Doctoral School of Physics 

TTK, Department of Physics

Supervisor: Dr. ERDEI Gábor

Development of correlated photon-pair sources

Introducing the research area

Quantum technology, as an emerging branch of physics, has fueled a lot of experimental work in recent years. Several research and theories have come to light, which have direct practical applications, such as quantum computers desired by many [1], or the next level of security, quantum key distribution [2]. A sparkling field in this area is quantum optics because its natural units, the photons, are easy to transmit over long distances and manipulate at room temperature. A fundamental building block of quantum optical systems and protocols is a photon source capable of producing photons or even pairs of photons of the correct state. During my work, I design photon pair sources, which generate the emitted photons coupled into a single-mode optical fiber. My research aims to develop a source that can be easily connected to telecommunication channels and is also suitable for the implementation of entanglement-based encryption [3].

 

Brief introduction of the research place

I do my research at the Department of Atomic Physics at BME. I have started it within the HunQuTech consortium, and currently, it is part of the Quantum Information National Laboratory. Both collaborations are aimed to accelerate Hungarian research and development in quantum technology. Our department contributes to this with the improvement of photon pair sources and low-intensity, picosecond time scale measurement techniques for plant fluorescence.

 

History and context of the research

The goal of quantum technology is to utilize quantum systems for the calculation of exponentially scalable problems, or other useful purposes such as quantum key distribution. The need for novel cryptography techniques is underlined by the fact that the security of standard RSA encryption depends only on the unattainable computational power required to crack it. With the advancement of quantum computers breaking the RSA cryptosystem would be possible in polynomial time [4]. Hence, the security of quantum cryptography protocols [3], [5] is based on physical laws. The deployment of an international network, where quantum communication is a routine task, is a united European initiative (EuroQCI).

Over the past decades, several experiments demonstrated quantum key distribution. Some of them were conducted in free space [6], others in telecom optical fiber [7]. A common technique is to transmit quantum information via attenuated laser pulses, where each pulse has an average energy of less than one photon [8]. There are already commercial solutions (by e.g. Toshiba, IDQuantique) utilizing this technique. Another, yet experimental approach uses entangled photon pairs. The latter usually requires whole photonic laboratory equipment. A severe disadvantage of both is that quantum information can only be forwarded over limited distances due to transmission losses. However, entanglement provides a theoretical possibility of using quantum repeaters, enabling the communication between more distant parties.

 

The research goals, open questions

My research objective is to design polarization-entangled photon pair sources in a compact size, featuring a single-mode optical fiber output. This provides a convenient interface for connecting the source either to free space or to fiber optic communication lines. Polarization, as a degree of freedom of light, is easy to measure and manipulate, therefore an ideal choice for this quantum correlation. Experimental applications set numerous requirements for these sources. One of these is the great photon pair flux since this represents a bottleneck in terms of the speed of communication. Another important feature is the fidelity, which describes the similarity between the theoretical and experimentally obtained quantum state. The heralding ratio is defined as the conditional probability of detecting a photon on the output, given that its pair was already detected on the other. During my work, I strive to optimize these parameters. Besides, my other motivation is to create frequency degenerate pairs, meaning that both photons have the same spectral distribution. One possible realization of quantum repeaters is interference between independent sources, although this requires that the interacting photons have narrow and identical spectral distribution.

 

Methods

Photon pairs in my experiments are created via spontaneous parametric down-conversion (SPDC) [9] in nonlinear crystals. For this purpose, frequently selected materials are potassium-titanyl-phosphate (KTP), lithium-niobate, or β-barium-borate (BBO), of which the latter is used in our sources so far. In these crystals the ever-present vacuum field and a pump are mixed in a parametric process which results in the generation of the down-converted pairs. Counting these photons is possible with avalanche photodiodes which are capable of producing a significantly large electric signal, even if they were excited by the energy of only a single photon. The coincidence of the pairs is determined by temporally correlating the detector signals. For this purpose, a time-tagger electronics with picosecond resolution is used, which makes it easy to determine if two detector events happened in the same narrow time window.

In the initial phase, all experiments are built in the laboratory on a mechanically isolated optical table. In this way, the physical principles can be easily tested. The investigation of type-I and type-II phase-matched BBO and the first polarization entanglement in our laboratory [S1] was also completed in this manner, using a goniometer schematically depicted in Figure 1.

1. Figure a) Goniometer for the investigation of the SPDC process in BBO crystal [S1].
   b) Scanning the intersection of cones in type-II phase matching.

Both the transformation of the experimental concept into a compact form and the high-quality single-mode fiber-coupling of the down-converted pairs require an optical design process. For this purpose, I use ZEMAX OpticStudio optical design software. The whole optical system can be built in the software either from commercially available parts (e.g., lenses, prisms, etc.) or one can even design custom lenses if necessary. This allows geometrical or diffractive optical modeling of the apparatus and estimation of the fiber coupling efficiency. In several cases the design and manufacturing of unique mechanical parts are also unavoidable, to assure the compatibility of optics mounting with commercial adjusters and actuators. As a CAD software, I use PTC Cero for generating the 3D models and production drawings.

2. Figure a) Design of the fiber coupling optics of photon pairs in ZEMAX OpticStudio. b) Model of the type-I SPDC cone and the aperture of the fiber coupling optics (light purple) for estimating the coupling efficiency by diffractive calculations [S2].

