response to a single photoelectron, they yield a fast, high-amplitude, electrical
pulse that can be used to trigger high-precision timing circuitry. Randomly generated
dark counts and after-pulsing effects due to traps severely limit the performance of
Geiger-mode APDs by introducing noise counts that are fundamentally indistinguishable
from signal counts. The gate repetition frequency, width, and magnitude also affect the
overall device performance, and their effects need to be investigated when designing a
custom photon counter.
24
3.4. Review of Photon Counting with InGaAs/InP APDs
When reverse-biased with 1 to 2V below the breakdown voltage an APD is said to be
operated in the linear mode.
InGaAs APDs designed for linear-mode operation are
commercially available from manufacturers like Alcatel, JDS Uniphase, PerkinElmer,
and Fujitsu.
All these devices are however not designed for operation above the
breakdown voltage, in photon counting or Geiger mode.
Manufacturers do not test,
recommend, or otherwise provide any information concerning the operation of their
devices in photon-counting configuration and usually - attesting to their frailty - warranty
is voided if Geiger-mode operation by the customer is suspected. A researcher has to
select several devices, investigate the behavior of each of them in Geiger mode, and
ultimately pick the best device of the pack. Linear-mode parameters such as dark current
and breakdown voltage are not necessarily good indicators of Geiger-mode performance.
In addition, the breakdown voltage, dark current, figures of merit (FOM) such as the
noise-equivalent power (NEP), and other device parameters, have been found to vary
greatly not only from manufacturer to manufacturer, but even between successive
production rounds within the same detector design. For example, Ribordy et al. [35]
evaluated the performance of seven Fujitsu FPD5W1KS InGaAs APDs and found orders
of magnitude variations in dark count probability among devices. This makes the task of
selecting a good device more challenging.
Unlike their Si counterparts, today's
commercial InGaAs devices are plagued by extremely high dark counts and afterpulses
when overbiased in Geiger mode at room temperature. To qualify for photon-counting
operation they must be kept at low, potentially cryogenic, temperatures. They also need
to be operated with short-duration gates since continuous-mode operation in Geiger mode
is precluded by the abundance of trapped-carrier-induced afterpulses.
The two main sources of noise are spontaneously excited dark counts and
afterpulses.
Dark counts constitute random noise and follow a Boltzmann-type
exponential curve as a function of device temperature - they decrease exponentially with
decreasing temperature. Afterpulses are generated by the trapping of charged carriers
during avalanche events. These traps can be long-lived and their subsequent release
constitutes an indistinguishable contribution to the measured count rate. To isolate and
limit their effect the device must be gated with short-duration pulses at low enough duty
25
cycle. Afterpulsing appears to vary inversely with temperature - more traps are filled at
lower temperatures - and linearly with gate duration and gate pulse repetition frequency
(PRF). As the device temperature is increased the thermally excited dark counts increase
(bad), but the lifetime of trapped carriers and thus the afterpulsing probability decreases
(good). Significant cooling is required to reduce the thermally excited dark counts. In
addition, the QE also decreases with decreasing temperature and excessive cooling
beyond an optimum point increases the afterpulse contribution without further gain in
QE. While the QE also increases with overbias, so do the dark counts. Gate-on duration
and the PRF also affect device performance.
Moreover, all these effects may be
intertwined making it challenging to find an optimum set of operating parameters.
InGaAs APDs can only be overbiased in Geiger-mode for short durations and DC
operation in the Geiger mode is out of the question with current devices because the
afterpulse-dominated overall dark count rate is on the order of 2 MHz.
The performance of commercially available InGaAs APDs as single-photon
detectors has been evaluated by several research groups [31,35,36], and more recently by
Rarity et al. [37], Hiskett et al. [38], and Stucki et al. [39].
Since the two effects
mentioned above, dark counts and afterpulses, have different temperature dependence a
local minimum or optimal operation point may exist. For example, Bourennane et al.
[36] found an optimum NEP of -5x10-16 W/Hz
in the neighborhood of 210K (-60'C).
Data from Ribordy et al. [35] shows peaks in the QE vs. T curve between 180 and 200K
with dark count probabilities of approximately 10-5 to 10
4
per 2.6 ns gate at 1.55 Ltm.
Their data suggest that cooling the APDs below a certain, device-specific, temperature is
in fact detrimental due to increase afterpulsing.
While there is no agreement in the
literature on this issue, more recent published data show device temperatures between
180 and 220K to be optimal for gated Geiger-mode operation for several commercial
APDs. This is in fact a much-needed piece of good news because operation at -50'C to
-80'C is within the cooling range of solid-state Peltier thermoelectric coolers - a desirable
alternative to more complex and cumbersome LN cooling schemes. An absolute upper
limit of repetition frequency for gated InGaAs detectors appears to be in the MHz range,
due to afterpulsing. Ribordy et al. [35] were able to trigger their Fujitsu APDs at 5 MHz
using a passively quenched circuit. They achieved 0.1% afterpulse probability, 104 dark
26
count probability, and 7% QE at a temperature near 173K with 2.6-ns-long gates. Their
experiments involved the detection of sub-nanosecond laser pulses and the detectors were
biased with short-duration gates. Bourennane et al. [36] obtained a 2x10-4 dark count
probability per 5 ns gate (40,000 c/s) with PerkinElmer (EG&G) devices biased with -4V
above breakdown and cooled to -60'C using LN with electrical heating. They reported a
peak QE of 18% at 1.55 pm measured with attenuated short-duration laser pulses. More
recently, Rarity et al. [37] obtained a QE of 10.5% at 220K with 50 ns gates at 1 kHz
with 3V excess voltage using EG&G APDs while Stucki et al. [39] obtained a QE of
10% and 2.8x10-5 dark count probability per 2.4 ns gate (11,667 c/s) with Epitaxx APDs
cooled with LN to -60*C.
3.5. Geiger-Mode InGaAs APDs for Entangled-Photon Detection
We decided to built a compact, all-solid state single-photon counter near 1.55 gm using
passively-quenched, gated, and entirely TE-cooled InGaAs APDs. Our ultimate goal was
to detect the output of the frequency-nondegenerate parametric downconverter described
in Section 3.7. The overall design had to be a compromise between decent QE, low dark
count probability, and sufficiently fast PRF, when operated at temperatures that can be
achieved and long-term stabilized by Peltier elements. We also desired an unobtrusive
package that can be used in bench-top optical experiments. We should point out that we
did not attempt to fully characterize the InGaAs APDs as such experiments have been
done in the past. Our aim was to construct a photon counter that fit the specific needs of
our quantum communication project.
We purchased several APDs in order to evaluate their suitability for photoncounting operation near 1.55 tm. Out of a total of 5 detectors, 2 were from PerkinElmer
Optoelectronics Canada (C30644E-DTC) and 3 from JDS Uniphase's Epitaxx division
(EPM239BA). One of the PerkinElmer detectors was pronounced dead upon arrival and
the other 4 were tested to assess their suitability as photon counters. The detectors from
the Epitaxx division of JDS Uniphase have 40-gm-diameter active area and were
packaged with 9/128 pm hermetically sealed SMF 28 single mode fiber pigtails. These
devices were designed to operate as optical receivers for wide-range Optical Time
Domain Reflectometry (OTDR), have bandwidth > 1.5 GHz, high responsivity at 1550
27
nm (0.85 A/W at unity gain), and low linear-mode dark current (<0.25 nA) with 0.6 pF
capacitance. They have breakdown voltages on the order of 50V and gains of up to 50
(M = 50) when operated at -2V below the breakdown voltage. These detectors were first
connectorized with standard FC/PC connectors by Flextronics Photonics and then
thoroughly evaluated in the linear regime before being tested in photon-counting mode.
