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Nonreciprocal multiphoton bundle emission in a spinning resonator
Phys. Rev. Research 8, 033090 – Published 22 July, 2026
DOI: https://doi.org/10.1103/n1pp-vwbg
Abstract
We propose a scheme to realize nonreciprocal multiphoton bundle emission in a spinning resonator. The system consists of a rotating two-mode cavity directly coupled to a two-level atom, enabling efficient excitation of the desired multiphoton bundle states. These photon bundles originate from leapfrog transitions between dressed states, established through the coherent atom-cavity coupling under multiphoton resonance conditions. When the rotating resonator is driven in different directions, it generates opposite Sagnac-Fizeau shifts, making the resonant conditions dependent on the direction. As a consequence, distinct multiphoton transition channels can be selectively activated by tuning the driving direction and frequency. The nonreciprocal two-photon or three-photon bundle emission with the same and different modes can be implemented with a high tunability. This scheme provides a feasible route toward direction-controlled multiphoton emitters with potential applications in chiral quantum information processing.
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References (97)
- R. J. Potton, Reciprocity in optics, Rep. Prog. Phys. 67, 717 (2004).
- D. L. Sounas and A. Alù, Non-reciprocal photonics based on time modulation, Nat. Photon. 11, 774 (2017).
- P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, Chiral quantum optics, Nature (London) 541, 473 (2017).
- Y.-P. Wang, J. W. Rao, Y. Yang, P.-C. Xu, Y. S. Gui, B. M. Yao, J. Q. You, and C.-M. Hu, Nonreciprocity and unidirectional invisibility in cavity magnonics, Phys. Rev. Lett. 123, 127202 (2019).
- Y. Xu, J.-Y. Liu, W. Liu, and Y.-F. Xiao, Nonreciprocal phonon laser in a spinning microwave magnomechanical system, Phys. Rev. A 103, 053501 (2021).
- Y.-J. Xu and J. Song, Nonreciprocal magnon laser, Opt. Lett. 46, 5276 (2021).
- B. E. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley Interscience, Hoboken, NJ, 2007).
- D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, What is—and what is not—an optical isolator, Nat. Photon. 7, 579 (2013).
- S. Maayani, R. Dahan, Y. Kligerman, E. Moses, A. U. Hassan, H. Jing, F. Nori, D. N. Christodoulides, and T. Carmon, Flying couplers above spinning resonators generate irreversible refraction, Nature (London) 558, 569 (2018).
- A. Kamal, J. Clarke, and M. H. Devoret, Noiseless nonreciprocity in a parametric active device, Nat. Phys. 7, 311 (2011).
- J. Kerckhoff, K. Lalumière, B. J. Chapman, A. Blais, and K. W. Lehnert, On-chip superconducting microwave circulator from synthetic rotation, Phys. Rev. Appl. 4, 034002 (2015).
- K. M. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Reconfigurable Josephson circulator/directional amplifier, Phys. Rev. X 5, 041020 (2015).
- L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Nonreciprocal light propagation in a silicon photonic circuit, Science 333, 729 (2011).
- S. Manipatruni, J. T. Robinson, and M. Lipson, Optical nonreciprocity in optomechanical structures, Phys. Rev. Lett. 102, 213903 (2009).
- Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-F. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and C.-H. Dong, Experimental realization of optomechanically induced nonreciprocity, Nat. Photon. 10, 657 (2016).
- G. A. Peterson, F. Lecocq, K. Cicak, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Demonstration of efficient nonreciprocity in a microwave optomechanical circuit, Phys. Rev. X 7, 031001 (2017).
- N. R. Bernier, L. D. Toth, A. Koottandavida, M. A. Ioannou, D. Malz, A. Nunnenkamp, A. K. Feofanov, and T. J. Kippenberg, Nonreciprocal reconfigurable microwave optomechanical circuit, Nat. Commun. 8, 604 (2017).
- L. M. de Lépinay, E. Damskägg, C. F. Ockeloen-Korppi, and M. A. Sillanpää, Realization of directional amplification in a microwave optomechanical device, Phys. Rev. Appl. 11, 034027 (2019).