 

Results

I have designed and assembled a portable photon pair source that emits pairs of identical linear polarization on its polarization-maintaining fiber outputs [S2]. This device operates in a type-I critical phase-matching condition with a BBO crystal, and has great brightness compared to similar fiber-coupled, frequency-degenerate sources. The bandwidth of the fiber coupled SPDC spectrum is 200 nm according to our measurements, which strongly restricts the temporal uncertainty of the pairs. With this feature, our apparatus offers a solution to the time synchronization problem frequently occurring in telecommunication [10]. Further development resulted in enhanced mechanical stability, a prerequisite for maintaining high-quality fiber coupling in the long term. I have decreased the chromatic aberration of the coupling by spectral filtering. Due to the increased coupling efficiency, the heralding ratio of the source also grew from 20% to 39% [S3]. Successful Hong-Ou-Mandel interference verified the indistinguishability of the photons.

I have presented a phase-stable method for creating polarization entanglement based on wavefront-splitting interference [S4]. To achieve this, I modified the device by inserting segmented half-wave plates (SHWP) in the SPDC cone as shown in Figure 3. These render the polarization of the members of the pairs orthogonal since they propagate in conjugate directions according to the phase matching condition. Due to single-mode fiber coupling, the wavenumber distinguishability of different polarizations vanishes, therefore a polarization entanglement is produced on the output.

 

3. Figure Conversion of momentum correlation of the SPDC pairs into polarization entanglement.

By performing polarization state tomography on the source presented in Figure 4, I could determine a fidelity of 0.951±0.004. A major part of the deviation from the ideal can be explained by the imperfect fabrication of the custom SHWP-s in our optical workshop, however, this it does not pose a theoretical limitation on our method. The device is modular in the sense that it only requires refocusing and slight realignment when switching between 200 nm wide spectrum, 10 nm narrow spectrum and polarization entangled operational modes. Thus, it is adequate not only for research applications but also excellent for educational purposes.

4. Figure a) Schematics of the polarization entangled photon-pair source [S4], and b) the realization of the equipment [S3].

 

Expected impact and further research

The source described above currently operates at the Department of Networked Systems and Services at BME, as a part of a quantum communication experiment that will be the first free space demonstration of quantum key distribution in Hungary.

I will continue my research by further increasing the flux of our sources by utilizing quasi phase-matched periodically poled crystals. Currently, I am developing a Sagnac-interferometer based assembly that exploits quantum interference and contains a pp-KTP crystal. A huge advantage of these crystals is their larger effective volume, which allows for a more efficient SPDC process. In addition, my further goal is to design sources with operational principles that do not require special, multi-wavelength polarization elements.

Publications, references, links

List of corresponding own publications:

[S1]     C. T. Holló, G. Erdei, and T. Sarkadi, "Increasing the correlation level of polarization entangled photon pairs generated by type-II SPDC in BBO," in Frontiers in Optics / Laser Science, B. Lee, C. Mazzali, K. Corwin, and R. Jason Jones, eds., OSA Technical Digest (Optica Publishing Group, 2020), paper JTh4A.36.

[S2]     Csaba T. Holló, Tamás Sarkadi, Máté Galambos, Dániel Bíró, Attila Barócsi, Pál Koppa, Gábor Erdei, "Compact, single-mode fiber-coupled, correlated photon pair source based on type-I beta-barium borate crystal," Opt. Eng. 61(2) 025101 (7 February 2022)

[S3]     C. T. Holló, T. Sarkadi, M. Galambos, B. Bodrog, A. Barócsi, P. Koppa, and G. Erdei, "Compact, Portable, Fiber-Coupled Correlated Photon Pair Source with Enhanced Performance," in Quantum 2.0 Conference and Exhibition, Technical Digest Series (Optica Publishing Group, 2022), paper QTu2A.18.

[S4]     Holló, C. T., Sarkadi, T., Galambos, M., Barócsi, A., Koppa, P., Hanyecz, V., & Erdei, G. (2022). Conversion of transverse momentum correlation of photon pairs into polarization entanglement by using wavefront-splitting interference. Physical Review A, 106(6), 063710.

 

Table of links:

Department of Atomic Physics

HunQuTech

Quantum Information National Laboratory

quantum key distribution

RSA

EuroQCI

Toshiba

IDQuantique

quantum repeaters

entanglement

fidelity

spontaneous parametric down-conversion

avalanche photodiodes

time-tagger

ZEMAX OpticStudio

PTC Cero

chromatic aberration

Hong-Ou-Mandel interference

polarization state tomography

Department of Networked Systems and Services

quasi phase-matching

periodically poled

 

List of references:

[1]    Ladd, T., Jelezko, F., Laflamme, R. et al. Quantum computers. Nature 464, 45–53 (2010). https://doi.org/10.1038/nature08812

[2]    Lo, HK., Curty, M. & Tamaki, K. Secure quantum key distribution. Nature Photon 8, 595–604 (2014). https://doi.org/10.1038/nphoton.2014.149

[3]    Ekert, Artur K. "Quantum cryptography based on Bell’s theorem." Physical review letters 67.6 (1991): 661.

[4]    Shor, Peter W. "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer." SIAM review 41.2 (1999): 303–332.

[5]    Charles H. Bennett, Gilles Brassard, "Quantum cryptography: Public key distribution and coin tossing", Theoretical Computer Science, 560.1 (2014): 7–11, https://doi.org/10.1016/j.tcs.2014.05.025.

[6]    R. Ursin et al., “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3(7), 481–486 (2007).

[7]    Mao, Yingqiu, et al. "Integrating quantum key distribution with classical communications in backbone fiber network." Optics express 26.5 (2018): 6010-6020.

[8]    Jouguet, Paul, et al. "Experimental demonstration of long-distance continuous-variable quantum key distribution." Nature photonics 7.5 (2013): 378–381.

[9]    Christophe Couteau (2018): Spontaneous parametric down-conversion, Contemporary Physics, DOI: 10.1080/00107514.2018.1488463

[10] J. Lee et al., „Symmetrical clock synchronization with time- correlated photon pairs,” Appl. Phys. Lett. 114(10), 101102 (2019).