The PerkinElmer devices have a 50-+m-diameter active area, were hermetically sealed
but not fiber coupled.
We first tested our photon-counting circuit on free samples of InGaAs APDs
generously offered by PerkinElmer Optoelectronics (C30662CER). These devices have
200 gm-diameter active area, were supplied to us on a 2x2x4 mm ceramic substrate, and
were mounted on 16-pin TO-type headers.
Room-temperature operation at 2V above
breakdown with a DC voltage source showed total dark count rates on the order of 1
MHz.
The PerkinElmer C30644E-DTC APD (serial# 0015) was then tested in the
laboratory. When cooled to -25"C and continuously biased with 2V above breakdown we
achieved a factor of two total dark count rate reduction. The dark count reduction for
AT-50'C was not as large as expected, which attested to the overwhelming existence of
afterpulses for this device. Additional tests were then performed on the JDS Uniphase
detectors, as they appeared to be superior to the PerkinElmer devices. We also preferred
the flexibility afforded by the fiber-coupled detectors, which allowed us to use precision
fiberoptic attenuators for quantum efficiency measurements and also made it easy to
introduce the fiberoptic delay needed for the time-entangled measurements.
The
following experimental setup description and results refer exclusively to the JDS
Uniphase devices.
3.5.1. Thermoelectric Cooling
The currently available InGaAs devices are notoriously noisy when operated above
breakdown voltage at room temperature.
To reduce the dark count probability the
detectors must be cooled. Although several research groups have had success cooling
APDs with LN, we focused on Peltier all-solid-state cooling for a simpler and more
manageable bench top setup that is more suitable for potential real-world use. The
disadvantage of Peltier-cooling is that it is difficult to achieve and maintain temperatures
28
below approximately -70*C. We were however encouraged by previous research, which
appeared to indicate that the most desirable regime of operation could be near -60'C,
within the reach of TE cooling.
We built small rectangular aluminum box (cold box) to house our fiber-coupled
InGaAs APD.
The cold box had removable sidewalls and a slide-on cover for easy
access to the device area for replacement, inspection, and troubleshooting. The 14-cmlong, 15-cm-high, and 12.5-cm-wide cold box could be purged with a slow flow of
nitrogen gas to keep the inside at a positive pressure with respect to the outside. In this
way humidity could be removed from the enclosure to prevent dew-point condensation.
The TE cooler, detector, and pre-amplifier circuit board were all housed inside this box.
The fiber-pigtailed detectors were mounted in a small copper block, which sat on the top
(cold side) of a Melcor 4-stage, moisture-protected, TE cooler (4CP055065-127-71-3117-L-EC). The bottom (hot side) of the TE cooler was in contact with a trapezoidal brass
heat sink. The TE cooler was capable of a maximum temperature differential of 107'C
with 3.A maximum current at a 14.6V voltage drop. Figures 3.1 and 3.2 show pictures
of the APD cold box with the cover off and on, respectively.
Figure 3.1. Custom cold box for InGaAs APD with the top cover and side walls
removed. The fiber-coupled detector is mounted in a small copper block that is
cooled with a multistage TE cooler (arrow).
29
Figure 3.2. Detector cold box with the cover on. Bias "T" (top arrow),
output amplifier (bottom arrow).
Thermal grease was applied at the interface between the copper block and the cold plate
while indium foil was used between the brass heat sink and the bottom of the cold box for
better thermal contact. Two precision thermistors (Omega Engineering 44033), with a
resistance of 2.252 k.2 at 25*C were used to monitor the temperatures of the copper
block-APD fixture and the heat sink. We used an Alpha-Omega Instruments Series 800
TE cooler controller to adjust the temperature of the detector and hold it constant with
±0.1"C resolution on the 1 MQ sensor range. We placed the entire cold box on top of
four Marlow Industries TE coolers (DT12-8-01LS) (with super-flat faces and moisturesealed) that were wired in series. They were rated at 7.4A maximum current and 14.7V
maximum voltage. If required, these coolers could actively heat sink the cold box. The
bottom plane of these coolers was mounted on a slightly larger aluminum block serving
as a secondary heat sink. Water could be run through this secondary heat sink to provide
additional heat dissipation flexibility for the setup.
30
3.5.2. Linear-Mode Operation
The APDs were first operated in linear regime to check their reliability as linear-mode
detectors and verify the performance values provided by the manufacturer.
We also
wanted to investigate the effects of low temperatures on the detector performance. The
manufacturer listed -40*C as the lowest allowed temperature for device storage and
operation. We were concerned that cooling the APDs to -60'C might cause the devices
to either stop working or exhibit significant deviations from reported performance values
due perhaps to thermal shifting of the fiber pigtail relative to the detector active area,
fiber brittleness, or moisture.
One FOM for overall device performance is the
responsivity (R) in units of Amperes of current generated per Watt of incident photons.
The circuit shown in Figure 3.3 was built to test the APDs in linear mode.
GND
DC V
R2
100K
e
GN
Vdc
GND
R1
1K
C
APD
A
390
-20V
V
pF -
Bypass
C2
Vop
-
GND
Figure 3.3. Linear-mode APD bias circuit. A: anode (positive port),
C: cathode (negative port).
31
Referring to the circuit diagram, the APD was reverse-biased with voltages (V0 p) just
below breakdown by applying a negative voltage directly on the detector's anode. We
injected -1
gW of cw light at 1.55 tm from an Alcatel (A1905LMI) fiber-coupled
distributed-feedback (DFB) laser into the fiber-pigtailed APD. The anode voltage was
increased in magnitude from 20 to 40V while the DC voltage response (Vdc) was
measured with a high-impedance oscilloscope (LeCroy 9304A). The measurements were
done at 25'C and -55'C. Plots of the DC response versus reverse-applied voltage are
shown in Figure 3.4, a), and b).
a)
Linear-mode response at T=25C with P=1 uW @ 1.55um
250
A
-. -
200
E
-.-.-.-
42150
0
-
-
---
CM
0
-
-
-A
*100 1-
501F
A
A
24
26
28
30
32
34
36
Net APD bias voltage (V)
32
38
40
42
44
b)
Linear-mode response at T=-55C with P=1 uW @ 1.55um
350
300.
-250
E
Cn
a00
0
0 150
100
-
--
-
-
++++7
- - - - -.
-. 1 .....
-. ... -.
50 - .......
- -
.
i
25
i
30
35
40
Net APD bias voltage (V)
Figure 3.4. Linear-mode performance of InGaAs APD at, a) 25'C and b) -55 0C.
Approximate locations of M = 1 are indicated by the arrows.
The responsivity (photocurrent I = V/R) computed from this data near unity gain (M = 1)
was 0.78 A/W at -55 0C and 0.75 A/W at 25 0C.
The measurement indicates us that
cooling to -55'C did not degrade but rather slightly improved the performance of the
APD as quantified by its responsivity to a fixed flux of light.
3.5.3. Photon-Counting Operation
The APD was mounted on a two-layer printed circuit board (PCB). The pre-amplifier
electronics diagram for passively quenched Geiger-mode operation is shown in Figure
3.5.