- L. M. de Lépinay, C. F. Ockeloen-Korppi, D. Malz, and M. A. Sillanpää, Nonreciprocal transport based on cavity Floquet modes in optomechanics, Phys. Rev. Lett. 125, 023603 (2020).
- Z. Shen, Y.-L. Zhang, Y. Chen, Y.-F. Xiao, C.-L. Zou, G.-C. Guo, and C.-H. Dong, Nonreciprocal frequency conversion and mode routing in a microresonator, Phys. Rev. Lett. 130, 013601 (2023).
- L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, An all-silicon passive optical diode, Science 335, 447 (2012).
- Q.-T. Cao, H. Wang, C.-H. Dong, H. Jing, R.-S. Liu, X. Chen, L. Ge, Q. Gong, and Y.-F. Xiao, Experimental demonstration of spontaneous chirality in a nonlinear microresonator, Phys. Rev. Lett. 118, 033901 (2017).
- P. Yang, X. Xia, H. He, S. Li, X. Han, G. Li, J. Xu, Y. Yang, and T. Zhang, Realization of nonlinear optical nonreciprocity on a few-photon level based on atoms strongly coupled to an asymmetric cavity, Phys. Rev. Lett. 123, 233604 (2019).
- A. Graf, S. D. Rogers, J. Staffa, U. A. Javid, D. H. Griffith, and Q. Lin, Nonreciprocity in photon pair correlations of classically reciprocal systems, Phys. Rev. Lett. 128, 213605 (2022).
- A. Metelmann and A. A. Clerk, Nonreciprocal photon transmission and amplification via reservoir engineering, Phys. Rev. X 5, 021025 (2015).
- M. Liu, C. Zhao, Y. Zeng, Y. Chen, C. Zhao, and C.-W. Qiu, Evolution and nonreciprocity of loss-induced topological phase singularity pairs, Phys. Rev. Lett. 127, 266101 (2021).
- Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, and D. N. Christodoulides, Unidirectional invisibility induced by parity-time-symmetric periodic structures, Phys. Rev. Lett. 106, 213901 (2011).
- N. Bender, S. Factor, J. D. Bodyfelt, H. Ramezani, D. N. Christodoulides, F. M. Ellis, and T. Kottos, Observation of asymmetric transport in structures with active nonlinearities, Phys. Rev. Lett. 110, 234101 (2013).
- B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Parity-time-symmetric whispering-gallery microcavities, Nat. Phys. 10, 394 (2014).
- L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, Parity-time symmetry and variable optical isolation in active–passive-coupled microresonators, Nat. Photon. 8, 524 (2014).
- M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Quantum optical circulator controlled by a single chirally coupled atom, Science 354, 1577 (2016).
- Y. Shen, M. Bradford, and J.-T. Shen, Single-photon diode by exploiting the photon polarization in a waveguide, Phys. Rev. Lett. 107, 173902 (2011).
- K. Xia, F. Nori, and M. Xiao, Cavity-free optical isolators and circulators using a chiral cross-Kerr nonlinearity, Phys. Rev. Lett. 121, 203602 (2018).
- M.-X. Dong, K.-Y. Xia, W.-H. Zhang, Y.-C. Yu, Y.-H. Ye, E.-Z. Li, L. Zeng, D.-S. Ding, B.-S. Shi, G.-C. Guo, and F. Nori, All-optical reversible single-photon isolation at room temperature, Sci. Adv. 7, eabe8924 (2021).
- S.-Y. Ren, W. Yan, L.-T. Feng, Y. Chen, Y.-K. Wu, X.-Z. Qi, X.-J. Liu, Y.-J. Cheng, B.-Y. Xu, L.-J. Deng, G.-C. Guo, L. Bi, and X.-F. Ren, Single-photon nonreciprocity with an integrated magneto-optical isolator, Laser Photonics Rev. 16, 2100595 (2022).
