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Collective Enhancement of Photon Blockade via Two-Photon Interactions

Lijuan Dong1, Aanal Jayesh Shah2, Peter Kirton3, Hadiseh Alaeian4,2,*, and Simone Felicetti5,1,†

  • *Contact author: halaeian@purdue.edu
  • †Contact author: simone.felicetti@cnr.it
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PRX Quantum 7, 020349 – Published 3 June, 2026

DOI: https://doi.org/10.1103/l477-z8jr

Abstract

Photon blockade—the suppression of multiphoton transmission by quantum nonlinearities—enables on-demand nonclassical light, but it typically requires strong single-emitter coupling and does not improve by simply adding more emitters. We show that this limitation can be overcome when an ensemble of N identical two-level emitters couples to a single cavity mode through a two-photon exchange interaction. Using input-output theory together with a hierarchy of open-system descriptions (exact numerics, a Holstein-Primakoff model, and an approximated analytical treatment), we characterize the steady-state transmission and photon statistics of the two-photon Tavis-Cummings model. We find that blockade is collectively enhanced: the optimal antibunching improves with atom number (1/N2 scaling of the second-order correlation function) while maintaining near-unit transmission, eliminating the usual brightness-purity trade-off of interference-based weak-coupling schemes. We further identify driving configurations that yield collectively enhanced two-photon blockade, with strong suppression of higher-order autocorrelation functions that deepens with increasing N. The nonclassicality is ultimately limited by decoherence, with emitter dephasing providing the dominant constraint. These results establish collective two-photon light-matter coupling as a scalable route to photon blockade in platforms where individual strong coupling is not achievable.

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Popular Summary

Analogous to Coulomb blockade for electrons, photon blockade is a key quantum optical effect in which the presence of one photon prevents the transmission of subsequent ones through a nonlinear medium. Beyond its fundamental interest, photon and multiphoton blockade are actively studied as mechanisms for generating technologically relevant quantum states of light. Photon blockade can be controllably implemented in systems where quantum emitters—such as atoms or artificial atoms—interact with modes of light confined in optical cavities. However, this phenomenon takes place only in the strong coupling regime, where the interaction strength overcomes losses, a condition that is challenging to achieve due to fundamental and practical constraints. This requirement strongly limits the implementation of photon blockade to a few, extremely controllable experimental platforms. Unfortunately, it is well established that increasing the number of emitters does not alleviate the stringent requirement for strong coupling at the single-emitter level. In our work we show that this fundamental limitation can be lifted: we theoretically analyze an unconventional system where light and matter are coupled via nonlinear interactions, such that atoms can emit and absorb photons only in pairs. We show that in this case photon blockade profits from a collective enhancement, achieving a quadratic improvement with the number of emitters. This demonstrates that collective two-photon couplings are a powerful mechanism for realizing photon blockade even in platforms where individual strong coupling is not achievable. Our results can be applied in the design of atomic or solid-state devices, which harness collective light-matter interactions to generate nonclassical light for quantum sensing, communication, and computing tasks.

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References (77)