33
V Vbias
GND
Vgate
Bias "T"
Li
10kHz
DG535
C1
DC V
|
TP1
5 0 Ohm
~I
R2
50
on
C
nGaAs
To
+
Counter
20 dB Board
CLC100
A
R1
50
SMA
~GND
Figure 3.5. Geiger-mode APD pre-amplifier bias circuit. A: Anode (+), C: Cathode (-).
The board was populated on one side with microwave capacitors and lowfootprint resistors and had ground planes sandwiching 50 Q microstrip transmission
lines for the gate input and wide-bandwidth (WB) APD output signal.
All circuit
components were located in near proximity of the APD to minimize ripples in the
output signal resulting from high-speed operation of the device. An SMA output for the
APD signal and a test point (TP1) were available on the detector pre-amplifier board.
We used the test point to monitor the gate and cathode voltage using a high-impedance
(1M ) oscilloscope, while the WB output measured the photon arrival time. Referring
to the circuit diagram of Figure 3.5, a positive DC bias
(Vbias)
was applied to the diode's
cathode (C) or negative port. This DC bias varied from device to device but was
typically 0.2 to 1.OV lower in magnitude than the breakdown voltage. For Geiger-mode
operation, the cathode voltage was gated to a positive voltage
34
(Vgate)
large enough to
result in the desired voltage drop AV or overbias across the device. In photon-counting
operation, the APD was typically gated on with +2 to +4V pulses with rise and fall
times of -4 ns that were generated by a Stanford Research Systems DG535 Digital
Delay/Pulse Generator.
The pulses had typical durations of 20 ns at selectable
frequencies between 1 kHz and 1 MHz, and the gate was applied through an ORTEL
bias "T" circuit to the APD cathode. The voltage pulse created by the avalanche signal
was coupled across a 50 Q resistor into a 50 Q SMA coaxial cable, then to an off-board
RF amplifier and the counter board. To minimize the amount of heat dissipated on the
pre-amplifier board, an amplifier (Comlinear CL100) with 20 dB voltage gain was
mounted externally to amplify the pulses. The resulting avalanche WB pulses had rise
times of less than 2 ns and varying widths depending on when the photon arrived (early
or late within the gate). Figure 3.6 shows a typical trace of the amplified WB output as
monitored on an oscilloscope with a 50 Q input impedance.
Figure 3.6. Trace of several InGaAs Geiger-mode events as viewed on an oscilloscope
in persistence mode with light incident onto device. 10 ns/div horizontal, 500 mV/div
vertical. The approximate trigger level for counting is indicated by the arrow.
35
3.6. Results and Data Analysis
The behavior common to all tested JDS Uniphase devices is summarized in Figure 3.7
a), b), and c).
a)
45
46
47
48
49
5
50
51
52
53
54
-50
-40
-30
-20
-10
Temperature (C)
0
10
20
30
b)
0.8I.
a
0
-
--
-
-
0.6
I-
a
0.4
0
-70
-
- --
-
-60
-50
-40
-30
-20
-10
Temperature (C)
36
0
10
20
30
c)
100
90 -
-
80
c$
70---
8
60-
40 .3..7.
I-20
0
-
Gate Repetition Frequency (kHz)
Figure 3.7. Typical behavior of Geiger-mode and gated JDS Uniphase EPM239BA
APDs. a) breakdown voltage vs. temperature and linear data fit (solid line);
b) normalized dark count rate vs. temperature and exponential fit (solid line);
c) dark count probability per 20 ns gate vs. PRF at -60*C.
The data in Figure 3.7 confirms several known facts about semiconductor device and
Geiger-mode APD physics - dark counts increase exponentially with increasing device
temperatures while the breakdown voltage increases linearly with temperature (at a rate
of ~1V/*C).
The normalized dark count rate is nearly constant over a wide gate
repetition frequency range and shoots up when the contribution due to afterpulses
begins to dominate, typically above 200 kHz at -60'C for the devices we tested.
Quantum efficiency measurements were performed using a calibrated cw laser
diode (Alcatel A1905 LMIl) at 1.55 pm. The light was first sent through a polarizationindependent fiber isolator (PIFI) and then attenuated to ~0.13 photons per 20 ns (~0.85
pW) with daisy-chained variable fiberoptic attenuators and calibrated Ix2 wavelengthflattened fiberoptic tap couplers with 95-5% and 99-1% splitting ratios. An internally
triggered DG535 pulse generator gated the detector on. We monitored the diode laser
37
output power with a precision HP Lightwave multimeter (HP 8153A with 81532A
head) capable of measuring well into the pW regime with -100 dBm (0.1 pW) accuracy.
The APD output traces were recorded with a LabView-controlled Gage Scope data
acquisition card (and cross-measured with an SR620 counter) and post-processed in
Matlab 6.1. The time stamp for each event, defined by its rising edge crossing a pre-set
threshold (Fig. 3.6), was recorded in a data file and an event histogram with 2-ns bin
resolution was generated for each measurement cycle. At a fixed temperature we made
time-stamp measurements with no input light to record the dark levels and with the light
on in order to obtain the time-of-arrival histograms and compute the QE. Figures 3.8
and 3.9 show gated-count histograms for dark and light measurements, respectively, for
our best performing device at a temperature of -50'C. The gate pulses were 4V-high
(-3.7V overbias), 20-ns-long, and were applied to the APD at a 10 kHz PRF.
Gated-count Histogram for JDSU0110TI357 - Dark
.............
9
-
...
-....
.
8
......................
-.
..-.
.-
........... ........... - ......
...........
7
......................
..........
6
0
...........
-.
.......
...
..........
.............
.... .....
E
..............
...........
- .......
-. ...
..
3
.............
2
...............
1
..........
..
...........
.........
................
..........
..........
n
95
100
105
110
115
Bin Number (2 ns per bin)
120
125
130
Figure 3.8. Dark-count histogram using a 20 ns gate. The total number
of gated counts is 40.
38
For the data in Figure 3.8 the dark count probability per gate is 0.113%.
When
normalized, taking into account the overall measurement interval, the gate width and
duty cycle, the dark count rate is approximately 55,000 c/s.
Gated-count Histogram for JDSU01 1OT1 357 - Light
140
------------------------------
120
------------------
-----------------
100
C
C
E
------------------ ----------
80
---------------
60
-----------------
-I----
------------------ ----------
40
20
0t
100
105
115
110
Bin Number (2 ns per bin)
120
Figure 3.9. Histogram of detected counts produced with a light flux of 0.13 photons per
20-ns gate. The sum over all bins is 1219 counts, 3% of which
occurred in the first 2 ns bin.
Since the detector is passively quenched at most one count can be detected per gate.
Therefore, care must be taken when computing the quantum efficiency. With an input
light flux of 0.13 photons/gate the multiphoton (error) probability is, assuming a Poisson
process, less than 2%. No corrections to the count data are thus needed and the QE can
be determined directly from the following relation
39
QE = CountsLight -Counts Dark
(3.1)
InputLight
The consistently lower counts recorded during the first 2 ns bin can be explained by the
finite rise time of the gate pulse (-4 ns). A correction factor could be introduced to
account for this effect. This correction would however be small when compared with
other measurement uncertainties and was ignored in the final analysis of data.
