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 BIBLIOGRAPHY [1] A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 49, 91 (1982). [2] A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935). [3] J. S. Bell, Physics (N.Y.) 1, 195 (1965). [4] Z. Y. Ou and L. Mandel, "Violation of Bell's inequality and classical probability in a two-photon correlation experiment," Phys. Rev. Lett. 61, 50-53 (1988). [5] V. Giovannetti, S. Lloyd, and L. Maccone, "Positioning and clock synchronization through entanglement," Phys. Rev. A 65, 022309, (2002). [6] G. Ribordy, J. Brendel, J. D. Gautier, N. Gisin, and H. Zbinden, "Long-distance entanglement-based quantum key distribution," Phys. Rev. A 63, 012309, (2000) [7] E. Schrbdinger, Proc. Cambridge Philos. Soc. 31, 555 (1935). [8] S. Lloyd, M. S. Shahriar, J. H. Shapiro, and P. R. Hemmer, "Long-distance unconditional teleportation of atomic states via complete Bell state measurements," Phys. Rev. Lett. 87, 167903, (2001). [9] P. G. Kwiat, K. Mattle, H. Weinfurter, and A. Zeilinger, "New high-intensity source of polarization-entangled photon pairs, Phys. Rev. Lett. 75, 4337-4341 (1995). [10] P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, "Ultrabright source of polarization-entangled photons," Phys. Rev. A 60, R773-R776 (1999). [11] M. Oberparleiter and H. Weinfurter, "Cavity-enhanced generation of polarizationentangled photon pairs," Opt. Commun. 183, 133-137 (2000). [12] J. H. Shapiro, "Long-distance high-fidelity teleportation using singlet states," volume 3 of Quantum Communication, Measurement, and Computing, pages 367-374. Kluwer, New York, NY, 2001. [13] J. H. Shapiro and N. C. Wong, "An ultrabright narrowband source of polarizationentangled photon pairs," J. Opt. B: Quantum Semiclass. Opt. 2, L1-L4 (2000). [14] R. W. Boyd, Nonlinear Optics, Academic Press, 1992. [15] G. D. Boyd and A. Ashkin, Phys. Rev. 146, 187 (1966). 69 [16] G. D. Boyd and D. A. Kleinman, "Parametric Interaction of Focused Gaussian Light Beams," J. Appl. Phys. 39, 3597 (1968). [17] M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-Phasematched Second Harmonic Generation: Tuning and Tolerances, IEEE J. Quant. Electr. 28, 2631 (1992). [18] J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918 (1962). [19] M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, "First-order quasi-phase matched LiNbO 3 waveguide periodically poled by applying an external field for efficient blue second-harmonic generation," Appl. Phys. Lett. 62, 435-436 (1992). [20] L. E. Myers, R. C. Eckardt, M. M. Fejer, and R. L. Byer, "Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO 3," J. Opt. Soc. Am. B. 12, 2102-2116 (1995). [21] L. E. Myers, and W. R. Bosenberg, "Periodically poled lithium niobate and quasiphase-matched optical parametric oscillators," IEEE J. Quant. Electron. 33, 1663-1672 (1997). [22] G. D. Miller, "Periodically Poled Lithium Niobate: Modeling, Fabrication, and Nonlinear-Optical Performance," PhD Dissertation, Stanford Univ., 1998. [23] G. J. Edwards, M Lawrence, Optical and Quantum Electronics vol. 16, p.373, (1984). [24] D. H. Jundt, Optics Letters vol. 22, p. 1553, (1997). [25] I. Shoji, T. Kondo, A. Kitamoto et al., "Absolute scale of second-order nonlinearoptical coefficients," J. Opt. Soc. Am. B. (Optical Physics) 14, 2268-94 (1997). [26] Elliott J. Mason, III, "Applications of optical parametric downconversion: I. Selfphase locking; II. Generation of entangled photon pairs in periodically-poled lithium niobate," PhD Thesis, MIT, 2002. [27] B. F. Aull, A. H. Loomis, D. J. Young et al., "Geiger-mode avalanche photodiodes for three-dimensional imaging," Linc. Lab. J. 13, (2001). [28] M. A. Albota, R. M. Heinrichs, D. G. Kocher et al., "Three-dimensional imaging laser radar using a photon-counting APD array and microchip laser," Submitted to Appl. Optics. 70 [29] E. Keskiner, "An ultrabright, narrowband source of polarization-entangled photons," M. Eng. Thesis, MIT, August 2001. [30] A. Lacaita, P. A. Francese, F. Zappa, and S. Cova, "Single photon detection beyond 1 pm: performance of commercially available germanium photodiodes," Appl. Opt. 33, 6902-6918 (1994). [31] A. Lacaita, F. Zappa, S. Cova, and P. Lovati, "Single-photon detection beyond 1 [tm: performance of commercially available InGaAs/InP detectors, "Appl. Opt. 35, 29862996 (1996). [32] R. G. Brown, R. Jones, J. G. Rarity, and K. Ridley, "Characterization of silicon avalanche photodiodes for photon correlation measurements. 2: Active quenching," Appl. Opt. 26, 2383-2389 (1987). [33] F. Zappa, A. L. Lacaita, S. D. Cova, and P. Lovati, "Solid-state single-photon detectors," Opt. Eng. 35, 938-945 (1996). [34] S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, "Avalanche photodiodes and quenching circuits for single-photon detection," Appl. Opt. 35, 1956-1976 (1996). [35] G. Ribordy, J.-D. Gautier, H. Zbinden, and N. Gisin, "Performance of InGaAs/InP avalanche photodiodes as gated-mode photon counters," Appl. Opt. 37, 2272-2277 (1998). [36] M. Bourennane, F. Gibson, A. Karlsson, A. Hening, P. Jonsson, T. Tsegaye, D. Ljunggren, and E. Sundberg, "Experiments on long wavelength (1550 nm) plug and play quantum cryptography systems," Opt. Express 10, 383-387 (1999). [37] J. G. Rarity, T. E. Wall, K. D. Ridley, P. C. M. Owens, and P. R. Tapster, "Singlephoton counting for the 1300-1600-nm range by use of Peltier-cooled and passively quenched InGaAs avalanche photodiodes," Appl. Opt. 39, 6746-6753 (2000). [38] P. A. Hiskett, G. S. Buller, J. M. Smith, A. Y. Loudon, I. Gontijo, A. C. Walker, P. D. Townsend, and M. J. Robertson, "Performance and design of InGaAs/InP photodiodes for single-photon counting at 1.55 pm," Appl. Opt. 39, 6818-6829 (2000). [39] D. Stucki, G. Ribordy, A. Stefanov, H. Zbinden, J. G. Rarity, and T. Wall, "Photon counting for quantum key distribution with Peltier cooled InGaAs/InP APDs," J. Mod. Optics, vol. 48, no. 13, p. 1967-1981 (2001) 71 [40] D. N. Klyshko, Photons and Nonlinear Optics, Gordon and Breach Science Publishers, 1988. [41] H. Kogelnik and T. Li, "Laser Beams and Resonators," Appl. Opt. 5, 1550-1567 (1966). [42] P. Kumar, "Quantum frequency conversion," Opt. Lett. 15, 1476-1478 (1990). [43] J. M. Huang and P. Kumar, "Observation of quantum frequency conversion," Phys. Rev. Lett. 68, 2153-2156 (1992). 72