  1. H. Grabert and M. H. Devoret, Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures (Springer Science & Business Media, New York, 2013), Vol. 294.
  2. A. Îmamoğlu, H. Schmidt, G. Woods, and M. Deutsch, Strongly interacting photons in a nonlinear cavity, Phys. Rev. Lett. 79, 1467 (1997).
  3. J. A. Souza, E. Figueroa, H. Chibani, C. J. Villas-Boas, and G. Rempe, Coherent control of quantum fluctuations using cavity electromagnetically induced transparency, Phys. Rev. Lett. 111, 113602 (2013).
  4. 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).
  5. 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 436, 87 (2005).
  6. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, Quantum nature of a strongly coupled single quantum dot-cavity system, Nature 445, 896 (2007).
  7. K. Müller, A. Rundquist, K. A. Fischer, T. Sarmiento, K. G. Lagoudakis, Y. A. Kelaita, C. Sánchez Muñoz, E. del Valle, F. P. Laussy, and J. Vučković, Coherent generation of nonclassical light on chip via detuned photon blockade, Phys. Rev. Lett. 114, 233601 (2015).
  8. A. J. Hoffman, S. J. Srinivasan, S. Schmidt, L. Spietz, J. Aumentado, H. E. Türeci, and A. A. Houck, Dispersive photon blockade in a superconducting circuit, Phys. Rev. Lett. 107, 053602 (2011).
  9. T. C. H. Liew and V. Savona, Single photons from coupled quantum modes, Phys. Rev. Lett. 104, 183601 (2010).
  10. H. Flayac and V. Savona, Unconventional photon blockade, Phys. Rev. A 96, 053810 (2017).
  11. M. Radulaski, K. A. Fischer, K. G. Lagoudakis, J. L. Zhang, and J. Vučković, Photon blockade in two-emitter-cavity systems, Phys. Rev. A 96, 011801(R) (2017).
  12. H. J. Snijders, J. A. Frey, J. Norman, H. Flayac, V. Savona, A. C. Gossard, J. E. Bowers, M. P. van Exter, D. Bouwmeester, and W. Löffler, Observation of the unconventional photon blockade, Phys. Rev. Lett. 121, 043601 (2018).
  13. C. Vaneph, A. Morvan, G. Aiello, M. Féchant, M. Aprili, J. Gabelli, and J. Estève, Observation of the unconventional photon blockade in the microwave domain, Phys. Rev. Lett. 121, 043602 (2018).
  14. J. Tang, L. Tang, H. Wu, Y. Wu, H. Sun, H. Zhang, T. Li, Y. Lu, M. Xiao, and K. Xia, Towards on-demand heralded single-photon sources via photon blockade, Phys. Rev. Appl. 15, 064020 (2021).
  15. M. M. Mahana, S. Das, and T. N. Dey, Unconventional photon blockade in cavity QED with parametric amplification, Phys. Rev. A 113, 013724 (2026).
  16. P. Kómár, S. D. Bennett, K. Stannigel, S. J. M. Habraken, P. Rabl, P. Zoller, and M. D. Lukin, Single-photon nonlinearities in two-mode optomechanics, Phys. Rev. A 87, 013839 (2013).
  17. 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).
  18. A. V. Poshakinskiy and A. N. Poddubny, Biexciton-mediated superradiant photon blockade, Phys. Rev. A 93, 033856 (2016).
  19. M. A. Carroll, G. D’Alessandro, G. L. Lippi, G.-L. Oppo, and F. Papoff, Thermal, quantum antibunching and lasing thresholds from single emitters to macroscopic devices, Phys. Rev. Lett. 126, 063902 (2021).
  20. M. Chen, J. Tang, L. Tang, H. Wu, and K. Xia, Photon blockade and single-photon generation with multiple quantum emitters, Phys. Rev. Res. 4, 033083 (2022).
  21. B. Kass, S. Talkington, A. Srivastava, and M. Claassen, Many-body photon blockade and quantum light generation from cavity quantum materials, arXiv:2411.08964.
  22. R. Trivedi, M. Radulaski, K. A. Fischer, S. Fan, and J. Vučković, Photon blockade in weakly driven cavity quantum electrodynamics systems with many emitters, Phys. Rev. Lett. 122, 243602 (2019).
  23. R. Hou, W. Zhang, D.-Y. Wang, S.-L. Su, X. Han, H.-F. Wang, and S. Zhang, Conventional photon blockade in the dispersive limit for Tavis-Cummings model, Opt. Express 31, 24939 (2023).
  24. B. Marinelli, A. H. Rubin, V. A. Norman, S. Yang, R. Naik, B. M. Niedzielski, D. K. Kim, R. Das, M. Schwartz, D. I. Santiago, C. Spitzer, I. Siddiqi, and M. Radulaski, Observation of photon blockade in a Tavis-Cummings system, arXiv:2501.18751.
  25. S. Felicetti, D. Z. Rossatto, E. Rico, E. Solano, and P. Forn-Díaz, Two-photon quantum Rabi model with superconducting circuits, Phys. Rev. A 97, 013851 (2018).