We
believe that the slight (-10%) drop of the counts toward the end of the 20-ns gate in
Figure 3.9 is partly due to small overshoot and ripples in the effective cathode gate
voltage and also normal fluctuations of a Poisson process.
We varied the device
temperature, gate repetition frequency, gate width and height, and DC bias to obtain a
desirable set of operating parameters. A good combination of parameters consisted of a
temperature of -50'C with -3.7V overbias, a gate repetition frequency of 10 kHz and a
20-ns-long gate. This set of parameters has yielded a QE of approximately 20% with a
corresponding normalized dark count rate of -55 kHz (0.11% per gate). A QE of -12%
and a dark count probability per gate of -0.05% was also obtained with a lower overbias
of -2.5V. In Figure 3.10 we summarize the data collected with one of our devices.
40
(104
8 (a)
*
0.15
(b)
*
0.1
4
*
*
*
*
....
. . .. ..
*.
*.........
...........
*
*
.. . ...
0.05
..
0
0
2
3
4
4
3
Overbias (V)
12
Overbias (V)
20
.... .. -..
- - --
-.
.... .
600
(c)
500
,15
z
400
300
10
A
AA
200
5
1.5
2
2.5
3
Overbias (V)
100
3.5
1.5
2
2.5
3
Overbias (V)
3.5
Figure 3.10. Geiger-mode device performance at -50'C: (a) dark counts, (b) dark-count
probability per 20 ns gate, (c) QE, and (d) signal-to-noise ratio (SNR).
We note that while the QE increases at higher bias voltages, so does the dark count rate.
As a figure of merit we computed the signal-to-noise ratio (SNR), defined as the ratio of
the effective QE (%) to the dark count probability per 20 ns gate (%). We point out that
the SNR degrades monotonically with overbias.
We have demonstrated excellent performance using a compact all-solid-state
single-photon-counting detector near 1.55 gm. Commercial InGaAs APDs were TEcooled, gated-on, and passively quenched to operate in Geiger mode.
The operating
conditions could be easily varied for optimal detection under different experimental
conditions. If dark counts are a concern the temperature can be lowered to exponentially
reduce this contribution. If high quantum efficiency is needed, larger overbiases may be
41
required. Quantum efficiency or SNR constraints can be accommodated by controlling
the operating temperature, bias voltage, gate width, and duty cycle. This setup can also
be adapted to work with pulsed-laser experiments.
In the next section we utilize an
InGaAs single-photon counter for entanglement measurements.
42
3.7. Detection of Entangled Light
As an important application of the InGaAs single-photon counter, we have incorporated it
in a time-entanglement experiment to demonstrate excellent time coincidence between
nondegenerate photon pairs from a PPLN parametric downconverter.
The three-wave mixing process of spontaneous parametric downconversion
(SPDC) involves the transfer of power from a pump field to newly generated signal and
idler fields. The coupled wave equations governing parametric downconversion are very
similar to those describing SFG, Eq. (2.1). The pump (we), signal (ows) and idler (WIi)
frequencies are constrained by energy conservation to obey wp = 0o_ + W1i where we
assume, by convention, w%> ". Efficient SPDC occurs if the phase matching condition,
dictated by momentum conservation, is satisfied inside the nonlinear crystal. One can
show that for every single pump photon annihilated in the process a signal photon and an
idler photon that share non-classical correlations in time and energy are simultaneously
created [40]. Pairs of entangled photons generated via SPDC have direct application in
the fields of quantum cryptography and quantum communication.
3.7.1. Experimental Setup for Entanglement Generation
We describe herein a frequency-nondegenerate parametric downconversion experiment
that produced photon twins at 808 nm and at 1.56 pm. We used one of the custom
InGaAs single-photon counters and a PerkinElmer Si SPCM to characterize the output of
this entanglement source. The schematic of the experimental setup is shown in Figure
3.11.
43
20ns
_ -1
1600 nm idler
fiber&delay line
to InGaAs APD
DG535
Delay/Pulse
Generator
OUT
TRIG.
800 nm signal
fiber to Si counter
HWP
HWP
PPLN in oven
Verdi 8 pump
laser - 532 nm
PC-based
counting
boards
Figure 3.11. Schematic of single-pass frequency-nondegenerate downconversion
experiment using bulk PPLN. HWP: half-wave plate. The Si APD triggers the pulse
generator, which in turn gates the InGaAs APD on.
We used a 0.5x12x20 mm periodically poled LiNbO 3 (PPLN) crystal with a grating
period of 21.6 ptm for third-order quasi-phase-matching that was AR-coated at all three
44
wavelengths of 0.53 gm, 0.8 gm, and 1.6 pm. The bulk PPLN was pumped at 532 nm
with a cw Coherent Verdi 8 laser. The crystal was temperature stabilized inside a Super
Optronics, Inc. oven and mounted on an x-y-z micrometer stage. We employed type-I
QPM to generate two collinearly propagating and co-polarized signal and idler beams in
a single-pass configuration.
When operated at a temperature of -142.4*C the PPLN
generates frequency-nondegenerate outputs at 1.559 gm (idler) and 808 nm (signal), and
temperature tuning over a 50'C range was obtained. This pair of wavelengths is of
interest because the idler lies in the middle of the low-loss fiber transmission window and
the signal is near the detection efficiency peak of the Si SPCM. The output beams were
separated using a prism. The signal was coupled into a single-mode fiber and detected
using a commercial SPCM (PerkinElmer SPCM-AQR-14). This module has a quantum
efficiency of -55% at 808 nm and could be operated continuously in Geiger mode. In
response to generated photoelectrons the Si APD produced 30-ns-long, 3V-high pulses
with rise times on the order of 5 ns. A sample output from the Si photon-counter
recorded with a digital oscilloscope (Gage Scope) is shown in Figure 3.12. The threshold
voltage for registering a count is indicated by the arrow.
Counter
Threshold
Figure 3.12. Sample 20-ms-long trace from Si SPCM as recorded with Gage Scope.
Individual pulses are TTL-level and 25 ns wide. The y-axis scale is 1V/div. The time
stamps for the leading pulse edges were recorded for processing of coincidences.
45
The idler photons were delayed with a fiberoptic patch cord and were coupled into the
fiber-pigtailed photon-counting InGaAs APD, which was gated-on electronically by the
conjugate signal photon via the Si SPCM. The output from the Si APD triggered the
DG535 delay/pulse generator, which sent a gate pulse to the InGaAs detector to turn it on
and prepare it for the expected arrival a photon. This gate pulse could be timed and
delayed with sub-nanosecond precision. The InGaAs APD was in ON mode only for a
20-ns-wide window around the expected time of arrival of the twin idler photon. The
PRF of the gate pulse was limited in hardware (by our choice) to 10 kHz and a fiberoptic
delay line was introduced to account for the finite turn-on times of bias electronics and
other components. The output from the InGaAs detector and that from the Si SPCM
were fed into software-controlled Gage Scope digitizing data acquisition PC boards.
Data analysis was performed using LabView 5.1 and Matlab 6.1. The Gage Scope card
was configured for a sampling rate of 500 MHz sampling rate (max. rate), fast enough to
capture all triggered events and allowing data acquisition periods of 4 ms, limited by the
on-board memory size of 2 MB. Typically 10 subsequent traces, 4-ms-long each were
recorded for a total measurement duration of 4 sec. These traces were later processed for
timing and coincidence calculations.
3.7.2. Entanglement Data
Figure 3.13 shows a histogram of idler photon detection probability, conditional on the
detection of a signal photon.