- J.-S. Tang, W. Nie, L. Tang, M. Y. Chen, X. Su, Y. Q. Lu, F. Nori, and K. Y. Xia, Nonreciprocal single-photon band structure, Phys. Rev. Lett. 128, 203602 (2022).
- I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, Deterministic photon–emitter coupling in chiral photonic circuits, Nat. Nanotechnol. 10, 775 (2015).
- H. Pichler, T. Ramos, A. J. Daley, and P. Zoller, Quantum optics of chiral spin networks, Phys. Rev. A 91, 042116 (2015).
- K. Stannigel, P. Rabl, and P. Zoller, Driven-dissipative preparation of entangled states in cascaded quantum-optical networks, New J. Phys. 14, 063014 (2012).
- D. Malz, L. D. Tóth, N. R. Bernier, A. K. Feofanov, T. J. Kippenberg, and A. Nunnenkamp, Quantum-limited directional amplifiers with optomechanics, Phys. Rev. Lett. 120, 023601 (2018).
- S. Barzanjeh, M. Aquilina, and A. Xuereb, Manipulating the flow of thermal noise in quantum devices, Phys. Rev. Lett. 120, 060601 (2018).
- R. Huang, A. Miranowicz, J.-Q. Liao, F. Nori, and H. Jing, Nonreciprocal photon blockade, Phys. Rev. Lett. 121, 153601 (2018).
- B. Li, R. Huang, X. Xu, A. Miranowicz, and H. Jing, Nonreciprocal unconventional photon blockade in a spinning optomechanical system, Photonics Res. 7, 630 (2019).
- K. Wang, Q. Wu, Y.-F. Yu, and Z.-M. Zhang, Nonreciprocal photon blockade in a two-mode cavity with a second-order nonlinearity, Phys. Rev. A 100, 053832 (2019).
- H. Z. Shen, Q. Wang, J. Wang, and X. X. Yi, Nonreciprocal unconventional photon blockade in a driven dissipative cavity with parametric amplification, Phys. Rev. A 101, 013826 (2020).
- Y.-W. Jing, H.-Q. Shi, and X.-W. Xu, Nonreciprocal photon blockade and directional amplification in a spinning resonator coupled to a two-level atom, Phys. Rev. A 104, 033707 (2021).
- Y. Wang, W. Xiong, Z. Xu, G.-Q. Zhang, and J.-Q. You, Dissipation-induced nonreciprocal magnon blockade in a magnon-based hybrid system, Sci. China Phys. Mech. Astron. 65, 260314 (2022).
- Y.-F. Jiao, S.-D. Zhang, Y.-L. Zhang, A. Miranowicz, L.-M. Kuang, and H. Jing, Nonreciprocal optomechanical entanglement against backscattering losses, Phys. Rev. Lett. 125, 143605 (2020).
- Y.-L. Ren, Nonreciprocal optical–microwave entanglement in a spinning magnetic resonator, Opt. Lett. 47, 1125 (2022).
- Y.-F. Jiao, J.-X. Liu, Y. Li, R. Yang, L.-M. Kuang, and H. Jing, Nonreciprocal enhancement of remote entanglement between nonidentical mechanical oscillators, Phys. Rev. Appl. 18, 064008 (2022).
- D. Kong, J. Xu, and F. Wang, Nonreciprocal entanglement of ferrimagnetic magnons and nitrogen-vacancy-center ensembles by Kerr nonlinearity, Phys. Rev. Appl. 21, 034061 (2024).
- V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photon. 5, 222 (2011).
- M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
- D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 2008).
- J. P. Dowling and G. J. Milburn, Quantum technology: The second quantum revolution, Philos. Trans. R. Soc. London Ser. A 361, 1655 (2003).
- C. S. Muñoz, E. del Valle, A. G. Tudela, K. Müller, S. Lichtmannecker, M. Kaniber, C. Tejedor, J. J. Finley, and F. P. Laussy, Emitters of -photon bundles, Nat. Photon. 8, 550 (2014).
