Entanglement dynamics of photon pairs and quantum memories in the gravitational field of the earth

Roy Barzel1, Mustafa Gündoğan2,3, Markus Krutzik2,3,4, Dennis Rätzel1,2, and Claus Lämmerzahl1,5

1ZARM, University of Bremen, Am Fallturm 2, 28359 Bremen, Germany
2Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
3IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 2, 12489 Berlin, Germany
4Ferdinand-Braun-Institut (FBH), Gustav-Kirchoff-Str.4, 12489 Berlin, Germany
5Institute of Physics, Carl von Ossietzky University Oldenburg, Ammerländer Heerstr. 114-118, 26129 Oldenburg, Germany

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We investigate the effect of entanglement dynamics due to gravity – the basis of a mechanism of universal decoherence – for photonic states and quantum memories in Mach-Zehnder and Hong-Ou-Mandel interferometry setups in the gravitational field of the earth. We show that chances are good to witness the effect with near-future technology in Hong-Ou-Mandel interferometry. This would represent an experimental test of theoretical modeling combining a multi-particle effect predicted by the quantum theory of light and an effect predicted by general relativity. Our article represents the first analysis of relativistic gravitational effects on space-based quantum memories which are expected to be an important ingredient for global quantum communication networks.

It has become one of the major problems of theoretical physics to understand the interplay between our most successful theories, quantum mechanics (QM) and general relativity (GR). A resolution of this problem can only be driven by experiments or observations at the interface of the two theories. In addition, the race in the development of space-based quantum technologies, where quantum resources are generated and probed locally or are exchanged over thousands of kilometers through the inhomogeneous gravitational field of Earth, fuels the need to understand the influence of general relativistic effects on quantum resources also from a practical point of view.

A particular example of an interesting fundamental effect at the interface of quantum mechanics and general relativity is the generation of entanglement between the internal energy structure of a quantum system and its external (motional) degrees of freedom (DOFs) due to gravitational time dilation or redshift. These entanglement dynamics (EDs) due gravity have been proposed to be witnessed in atom interferometry, with single photons in Mach-Zehnder (MZ) interference, photon pairs in Hong-Ou-Mandel (HOM) interference and phonons in Bose-Einstein condensates. For the case of massive quantum systems that are in superposition states of their center of mass degree of freedom, EDs due to gravity were found to induce decoherence, underlining their fundamental significance.

In this article, the case of EDs of photons and Quantum Memories (QMems) due to gravity in MZ and HOM interferometry setups is investigated. Furthermore, the article provides an experimental proposal and a feasibility study to witness the effect in HOM experiments whose necessary spatial extensions are dramatically smaller than those of proposed experiments that only employ photons. Such an experiment would represent an experimental test of theoretical modeling combining a multi-particle effect predicted by the quantum theory of light and an effect predicted by general relativity. On the applied side, the article represents the first analysis of relativistic gravitational effects on space-based quantum memories which are expected to be an important ingredient for global quantum communication networks.

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[1] Richard Feynman. ``Feynman lectures on gravitation''. CRC Press. (2018).

[2] David C. Aveline, Jason R. Williams, Ethan R. Elliott, Chelsea Dutenhoffer, James R. Kellogg, James M. Kohel, Norman E. Lay, Kamal Oudrhiri, Robert F. Shotwell, Nan Yu, and Robert J. Thompson. ``Observation of bose–einstein condensates in an earth-orbiting research lab''. Nature 582, 193–197 (2020).

[3] Maike D. Lachmann, Holger Ahlers, Dennis Becker, Aline N. Dinkelaker, Jens Grosse, Ortwin Hellmig, Hauke Müntinga, Vladimir Schkolnik, Stephan T. Seidel, Thijs Wendrich, André Wenzlawski, Benjamin Carrick, Naceur Gaaloul, Daniel Lüdtke, Claus Braxmaier, Wolfgang Ertmer, Markus Krutzik, Claus Lämmerzahl, Achim Peters, Wolfgang P. Schleich, Klaus Sengstock, Andreas Wicht, Patrick Windpassinger, and Ernst M. Rasel. ``Ultracold atom interferometry in space''. Nature Communications 12, 1317 (2021).

[4] Juan Yin, Yuan Cao, Yu-Huai Li, Sheng-Kai Liao, Liang Zhang, Ji-Gang Ren, Wen-Qi Cai, Wei-Yue Liu, Bo Li, and Hui Dai et.al. ``Satellite-based entanglement distribution over 1200 kilometers''. Science 356, 1140–1144 (2017).