46
0.02
0.018
- . .. . . .. . .
. ... -..
. -..
-.. .. . . .. . .
.. ..-..
...
0.016
0.014
-
. .. . . .
. . -..
..
0.012
0.01
PO
0
0.008
. . ...- . . . - -
0.006
-
0.004
-
-
0.002
0
90
91
92
93
95
94
96
97
98
99
100
Time bin (2 ns/bin)
Figure 3.13. Histogram of conditional detection probability of an idler photon versus
measurement time bin (2ns/bin).
With this setup we have measured a 3% conditional probability within a 4 ns counting
interval with insignificant dark count probability using -2 mW of pump power at 532
nm. The measured conditional detection probability is limited by the detector quantum
efficiency, propagation loss, and fiber coupling efficiency of the idler mode that was
matched to the signal mode. In additional measurements, we measured an inferred pair
generation rate of 1.4x107 pairs/s per mW of pump power tunable over a signal
bandwidth of -150 GHz [26]. This data suggests that the PPLN SPDC can serve as a
high-flux entanglement source for a number of applications including the MIT/NU
quantum communication protocol.
47
CHAPTER 4.
FREQUENCY UPCONVERSION IN PERIODICALLY POLED
LITHIUM NIOBATE
4.1. Introduction
An alternative to direct detection with gated, Geiger-mode InGaAs APDs is frequency
upconversion followed by single-photon detection with Si APDs.
This scheme is
attractive because of potentially higher overall quantum efficiency and much lower dark
counts when compared to InGaAs detection. Frequency upconversion would allow for
continuous counting of single photons near 1.55 gm using commercial PerkinElmer
SPCMs and also for loading of remote quantum atomic memories. We describe in this
chapter the results of a single-pass sum frequency generation (SFG) experiment using
PPLN, contrast the data with expected theoretical numbers, and discuss our plans for
future single-pass and cavity-enhanced frequency upconversion experiments in both
classical and quantum regimes.
4.2. PPLN Design and Fabrication
We have designed and fabricated a 6-mm-long, 0.5-mm-thick PPLN crystal for type-I,
first order, quasi-phase-matched SFG at -640 nm with 1.064 gm and -1.6 9m inputs. As
discussed in Chapter 2, QPM in PPLN is the best choice for efficient nonlinear frequency
generation. Here, we note that by employing type-I noncritical phase matching in PPLN
we engineer access to one of the highest nonlinear coefficients of all available inorganic
media, the d33 in lithium niobate. A theoretical plot of the required grating period versus
temperature for optimal phase matching at these three interacting wavelengths is shown
in Figure 4.1.
The curves were computed from the temperature-dependent Sellmeier
equations as reported by Edwards and Lawrence [23] and Jundt [24], and include the
thermal expansion of congruently grown LiNbO 3 at elevated temperatures.
The third
curve is an average of the two reported values. As shown in Figure 4.1, phase matching
can be achieved over a wide temperature range.
48
12
-
Edwards and Lawrence [1984]
Jundt [1997]
Average
11.9
0
11.81
0
I..
11.7
..
. S.. . . . .,
....-.
Cu
I..
0
11.6
11.51
,.
-..-.-
-
11.4
60
80
100
-
120
140
160
180
Temperature (C)
-
200
220
-
-4
240
260
Figure 4.1. Optimum PPLN grating period for SFG versus temperature.
In order to avoid photorefractive damage due to high pump powers of up to 0.5 W at
1.064 pm the PPLN was designed to operate near 200'C where the temperature of the
PPLN can be controlled reliably using commercial heaters with an accuracy of ±0.1 C.
Using the data reported by Edwards and Lawrence [23], we selected an 11.6 pm grating
period and an operating temperature of 191.6'C for the design. The photolithographic
grating mask was designed using an AutoCad routine and was manufactured to our
specifications by DuPont Photomasks, Inc.
The LiNbO 3 bulk sample was cut out of a 3-inch-diameter optical grade z-cut
wafer made by Crystal Technology Inc., and the PPLN was fabricated using a procedure
developed by Mason [26].
The +z face was photo-lithographically patterned with
periodic linear arrays of thin nickel chrome (NiCr) line electrodes. Contact pads were
also patterned on the +z face around the electrodes for electrical contact purposes. The
49
NiCr lines were 1.8 ptm wide corresponding to a 15.5% nominal duty cycle.
The
designed duty cycle is less than the optimal 50% duty cycle due to expected domain
spreading beyond the physical width of the metal electrodes during electric-field poling.
The sample thickness was measured at all four corners and the average thickness value
was used to determine the desired poling voltage. The sample was mounted in a custom
fixture, surrounded on both faces by lithium chloride (LiCl) electrolyte solution. The -z
face was fully surrounded by LiCl while on the +z face the LiCl was in contact with the
photoresist-fused silica insulator and with the metal contacts via the contact pads. The
effective electrode area was 0.669 cm 2. A voltage was applied to the sample using a
LabView-controlled Trek 20/20A high-voltage amplifier. Periodic poling was achieved
in this LiNbO3 sample (device #M8D3-2 on mask QPM8) by applying a field of 20.2
kV/mm across the electrode-patterned crystal for several ms at room temperature. The
sample was pre-poled with a field of 18 kV/mm, the nucleation spike was 19.10 kV/mm,
and the post poling voltage was set at 17 kV/mm. The corresponding voltage, current,
and charge-transfer traces were recorded in LabView and are shown in Figure 4.2.
Va (kV)
I (mA)
Vc (kV)
Q (C)
Time(s)
Figure 4.2. Electric-field poling trace for the PPLN. First from the top: monitored
voltage output from the amplifier Va (kV), Second: current trace I (mA),
Third: effective voltage applied across the crystal Vc (kV),
Fourth: charge-transfer curve Q (C).
50
After poling, the metal electrodes and insulator were polished away from the top surface
of the sample. The device was then etched in hydrofluoric acid (HF) to reveal the
domain structure, cut to the proper dimensions, and the faces were polished flat but left
uncoated. Figure 4.3 shows a picture of the poled LiNbO3 sample at the end of all
processing steps.
The 24 identical, 0.5-mm-wide channels (light shade), are clearly
visible. We left a 1-mm-wide unpoled bulk LiNbO3 region on each side of the poled area
for calibration purpose.
Figure 4.3. Picture of PPLN crystal used for frequency upconversion. The horizontal (x)
dimension of the sample is 12 mm while the vertical (y) dimension is 6 mm.
The device is 0.5 mm thick.
Figure 4.4 shows the top view (+z) of a portion of a single channel taken with a
microscope, showing clearly about 19 periodically inverted domains. Note the slightly
rounded edges of the unpoled regions. Good device uniformity was observed across the
device when seen from the front side, without significant domain merging.
51
Gap
Light Propagation
Channels
Figure 4.4. Photograph of a single PPLN channel (top view +z). The channels are 500
gm-wide and are separated by a 50 gm gap. The direction of light propagation is along
the channel, as indicated by the large arrow.
Figure 4.5 shows a portion of the device's back side (-z). The inverted domains are now
represented by the light-colored regions. Although poling pattern is not as uniform on
the back side as it is on the front side, it shows that poling has reached the bottom of the
sample. Some domain merging is clearly visible.
52
Figure 4.5. Picture of the bottom face of the PPLN crystal (-z). Note the less uniform
overall domain pattern compared to the +z face, Fig. 4.4.