- C. Sánchez Muñoz, F. P. Laussy, E. del Valle, C. Tejedor, and A. González-Tudela, Filtering multiphoton emission from state-of-the-art cavity quantum electrodynamics, Optica 5, 14 (2018).
- Q. Bin, X.-Y. Lü, F. P. Laussy, F. Nori, and Y. Wu, -phonon bundle emission via the Stokes process, Phys. Rev. Lett. 124, 053601 (2020).
- Q. Bin, Y. Wu, and X.-Y. Lü, Parity-symmetry-protected multiphoton bundle emission, Phys. Rev. Lett. 127, 073602 (2021).
- F. Zou, J.-Q. Liao, and Y. Li, Dynamical emission of phonon pairs in optomechanical systems, Phys. Rev. A 105, 053507 (2022).
- C. Gou, X. Hu, and F. Wang, Antibunched two-mode two-photon bundles via atomic coherence, Phys. Rev. A 106, 063718 (2022).
- S.-Y. Jiang, F. Zou, Y. Wang, J.-F. Huang, X.-W. Xu, and J.-Q. Liao, Multiple-photon bundle emission in the -photon Jaynes–Cummings model, Opt. Express 31, 15697 (2023).
- C. Liu, J.-F. Huang, and L. Tian, Deterministic generation of multi-photon bundles in a quantum Rabi model, Sci. China Phys. Mech. Astron. 66, 220311 (2023).
- Z. Chen, C. Gou, X. Hu, D. Kong, and F. Wang, Enhanced bundle emission of squeezed photons using parametric amplification, Phys. Rev. A 112, 063703 (2025).
- B. Xiong, Q. Bin, S.-L. Chao, J.-B. Liu, and X.-Y. Lü, Two-photon decay enhanced even photon bundle emission, Phys. Rev. Res. 7, 013238 (2025).
- A. González-Tudela, V. Paulisch, H. J. Kimble, and J. I. Cirac, Efficient multiphoton generation in waveguide quantum electrodynamics, Phys. Rev. Lett. 118, 213601 (2017).
- W. Qin, V. Macrì, A. Miranowicz, S. Savasta, and F. Nori, Emission of photon pairs by mechanical stimulation of the squeezed vacuum, Phys. Rev. A 100, 062501 (2019).
- J.-Q. Liao and C. K. Law, Correlated two-photon scattering in cavity optomechanics, Phys. Rev. A 87, 043809 (2013).
- P. Bienias, S. Choi, O. Firstenberg, M. F. Maghrebi, M. Gullans, M. D. Lukin, A. V. Gorshkov, and H. P. Büchler, Scattering resonances and bound states for strongly interacting Rydberg polaritons, Phys. Rev. A 90, 053804 (2014).
- M. F. Maghrebi, M. J. Gullans, P. Bienias, S. Choi, I. Martin, O. Firstenberg, M. D. Lukin, H. P. Büchler, and A. V. Gorshkov, Coulomb bound states of strongly interacting photons, Phys. Rev. Lett. 115, 123601 (2015).
- O. Firstenberg, C. S. Adams, and S. Hofferberth, Nonlinear quantum optics mediated by Rydberg interactions, J. Phys. B: At. Mol. Opt. Phys. 49, 152003 (2016).
- K. Jachymski, P. Bienias, and H. P. Büchler, Three-body interaction of Rydberg slow-light polaritons, Phys. Rev. Lett. 117, 053601 (2016).
- C. Gou, X. Hu, J. Xu, and F. Wang, Hybrid magnon-photon bundle emission from a ferromagnetic-superconducting system, Phys. Rev. Res. 6, 023052 (2024).
- Q. Bin, Q.-Y. Qiu, Y. Wu, and X.-Y. Lü, Entangled photon-magnon bundle emission, Laser Photonics Rev. 18, 2300977 (2024).
- J. Liu, S. Hu, W. Zhong, G. Cheng, and A. Chen, Controllable antibunching of two-magnon bundle in a hybrid ferromagnet-superconductor system, Opt. Lett. 50, 682 (2025).