[5] Ping Xu, Yiqiu Ma, Ji-Gang Ren, Hai-Lin Yong, Timothy C. Ralph, Sheng-Kai Liao, Juan Yin, Wei-Yue Liu, Wen-Qi Cai, Xuan Han, Hui-Nan Wu, Wei-Yang Wang, Feng-Zhi Li, Meng Yang, Feng-Li Lin, Li Li, Nai-Le Liu, Yu-Ao Chen, Chao-Yang Lu, Yanbei Chen, Jingyun Fan, Cheng-Zhi Peng, and Jian-Wei Pan. ``Satellite testing of a gravitationally induced quantum decoherence model''. Science 366, 132–135 (2019).

[6] Mustafa Gündoğan, Jasminder S. Sidhu, Victoria Henderson, Luca Mazzarella, Janik Wolters, Daniel K. L. Oi, and Markus Krutzik. ``Proposal for space-borne quantum memories for global quantum networking''. npj Quant. Inf. 7, 128 (2021).

[7] Jasminder S. Sidhu, Siddarth K. Joshi, Mustafa Gündoğan, Thomas Brougham, David Lowndes, Luca Mazzarella, Markus Krutzik, Sonali Mohapatra, Daniele Dequal, Giuseppe Vallone, Paolo Villoresi, Alexander Ling, Thomas Jennewein, Makan Mohageg, John Rarity, Ivette Fuentes, Stefano Pirandola, and Daniel K. L. Oi. ``Advances in space quantum communications''. IET Quant. Comm. 2, 182–217 (2021).

[8] Chao-Yang Lu, Yuan Cao, Cheng-Zhi Peng, and Jian-Wei Pan. ``Micius quantum experiments in space''. Rev. Mod. Phys. 94, 035001 (2022).

[9] Magdalena Zych, Fabio Costa, Igor Pikovski, and Časlav Brukner. ``Quantum interferometric visibility as a witness of general relativistic proper time''. Nature Communications 2, 505 (2011).

[10] Magdalena Zych, Fabio Costa, Igor Pikovski, Timothy C Ralph, and Časlav Brukner. ``General relativistic effects in quantum interference of photons''. Classical and Quantum Gravity 29, 224010 (2012).

[11] Makan Mohageg, Luca Mazzarella, Charis Anastopoulos, Jason Gallicchio, Bei-Lok Hu, Thomas Jennewein, Spencer Johnson, Shih-Yuin Lin, Alexander Ling, Christoph Marquardt, Matthias Meister, Raymond Newell, Albert Roura, Wolfgang P. Schleich, Christian Schubert, Dmitry V. Strekalov, Giuseppe Vallone, Paolo Villoresi, Lisa Wörner, Nan Yu, Aileen Zhai, and Paul Kwiat. ``The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics''. EPJ Quantum Technology 9 (2022).

[12] David Edward Bruschi, Carlos Sabín, Angela White, Valentina Baccetti, Daniel K L Oi, and Ivette Fuentes. ``Testing the effects of gravity and motion on quantum entanglement in space-based experiments''. New Journal of Physics 16, 053041 (2014).

[13] Igor Pikovski, Magdalena Zych, Fabio Costa, and Časlav Brukner. ``Universal decoherence due to gravitational time dilation''. Nature Physics 11, 668–672 (2015).

[14] Igor Pikovski, Magdalena Zych, Fabio Costa, and Časlav Brukner. ``Time dilation in quantum systems and decoherence''. New Journal of Physics 19, 025011 (2017).

[15] Mikael Afzelius, Nicolas Gisin, and Hugues de Riedmatten. ``Quantum memory for photons''. Physics Today 68, 42–47 (2015).

[16] Khabat Heshami, Duncan G. England, Peter C. Humphreys, Philip J. Bustard, Victor M. Acosta, Joshua Nunn, and Benjamin J. Sussman. ``Quantum memories: emerging applications and recent advances''. Journal of Modern Optics 63, 2005–2028 (2016).

[17] Sam Pallister, Simon Coop, Valerio Formichella, Nicolas Gampierakis, Virginia Notaro, Paul Knott, Rui Azevedo, Nikolaus Buchheim, Silvio De Carvalho, Emilia Järvelä, et al. ``A blueprint for a simultaneous test of quantum mechanics and general relativity in a space-based quantum optics experiment''. EPJ Quantum Technology 4, 1–23 (2017).

[18] Roy Barzel, David Edward Bruschi, Andreas W. Schell, and Claus Lämmerzahl. ``Observer dependence of photon bunching: The influence of the relativistic redshift on hong-ou-mandel interference''. Phys. Rev. D 105, 105016 (2022).

[19] David Edward Bruschi and Andreas Wolfgang Schell. ``Gravitational redshift induces quantum interference''. Annalen der Physik 535, 2200468 (2023).