Although the crystal was designed with electrode widths such as to give an effective 5050 duty cycle following electric-field poling, the final duty cycle was found to be
different due to domain spreading beyond anticipated values. The effective domain duty
cycle, defined here as the width of the unpoled region divided by the grating period, was
measured with a calibrated microscope ruler by sampling several locations along the
channels. An average of these measurements resulted in a duty cycle of -0.69.
This
deviation from the optimal value of 0.5 is potentially responsible for an overall reduction
in the conversion efficiency. The analysis of the sum-frequency generation data collected
with this device is presented in Section 4.4. We should point out that the 11.6-gm-long
period, while not too short, was difficult to fabricate (low yield) because there was no
prior poling data available for devices with this period.
4.3. Experimental Apparatus
Figure 4.6 shows the schematic of the upconversion experimental setup and Figure 4.7
shows a picture of the main system components on the optical table.
53
1600 nm
tunable
laser
Astigmatic
Compensator
50 cm
f=38.1 mm E-
Chopper ( ]
Beam Block
mn
1064
FEG&G
Lock-In
Faraday
Rotator ]HWP
Detector
Amplifier
L
YAG lsr
f WP for 1600 nm
f=150 mm
I -]
Iris
f=75 mm
1600 nm AR
1064 nmAR
HWP
for 1064 nm
]
hroic
Mi rror
PPLN
Inside
Oven
f=47 mm
uncoated
HR Vis
Figure 4.6. Schematic of the frequency upconversion experiment. HWP: half-wave
plate, AR: anti-reflection coated, PBS: polarizing beam splitter, HR Vis: high-reflector
for the visible.
54
Figure 4.7. Picture of the central part of the frequency upconversion experiment. The
PPLN, inside the crystal oven (white rectangle), was mounted on an x-y-z-tilt-rotation
micrometer stage for alignment.
A 0.5 W cw Nd:YAG laser (Lightwave Electronics Series 122) operating at 1064.2 nm
was sent through a Faraday isolator to prevent back-reflections and a half-wave plate
(HWP) and polarizing beam splitter (PBS) that functioned as a variable attenuator. The
polarization of the pump beam was rotated by the second HWP to be horizontal relative
to the plane of the optical table. The beam was mode-matched into the PPLN crystal
with a 150 mm lens that was anti-reflection (AR) coated at 1064 nm.
A New Focus External-Cavity Tunable Diode Laser provided up to 3.8 mW of
light at 1.6 gm for upconversion.
This probe (idler) beam was compensated for
astigmatism by a tilted curved-mirror with a radius of curvature R = 2.5 cm at a 10.750
angle of incidence and collimated before being sent to the crystal.
Polarization
adjustment for the 1.6 pm light was achieved with a HWP and the beam was mode55
matched into the PPLN with an f = 75 mm AR-coated lens. After propagating through
the respective HWPs and optics, both lasers ended up being horizontal or TM-polarized
at the PPLN crystal. Horizontal polarization refers to polarization parallel to the surface
of the optical bench while vertical polarization refers to polarization that is normal to the
surface of the bench. The crystal's z-axis was oriented horizontally or parallel to the
table and all input and output beams were horizontally polarized, as required for type-I
phase matching.
ABCD-matrix formalism [41] was used to set up the proper beam radii of
curvature (R) and waists (w,) for the two laser beams inside the crystal, aided by actual
beam-parameter measurements (Photon Inc. Beam Scanner). We measured an average
wO (average of the tangential and sagittal waists of 19.2 pm and 25.7 pm respectively) for
the 1.06 pm pump beam of 22.45 pm. The waist of the 1.6 pm probe laser was 30.42 pm
(average of slightly elliptic radii of 28.56 gm and 32.18 gm).
These values were
measured with the beam scanner, which was also used to overlap the two beams in air.
The extraordinary refractive indices of congruent LiNbO 3 at the wavelengths of interest
to this thesis are tabulated below using the Sellmeier equation reported by Jundt [24].
X0 (.m)
ne
0.532 (SHG)
2.248
0.640 (SFG)
2.212
1.064 (Pump)
2.165
1.609 (Probe)
2.145
Table 4.1. Extraordinary refractive indices of LiNbO 3 at selected wavelengths
and T-200'C.
The corresponding confocal parameters for the pump and probe are given by
56
b = 2nnw2/A, where X, is the vacuum wavelength, n is the refractive index of PPLN at
Xo, and w, is the radius of the beam waist.
The pump and probe confocal beam
parameters inside the PPLN were 6.4 mm and 7.8 mm, respectively.
The two incident beams were combined at a 5-mm-thick dichroic mirror with -94%
transmission at 1064 nm while reflecting nearly all the 1600 nm light. The beams were
carefully aligned on top of each other with several irises and also with the help of a 632.8
nm HeNe laser not shown in the schematic of Figure 4.6 but visible in the upper left
corner of the photograph in Figure 4.7. Mode-matching b-parameter computations for
the pump and idler lasers were confirmed with beam-scanner measurements of the beam
radii and ellipticity at several points along the propagation path, with excellent fit to
theoretical Gaussian-propagation curves.
The pump and probe powers were monitored throughout the duration of each datacollection experiment with a Coherent FieldMaster GS power meter at 1064 nm and with
a Newport 835 Optical Power Meter at 1600 nm. Power levels were found to be stable to
within ±1.5% and ±1% for the YAG and 1600 laser, respectively.
Upon exiting the
PPLN crystal that was housed in a Super Optronics oven, the three diverging beams were
first collimated with an f = 47 mm uncoated lens and spatially dispersed with a 1-cm-long
Brewster-angled fused-silica prism. A flat mirror with R > 99% at 640 nm directed the
upconverted light through an iris to spatially filter the other wavelengths and then onto an
EG&G (HUV-1100BQ) Si detector with a 107 k. feedback resistor. The detector (with
the glass window removed) had a 5.1 mm2 active area and 0.45 A/W responsivity near
640 nm. The 1600 nm light was chopped at -460 Hz with an EG&G Model 196 Light
Chopper and lock-in detection was employed using an SRS 650 high-pass/low-pass filter
and an SRS 830 Lock-In Amplifier. The lock-in was calibrated using an attenuated
HeNe laser and also with a Coherent visible detector, and the lock-in (mV) to power
(nW) conversion factor was approximately 47 nW/mV.
Losses associated with the
propagation of the beams through the optics were due primarily to normal-incidence
Fresnel reflections at the front and back surfaces of the uncoated PPLN crystal (-16% per
surface) and at the surfaces of the uncoated f = 47 mm lens (-4% per surface). These
losses need to be taken into consideration when estimating the effective conversion
efficiency in our experiment.
57
4.4. Results and Analysis
We first tested all the channels accessible on our PPLN crystal to find the location of the
best and second best gratings. Although we found that all the 24 channels worked well,
some variation of up to 50% in output power was measured. Most measurements were
performed on the second best channel in order to reserve the best one in case unexpected
photorefractive damage occurred, especially when the crystal was operated at lower
temperatures. Using lock-in detection we measured the dependence of the upconverted
signal with pump power at 191.6'C and with a 1601.88 nm probe wavelength. The YAG
power was varied by rotating the first HWP.
In Figure 4.8 we plot the measured
upconverted signal power versus pump power along with a linear data fit with R2
0.9997 - almost perfectly linear.