  26. S. Felicetti, M.-J. Hwang, and A. Le Boité, Ultrastrong-coupling regime of nondipolar light-matter interactions, Phys. Rev. A 98, 053859 (2018).
  27. J. Goetz, F. Deppe, K. G. Fedorov, P. Eder, M. Fischer, S. Pogorzalek, E. Xie, A. Marx, and R. Gross, Parity-engineered light-matter interaction, Phys. Rev. Lett. 121, 060503 (2018).
  28. E. V. Stolyarov, V. L. Andriichuk, and A. M. Sokolov, Two-photon coupling via Josephson element: Breaking the symmetry with magnetic fields, Phys. Rev. B 111, 214517 (2025).
  29. M. Meguebel, M. Federico, S. Felicetti, N. Belabas, and N. Fabre, Generation of frequency entanglement with an effective quantum dot-waveguide two-photon quadratic interaction, Opt. Quantum 3, 617 (2025).
  30. X. Zhou and A. Mizel, Nonlinear coupling of nanomechanical resonators to Josephson quantum circuits, Phys. Rev. Lett. 97, 267201 (2006).
  31. B.-M. Ann, W. Kessels, and G. A. Steele, Two-photon sideband interaction in a driven quantum Rabi model: Quantitative discussions with derived longitudinal drives and beyond the rotating wave approximation, Phys. Rev. Res. 4, 013005 (2022).
  32. X. Wang, A. Miranowicz, H.-R. Li, and F. Nori, Method for observing robust and tunable phonon blockade in a nanomechanical resonator coupled to a charge qubit, Phys. Rev. A 93, 063861 (2016).
  33. C. Sánchez Muñoz, A. Lara, J. Puebla, and F. Nori, Hybrid systems for the generation of nonclassical mechanical states via quadratic interactions, Phys. Rev. Lett. 121, 123604 (2018).
  34. S. Felicetti, J. S. Pedernales, I. L. Egusquiza, G. Romero, L. Lamata, D. Braak, and E. Solano, Spectral collapse via two-phonon interactions in trapped ions, Phys. Rev. A 92, 033817 (2015).
  35. P. Schneeweiss, A. Dareau, and C. Sayrin, Cold-atom-based implementation of the quantum Rabi model, Phys. Rev. A 98, 021801(R) (2018).
  36. A. Dareau, Y. Meng, P. Schneeweiss, and A. Rauschenbeutel, Observation of ultrastrong spin-motion coupling for cold atoms in optical microtraps, Phys. Rev. Lett. 121, 253603 (2018).
  37. J. Casanova, R. Puebla, H. Moya-Cessa, and M. B. Plenio, Connecting nth order generalised quantum Rabi models: Emergence of nonlinear spin-boson coupling via spin rotations, npj Quantum Inf. 4, 47 (2018).
  38. X.-H. Cheng, I. Arrazola, J. S. Pedernales, L. Lamata, X. Chen, and E. Solano, Nonlinear quantum Rabi model in trapped ions, Phys. Rev. A 97, 023624 (2018).
  39. R. Puebla, J. Casanova, O. Houhou, E. Solano, and M. Paternostro, Quantum simulation of multiphoton and nonlinear dissipative spin-boson models, Phys. Rev. A 99, 032303 (2019).
  40. L. Cong, S. Felicetti, J. Casanova, L. Lamata, E. Solano, and I. Arrazola, Selective interactions in the quantum Rabi model, Phys. Rev. A 101, 032350 (2020).
  41. L. Garbe, I. L. Egusquiza, E. Solano, C. Ciuti, T. Coudreau, P. Milman, and S. Felicetti, Superradiant phase transition in the ultrastrong-coupling regime of the two-photon Dicke model, Phys. Rev. A 95, 053854 (2017).
  42. X.-Y. Chen and Y.-Y. Zhang, Finite-size scaling analysis in the two-photon Dicke model, Phys. Rev. A 97, 053821 (2018).
  43. S. Cui, F. Hébert, B. Grémaud, V. G. Rousseau, W. Guo, and G. G. Batrouni, Two-photon Rabi-Hubbard and Jaynes-Cummings-Hubbard models: Photon-pair superradiance, Mott insulator, and normal phases, Phys. Rev. A 100, 033608 (2019).
  44. L. Garbe, P. Wade, F. Minganti, N. Shammah, S. Felicetti, and F. Nori, Dissipation-induced bistability in the two-photon Dicke model, Sci. Rep. 10, 1 (2020).
  45. S. Cui, B. Grémaud, W. Guo, and G. G. Batrouni, Nonlinear two-photon Rabi-Hubbard model: Superradiance, photon, and photon-pair Bose-Einstein condensates, Phys. Rev. A 102, 033334 (2020).
  46. J. Li, R. Fazio, and S. Chesi, Nonlinear dynamics of the dissipative anisotropic two-photon Dicke model, New J. Phys. 24, 083039 (2022).
  47. A. Jayesh Shah, P. Kirton, S. Felicetti, and H. Alæian, Dissipative phase transition in the two-photon Dicke model, Phys. Rev. Lett. 135, 173602 (2025).
  48. A. Delmonte, A. Crescente, M. Carrega, D. Ferraro, and M. Sassetti, Characterization of a two-photon quantum battery: Initial conditions, stability and work extraction, Entropy 23, 612 (2021).