- H. Y. Yuan, J. K. Xie, and R. A. Duine, Magnon bundle in a strongly dissipative magnet, Phys. Rev. Appl. 19, 064070 (2023).
- C. Zhao, W. Li, B. Xiong, J.-X. Peng, L. Zhou, and W.-J. Gong, Heralded generation of entangled states based on -bundle emission in a waveguide magnonics system, Phys. Rev. A 112, 013723 (2025).
- C. Sánchez Muñoz, F. P. Laussy, C. Tejedor, and E. del Valle, Enhanced two-photon emission from a dressed biexciton, New J. Phys. 17, 123021 (2015).
- Y. Chang, A. González-Tudela, C. S. Muñoz, C. Navarrete-Benlloch, and T. Shi, Deterministic down-converter and continuous photon-pair source within the bad-cavity limit, Phys. Rev. Lett. 117, 203602 (2016).
- S.-L. Ma, X.-K. Li, Y.-L. Ren, J.-K. Xie, and F.-L. Li, Antibunched -photon bundles emitted by a Josephson photonic device, Phys. Rev. Res. 3, 043020 (2021).
- S.-L. Ma, J.-K. Xie, Y.-L. Ren, X.-K. Li, and F.-L. Li, Photon-pair blockade in a Josephson-photonics circuit with two nondegenerate microwave resonators, New J. Phys. 24, 053001 (2022).
- M. Cosacchi, A. Mielnik-Pyszczorski, T. Seidelmann, M. Cygorek, A. Vagov, D. E. Reiter, and V. M. Axt, -photon bundle statistics in different solid-state platforms, Phys. Rev. B 106, 115304 (2022).
- F. Zou, Y. Li, and J.-Q. Liao, Dynamical -photon bundle emission, New J. Phys. 25, 043027 (2023).
- Q. Bin, H. Jing, Y. Wu, F. Nori, and X.-Y. Lü, Nonreciprocal bundle emissions of quantum entangled pairs, Phys. Rev. Lett. 133, 043601 (2024).
- G. B. Malykin, The Sagnac effect: Correct and incorrect explanations, Phys.-Usp. 43, 1229 (2000).
- J. R. Johansson, P. D. Nation, and F. Nori, QuTiP: An open-source Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
- C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley, New York, 1992).
- J. R. Schrieffer and P. A. Wolff, Relation between the Anderson and Kondo Hamiltonians, Phys. Rev. 149, 491 (1966).
- R. J. Glauber, The quantum theory of optical coherence, Phys. Rev. 130, 2529 (1963).
- D. V. Strekalov, A bundle of photons, please, Nat. Photon. 8, 500 (2014).
- F. Boitier, A. Godard, E. Rosencher, and C. Fabre, Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors, Nat. Phys. 5, 267 (2009).
- T. Aoki, B. Dayan, E. Wilcut, W. J. Bowen, A. S. Parkins, T. J. Kippenberg, K. J. Vahala, and H. J. Kimble, Observation of strong coupling between one atom and a monolithic microresonator, Nature (London) 443, 671 (2006).
- B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, and H. J. Kimble, A photon turnstile dynamically regulated by one atom, Science 319, 1062 (2008).
- D. J. Alton, N. P. Stern, T. Aoki, H. Lee, E. Ostby, K. J. Vahala, and H. J. Kimble, Strong interactions of single atoms and photons near a dielectric boundary, Nat. Phys. 7, 159 (2011).
- E. Will, L. Masters, A. Rauschenbeutel, M. Scheucher, and J. Volz, Coupling a single trapped atom to a whispering-gallery-mode microresonator, Phys. Rev. Lett. 126, 233602 (2021).
- K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Photon blockade in an optical cavity with one trapped atom, Nature (London) 436, 87 (2005).
- C. Hamsen, K. N. Tolazzi, T. Wilk, and G. Rempe, Two-photon blockade in an atom-driven cavity QED system, Phys. Rev. Lett. 118, 133604 (2017).