300
250
200
150
------ ------
------------
-----
I
-----
j-----I
1 001
501
0
50
100
150
250
200
Pump Power (mW)
300
350
400
450
Figure 4.8. Upconverted signal vs. pump power (+) and linear fit (solid line).
The fit has an R of -0.9997.
58
=
This linear dependence agrees well with theory (Eq. 2.6) and confirms that there was no
pump saturation (for example due to high-power damage).
A very similar linear
dependence was found when the idler power was gradually attenuated (with calibrated
ND filters) while keeping the pump power fixed, also in agreement with theoretical
predictions. With 56 mW of pump power (all values refer to effective the power inside
the crystal) we did not observe device photodamage at temperatures as low as 140'C.
We also tested the photodamage limits of our crystal by pumping the PPLN at full power
with -335 mW while decreasing the crystal temperature in small steps from -192'C to
140*C and correspondingly changing the idler wavelength by -18.1 nm. We monitored
the upconverted power versus time and noticed that it started to exhibit instabilities at
approximately 140'C consisting of a drop in conversion efficiency followed by an almost
full recovery. This investigation gave us a quantitative feel for the upper limit in pump
power or lower limit of device temperature required for stable operation of the PPLN
upconverter without fear of laser-induced photorefractive damage to the device.
We have also measured the temperature dependence of the output signal at a fixed
pump power of 56 mW and with 2.37 mW of power at an idler wavelength of 1609 nm.
In Figure 4.9 we plot the output signal versus oven temperature. Although the higher
temperature tail of the curve might be less reliable due to temperature fluctuations of the
oven, the experimental data agrees well with theory - there is clear evidence of phase
matching as the fit function has the sinc2 shape predicted by Eq. (2.3).
59
45
35--------------------------------------- ----- -------- --------
2
~15 -----------------
5
0
195
----------------
-------
----- I--------------------------
---------------
-
-----
--------------------------------
30
---------------
-
-----------------------
---
205
200
-
-
-------
-----
I-----------.---------------
210
Temperature (C)
215
220
225
Figure 4.9. Temperature phase-matching tuning curve for 1609 nm idler wavelength (e)
and sinc2 fit (solid line). The optimum temperature is near 21 VC.
The FWHM temperature bandwidth is approximately 6.3 1C, and the optimal crystal
temperature corresponding to this wavelength was found near 21 1C. The observed AT
shift from the design specification (191.6*C for 1609 nm) is 19.4*C using the data of
Edwards and Lawrence [23].
The data from Jundt [24] agrees much better with the
experimental numbers as it predicts a phase-matching temperature of -208*C for a shift
of only 3*C, while the average value of the two data sets results in an optimum phase
matching temperature of -199 0 C. We found that for high-temperature operation the
values from Jundt better matched our experimental data. From the Sellmeier equation
[24], we computed a FWHM temperature bandwidth of 6.2'C for an ideal 6-mm-long
crystal. From the FHWM bandwidth of the data points we inferred an effective length for
nonlinear interaction of -5.8 mm suggesting that phase matching occurred over -96% of
the physical length of the crystal.
60
In Figure 4.10 we show the output signal as a function of probe laser wavelength.
The oven temperature was set at 21 PC and the wavelength ranged from 1605.75 nm to
1612 nm. Again, we see a good sinc 2 fit to the data.
40 ---------------------------------
----------
---------- I------------ ----------
-------- ------------ ----------- ---------35 ---------- ------------I---------- 1.------ ----
30
; 20
----------
-----------r ---------- T--
----------
----------------------
--------------------------------
------------------
---------- -----------
--------- -----------
----------
-----------
----------
-- -------
---------------------------
15
- ---- -- --- - ---- --- -- --- ---- --- -- ---- --- - -- ---- -- --- --- --- --11
10
----------
5 ----------
0
16(05
----------------
----------
1606
-----------------------------
---- ----------------------
- ---- -- --- - - --- --- ---
----------
------------
--------- ----------- ---------------------- --
1607
1610
1609
1608
Signal Wavelength (mn)
1611
-------
- --- --- ---
----------
1612
1613
Figure 4.10. Idler tuning bandwidth at 211'C (*) and sinc 2 fit (solid line). The optimum
wavelength is near 1.609 gm.
The FWHM wavelength bandwidth is -2.6 nm. From the Sellmeier equations we
inferred an effective phase-matching length of -5.03 mm (2.22 nm FWHM bandwidth is
predicted for a 6-mm-long PPLN crystal), which indicates that merged domains may
exist. The effective crystal length derived from the idler tuning curve is however less
reliable due to mode-jump power fluctuations of the laser. The effective length inferred
from the data in Figure 4.9 (-5.8 mm) is -3% less than the physical crystal length. The
data shown in Figures 4.9 and 4.10 were collected on the second best channel of the
PPLN and attest to the tunability of this frequency upconversion scheme.
61
In Figure 4.11 we plot the optimum idler wavelength for phase matching as a
function of crystal temperature for fixed pump and idler powers. We note that the idler
wavelength could be temperature-tuned over a 25-nm-wide bandwidth at a rate of
approximately 0.36 nm/C. The tuning rate is given by the slope of the linear function in
Figure 4.11.
210
200
190
180
- . . . . . ... . .
2W
. .. .. . . . . .. . .. . . . .
. . .
. . . . . .
. . . . . . .
170
160
150
140
130
1585
1590
1595
1600
1605
1610
Peak Wavelength (nm)
Figure 4.11. Device temperature vs. optimum idler wavelength for phase matching (+)
and linear fit (solid line). The wavelength tuning rate of the frequency upconverter is a
linear function of temperature.
4.4.1.
Single-Pass Conversion Efficiency
When pumping the best channel of the PPLN grating with all the available pump power
(332 mW at inside the crystal) we obtained an upconverted power of -15.3 [LW with 2.37
mW of idler power at a wavelength of 1601.88 nm and a temperature of 191.6'C. This
corresponded to a single-pass conversion efficiency of 0.65%. Theoretical calculations
(Eq. 2.7) with L/b = 1 and h.. = 0.776, using a 5.8-mm-long first order grating with a
62
perfect effective nonlinear coefficient of 16 pm/V, predict a maximum conversion
efficiency of 0.88% with 332 mW of pump power.
The experimental values of the
focusing parameter L/b were 0.94 for the pump and 0.77 for the idler (0.85 average, using
a physical length L = 6 mm) resulting in mode matching between the two beams that is
less than optimal.
Assuming an effective interaction length inferred from the phase
matching curve of 5.8 mm and using h,.(0,0.85)
0.7 we obtained a maximum expected
conversion efficiency of 0.79% with 332 mW of pump power. The observed conversion
efficiency is -17.7% less than expected. Assuming this is due to a smaller degbecause of
non-ideal grating duty cycle, we can estimate the actual value of the effective nonlinear
coefficient for this grating from the observed conversion efficiency. Solving Eq. 2.7 for
the effective nonlinear coefficient using a 5.8 mm effective we obtain d, = deff -14.6
pm/V. The duty cycle was measured directly using a microscope by sampling 10-20
locations on the device and measuring the ratio of the unpoled domains to the domain
period. We found significant deviations from the targeted 50-50 duty cycle across the
device.