[20] Thomas B. Mieling, Christopher Hilweg, and Philip Walther. ``Measuring space-time curvature using maximally path-entangled quantum states''. Phys. Rev. A 106, L031701 (2022).

[21] Dennis Philipp, Volker Perlick, Dirk Puetzfeld, Eva Hackmann, and Claus Lämmerzahl. ``Definition of the relativistic geoid in terms of isochronometric surfaces''. Phys. Rev. D 95, 104037 (2017).

[22] Dennis Philipp, Eva Hackmann, Claus Lämmerzahl, and Jürgen Müller. ``Relativistic geoid: gravity potential and relativistic effects''. Phys. Rev. D 101, 064032 (2020).

[23] J. C. Hafele and Richard E. Keating. ``Around-the-world atomic clocks: Observed relativistic time gains''. Science 177, 168–170 (1972).

[24] Yair Margalit, Zhifan Zhou, Shimon Machluf, Daniel Rohrlich, Yonathan Japha, and Ron Folman. ``A self-interfering clock as a “which path” witness''. Science 349, 1205–1208 (2015).

[25] Roy Barzel and Claus Lämmerzahl. ``Role of indistinguishability and entanglement in hong-ou-mandel interference and finite-bandwidth effects of frequency-entangled photons''. Phys. Rev. A 107, 032205 (2023).

[26] Irwin I. Shapiro. ``Fourth test of general relativity''. Phys. Rev. Lett. 13, 789–791 (1964).

[27] Irwin I. Shapiro, Michael E. Ash, Richard P. Ingalls, William B. Smith, Donald B. Campbell, Rolf B. Dyce, Raymond F. Jurgens, and Gordon H. Pettengill. ``Fourth test of general relativity: New radar result''. Phys. Rev. Lett. 26, 1132–1135 (1971).

[28] Daniel Rieländer, Andreas Lenhard, Osvaldo Jime`nez Farìas, Alejandro Máttar, Daniel Cavalcanti, Margherita Mazzera, Antonio Acín, and Hugues de Riedmatten. ``Frequency-bin entanglement of ultra-narrow band non-degenerate photon pairs''. Quantum Science and Technology 3, 014007 (2017).

[29] Nicolas Maring, Pau Farrera, Kutlu Kutluer, Margherita Mazzera, Georg Heinze, and Hugues de Riedmatten. ``Photonic quantum state transfer between a cold atomic gas and a crystal''. Nature 551, 485–488 (2017).

[30] Stéphane Clemmen, Alessandro Farsi, Sven Ramelow, and Alexander L. Gaeta. ``Ramsey interference with single photons''. Phys. Rev. Lett. 117, 223601 (2016).

[31] Manjin Zhong, Morgan P. Hedges, Rose L. Ahlefeldt, John G. Bartholomew, Sarah E. Beavan, Sven M. Wittig, Jevon J. Longdell, and Matthew J. Sellars. ``Optically addressable nuclear spins in a solid with a six-hour coherence time''. Nature 517, 177–180 (2015).

[32] Yu Ma, You-Zhi Ma, Zong-Quan Zhou, Chuan-Feng Li, and Guang-Can Guo. ``One-hour coherent optical storage in an atomic frequency comb memory''. Nat. Commun. 12, 2381 (2021).

[33] Mustafa Gündoğan, Patrick M. Ledingham, Kutlu Kutluer, Margherita Mazzera, and Hugues de Riedmatten. ``Solid state spin-wave quantum memory for time-bin qubits''. Phys. Rev. Lett. 114, 230501 (2015).

[34] Pierre Jobez, Cyril Laplane, Nuala Timoney, Nicolas Gisin, Alban Ferrier, Philippe Goldner, and Mikael Afzelius. ``Coherent spin control at the quantum level in an ensemble-based optical memory''. Phys. Rev. Lett. 114, 230502 (2015).

[35] Antonio Ortu, Adrian Holzäpfel, Jean Etesse, and Mikael Afzelius. ``Storage of photonic time-bin qubits for up to 20ms in a rare-earth doped crystal''. npj Quantum Information 8, 29 (2022).

[36] Philippe Goldner, Alban Ferrier, and Olivier Guillot-Noël. ``Chapter 267 - rare earth-doped crystals for quantum information processing''. In Jean-Claude G. Bünzli and Vitalij K. Pecharsky, editors, Handbook on the Physics and Chemistry of Rare Earths. Volume 46, pages 1–78. Elsevier (2015).

[37] Alessandro Seri, Dario Lago-Rivera, Andreas Lenhard, Giacomo Corrielli, Roberto Osellame, Margherita Mazzera, and Hugues de Riedmatten. ``Quantum storage of frequency-multiplexed heralded single photons''. Phys. Rev. Lett. 123, 080502 (2019).

[38] Alexandre Fossati, Shuping Liu, Jenny Karlsson, Akio Ikesue, Alexandre Tallaire, Alban Ferrier, Diana Serrano, and Philippe Goldner. ``A frequency-multiplexed coherent electro-optic memory in rare earth doped nanoparticles''. Nano Letters 20, 7087–7093 (2020).

[39] Jean-Daniel Deschênes, Laura C. Sinclair, Fabrizio R. Giorgetta, William C. Swann, Esther Baumann, Hugo Bergeron, Michael Cermak, Ian Coddington, and Nathan R. Newbury. ``Synchronization of distant optical clocks at the femtosecond level''. Phys. Rev. X 6, 021016 (2016).

[40] Hugo Bergeron, Laura C. Sinclair, William C. Swann, Isaac Khader, Kevin C. Cossel, Michael Cermak, Jean-Daniel Deschênes, and Nathan R. Newbury. ``Femtosecond time synchronization of optical clocks off of a flying quadcopter''. Nature Communications 10, 1819 (2019).

[41] Runai Quan, Yiwei Zhai, Mengmeng Wang, Feiyan Hou, Shaofeng Wang, Xiao Xiang, Tao Liu, Shougang Zhang, and Ruifang Dong. ``Demonstration of quantum synchronization based on second-order quantum coherence of entangled photons''. Scientific Reports 6, 30453 (2016).

[42] Raju Valivarthi, Lautaro Narváez, Samantha I. Davis, Nikolai Lauk, Cristián Peña, Si Xie, Jason P. Allmaras, Andrew D. Beyer, Boris Korzh, Andrew Mueller, Mandy Kiburg, Matthew D. Shaw, Emma E. Wollman, Panagiotis Spentzouris, Daniel Oblak, Neil Sinclair, and Maria Spiropulu. ``Picosecond synchronization system for quantum networks''. Journal of Lightwave Technology 40, 7668–7675 (2022).

[43] Y. O. Dudin, L. Li, and A. Kuzmich. ``Light storage on the time scale of a minute''. Phys. Rev. A 87, 031801 (2013).

[44] Sheng-Jun Yang, Xu-Jie Wang, Xiao-Hui Bao, and Jian-Wei Pan. ``An efficient quantum light–matter interface with sub-second lifetime''. Nature Photonics 10, 381–384 (2016).

[45] Or Katz and Ofer Firstenberg. ``Light storage for one second in room-temperature alkali vapor''. Nature Communications 9, 2074 (2018).

[46] Jiří Minář, Hugues de Riedmatten, Christoph Simon, Hugo Zbinden, and Nicolas Gisin. ``Phase-noise measurements in long-fiber interferometers for quantum-repeater applications''. Phys. Rev. A 77, 052325 (2008).

[47] R. Stockill, M. J. Stanley, L. Huthmacher, E. Clarke, M. Hugues, A. J. Miller, C. Matthiesen, C. Le Gall, and M. Atatüre. ``Phase-tuned entangled state generation between distant spin qubits''. Phys. Rev. Lett. 119, 010503 (2017).

[48] Yong Yu, Fei Ma, Xi-Yu Luo, Bo Jing, Peng-Fei Sun, Ren-Zhou Fang, Chao-Wei Yang, Hui Liu, Ming-Yang Zheng, Xiu-Ping Xie, Wei-Jun Zhang, Li-Xing You, Zhen Wang, Teng-Yun Chen, Qiang Zhang, Xiao-Hui Bao, and Jian-Wei Pan. ``Entanglement of two quantum memories via fibres over dozens of kilometres''. Nature 578, 240–245 (2020).

[49] Dario Lago-Rivera, Samuele Grandi, Jelena V. Rakonjac, Alessandro Seri, and Hugues de Riedmatten. ``Telecom-heralded entanglement between multimode solid-state quantum memories''. Nature 594, 37–40 (2021).

[50] Hwang Lee, Pieter Kok, and Jonathan P Dowling. ``A quantum rosetta stone for interferometry''. Journal of Modern Optics 49, 2325–2338 (2002).

[51] Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki. ``Separability of mixed states: necessary and sufficient conditions''. Physics Letters A 223, 1–8 (1996).

[52] Kyung Soo Choi. ``Coherent control of entanglement with atomic ensembles''. PhD thesis. California Institute of Technology. (2011).

[53] C K Hong, Z Y Ou, and L. Mandel. ``Measurement of subpicosecond time intervals between two photons by interference''. Phys. Rev. Lett. 59, 2044–2046 (1987).

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