We measured a duty cycle of approximately 0.69, which represents
approximately a 37.7% deviation from the targeted 0.5 duty cycle. From the sinusoidal
function in Eq. 2.8, using m = 1, d33 = 25.7 pm/V and, D = 0.69, we computed deff~13.5
pm/V, which is in good agreement with the inferred value of -14.5 pm/V.
4.4.2. Additional Observations
1) We have consistently observed the largest conversion efficiencies (most efficient
phase matching) near the edges of the channels. This phenomenon is not well understood
and was observed for all channels. Fringing fields and interactions for domain tips in
close proximity during poling that result in better duty cycles at the edges may be
responsible for this effect.
2) Although we designed our grating to optimize for SFG of 640 with inputs at 1064 and
1609 nm, we observed the second harmonic generation (SHG) of 532 nm. We show in
Figure 4.12 a picture of the light spots seen upon exiting the crystal and after dispersion
by the prism. The photograph was taken with a digital camera with the spots reflecting
off a piece of paper.
63
Figure 4.12. Photograph of the total output generated in the SFG experiment after prism
dispersion. From left to right: weak SHG light at 532 nm, upconverted signal near 640
nm, pump beam at 1064 nm (see text).
The Si-based sensors of the digital camera are much less sensitive at 1064 nm than at 532
or 640 nm, which explains why the pump, although strong and undepleted as measured
above, appears much dimmer than either of the visible wavelengths.
It is important to investigate the magnitude of the SHG contribution, since light at
532 nm is likely to create photorefractive damage inside the crystal. This could prove
catastrophic in a cavity-enhanced frequency upconversion experiment in which
circulating pump powers in excess of 1OW are expected and the SHG signal could be
much stronger.
Moreover, if the 532 nm light is strong enough, green-induced IR
absorption may also become important. The second harmonic power was strong enough
to be measured directly with a Coherent detector. We measured the 532 nm power
generated with -333 mW of pump power at 1064.2 nm and without any idler light going
into the crystal. The data is shown in Figure 4.13 as a function of the oven temperature.
64
190
180-
170 -
- - -
-
-.-
.160-S150..
-0 1 40 - .-. -.-.-.-.
.
.
.. .
.
.
.
.
.
.
..
.
.
.
.
.
.
. .
. .
.
.
.
.
.
.
.
-.-.-.-.-
130 -
110
150
160
170
190
180
Temperature (C)
200
210
220
Figure 4.13. Measured SHG power at 532 nm versus PPLN temperature.
We observed an oscillating behavior of SHG power with temperature, reaching a
maximum of about 184 nW at a temperature of 170'C. We note that at this temperature a
grating with a 6.55 [tm period would perfectly phase match the SHG. Variations in the
effective grating period due to non-uniform duty cycles were probably responsible for the
generation of second harmonic light, which was found to fluctuate in a random pattern
with temperature. The SHG contribution represents about 1.2% of the optimized
upconverted signal at this temperature and only accounts for a conversion efficiency from
the pump of -5.5x10- 7 (with -333 mW of pump power).
4.4.3. Analysis of Cavity-Enhanced Frequency Upconversion
In order to achieve near-100% conversion efficiency the pump needs to be resonated
inside a cavity. From Eqs. (2.9)-(2.11), allowing for complete depletion of the idler beam
65
with an undepleted pump and using a 4-cm-long first order PPLN with a conservative
value for the nonlinear coefficient of 14.5 pm/V, and h,, = 1, the required pump power for
100% single-pass conversion efficiency is approximately 13W. In a cavity configuration
that is resonant for the 1.064 pm pump, an input pump power of -400 mW requires a
cavity enhancement factor of -33, which can be easily achieved with a relatively low
finesse ring cavity.
4.5. Conclusion and Future Work
From the analysis of this chapter it is clear that longer crystals are needed for higher
conversion efficiencies.
A 5-cm-long first order PPLN crystal with a better effective
nonlinear coefficient would lower the constraints on the necessary pump power.
Upconverting 1.609 pm light to the visible using a first order grating with a nonlinear
coefficient of 16 pm/V would require a Nd:YAG pump power of only -250 mW in a
cavity-enhanced configuration with an enhancement factor of 34.
Loading of remote Rb memories requires quantum frequency upconversion of the
idler light in order to preserve the quantum state of the entangled photons. The feasibility
of the quantum frequency upconversion scheme has been shown theoretically [42] and
verified experimentally with pulsed twin beams of light using direct detection by Kumar
[43]. The calculations of Kumar [42] show a very high intensity requirement for the
pump beam, -4.2 MW/cm2 for 100% upconversion in a 10-mm-long KNbO 3 with a deff
-20.5x10-1 2 n/V. They demonstrated -80% quantum-state upconversion with pulsed
twin beams using direct-detection. Using type-II birefringently phase matched KTP they
measured nonclassical intensity correlations of -1.5dB
below the shot-noise limit
between the upconverted beam and the remaining beam.
We plan to use this sum frequency generation scheme to upconvert the idler
photons generated in the SPDC described in Section 3.7. Future experiments will require
that the upconversion takes place while conserving the quantum state so as to maintain
entanglement. The realization of a near-100% quantum-state frequency upconverter and
the generation of narrowband, high-flux source at 795 nm would make the loading of
remote quantum memory nodes more practical.
66
CHAPTER 5. CONCLUSION
5.1. Summary of Accomplishments
As part of this Master of Science thesis, we have investigated three key issues related to
an MIT/NU proposal for long-haul quantum communication. These issues included the
design of InGaAs APD-based single-photon counters at 1.55 jim, the use of these
detectors to demonstrate time entanglement from a bulk-PPLN-based frequencynondegenerate
parametric
downconverter,
and
the
investigation
of frequency
upconversion in PPLN.
In Chapter 3, we demonstrated excellent single-photon detection with QEs as high
as 20% and low dark counts using entirely TE cooled InGaAs APDs that were passively
quenched and gated to operate in Geiger mode.
In Section 3.7, we reported time
entanglement data from a frequency-nondegenerate SPDC with outputs at 808 nm and
1.56 gm. Using the InGaAs and Si single-photon counters we demonstrated that our
source is capable of temperature-tunable entangled-photon pair generation rates of up to
1.4x10 7 Hz per mW of pump power.
In Chapter 4, we reported on the design and
fabrication of a 6-mm-long bulk PPLN crystal with a grating period of 11.6 gm. Using
first order QPM we demonstrated single-pass upconversion efficiencies on the order of
0.65% using 332 mW of pump power, in good agreement with theoretical values. We
investigated the overall device performance as well as issues concerning optical damage
and its suppression. We estimated the required pump power, crystal length, and effective
nonlinear
coefficient
necessary
for improved
single-pass
and
cavity-enhanced
upconversion and discussed the future implementation of near-100% frequency
upconversion.
5.2. Concluding Remarks
The field of quantum communication is advancing at a rapid pace. New schemes for the
generation, transmission, storage, and detection of quantum information are being
proposed and developed by research groups around the world. Implementing quantumstate frequency upconversion would bring the loading of remotely located quantum
atomic memories closer to reality. The ability to generate a high-intensity narrowband
source of entangled photon pairs at telecommunication wavelengths and to efficiently
67
detect them will significantly advance the emerging field of quantum communication.
Demonstrating efficient single-photon detection in the 1.55 gm region would not only
help us in our specific experimental goals, but should also contribute to the field of
quantum optics. We believe that the progress reported in this thesis will help bring the
MIT/NU proposal for long-haul quantum communication closer to reality.
68
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