  49. N. Piccione, S. Felicetti, and B. Bellomo, Two-photon-interaction effects in the bad-cavity limit, Phys. Rev. A 105, L011702 (2022).
  50. U. Alushi, T. Ramos, J. J. García-Ripoll, R. Di Candia, and S. Felicetti, Waveguide QED with quadratic light-matter interactions, PRX Quantum 4, 030326 (2023).
  51. P. M. Mutter and G. Burkard, Transmission-based noise spectroscopy for quadratic qubit-resonator interactions, Phys. Rev. A 107, 052603 (2023).
  52. Z.-J. Ying, H.-H. Han, B.-J. Li, S. Felicetti, and D. Braak, Critical quantum metrology in a stabilized two-photon Rabi model, Adv. Quantum Technol. 8, e00263 (2025).
  53. C. A. González-Gutiérrez and J. M. Torres, Atomic Bell measurement via two-photon interactions, Phys. Rev. A 99, 023854 (2019).
  54. R. Gautier, A. Sarlette, and M. Mirrahimi, Combined dissipative and Hamiltonian confinement of cat qubits, PRX Quantum 3, 020339 (2022).
  55. C. J. Villas-Boas and D. Z. Rossatto, Multiphoton Jaynes-Cummings model: Arbitrary rotations in Fock space and quantum filters, Phys. Rev. Lett. 122, 123604 (2019).
  56. F. Zou, X.-Y. Zhang, X.-W. Xu, J.-F. Huang, and J.-Q. Liao, Multiphoton blockade in the two-photon Jaynes-Cummings model, Phys. Rev. A 102, 053710 (2020).
  57. C. Wang, H. Chen, and J.-Q. Liao, Nonequilibrium thermal transport and photon squeezing in a quadratic qubit-resonator system, Phys. Rev. A 104, 033701 (2021).
  58. H. Zhang and Z. Duan, Photon blockade in the Jaynes-Cummings model with two-photon dissipation, Opt. Express 31, 22580 (2023).
  59. H.-J. Li, L.-B. Fan, S. Ma, J.-Q. Liao, and C.-C. Shu, Exploring photon blockade in a two-photon Jaynes-Cummings model with atom and cavity drivings, Phys. Rev. A 110, 043707 (2024).
  60. X. Liu, M.-Y. Tian, X.-N. Cui, and X.-H. Zhang, Unconventional photon blockade in the two-photon Jaynes-Cummings model with two-frequency cavity drivings and atom driving, Chin. Phys. B 33, 020308 (2024).
  61. L. O. R. Solak, B. L. Vermes, A. S. M. de Castro, C. J. Villas-Boas, and D. Z. Rossatto, Quantum resonator as a directional quantum emitter, Adv. Quantum Technol. e00710 (2025).
  62. Y.-H. Zhou, T. Liu, Q.-P. Su, X.-Y. Zhang, Q.-C. Wu, D.-X. Chen, Z.-C. Shi, H. Z. Shen, and C.-P. Yang, Universal photon blockade, Phys. Rev. Lett. 134, 183601 (2025).
  63. J.-Q. Liao and F. Nori, Photon blockade in quadratically coupled optomechanical systems, Phys. Rev. A 88, 023853 (2013).
  64. P. Kirton and J. Keeling, Suppressing and restoring the Dicke superradiance transition by dephasing and decay, Phys. Rev. Lett. 118, 123602 (2017).
  65. P. Kirton and J. Keeling, Superradiant and lasing states in driven-dissipative Dicke models, New J. Phys. 20, 015009 (2018).
  66. N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, Open quantum systems with local and collective incoherent processes: Efficient numerical simulations using permutational invariance, Phys. Rev. A 98, 063815 (2018).
  67. T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940).
  68. F. Persico and G. Vetri, Dicke model and the Holstein-Primakoff representation, Lett. Nuovo Cimento 12, 449 (1975).
  69. M. Frasca, Dynamical decoherence in a cavity with a large number of two-level atoms, Opt. Spectrosc. 94, 796 (2003).
  70. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 2008), 2nd ed.
  71. T. Khazanov, S. Gunasekaran, A. George, R. Lomlu, S. Mukherjee, and A. J. Musser, Embrace the darkness: An experimental perspective on organic exciton-polaritons, Chem. Phys. Rev. 4, 041305 (2023).
  72. I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013).
  73. A. Delteil, T. Fink, A. Schade, S. Höfling, C. Schneider, and A. Imamoğlu, Towards polariton blockade of confined exciton-polaritons, Nat. Mater. 18, 219 (2019).
  74. H. J. Carmichael, Breakdown of photon blockade: A dissipative quantum phase transition in zero dimensions, Phys. Rev. X 5, 031028 (2015).
  75. J. B. Curtis, I. Boettcher, J. T. Young, M. F. Maghrebi, H. Carmichael, A. V. Gorshkov, and M. Foss-Feig, Critical theory for the breakdown of photon blockade, Phys. Rev. Res. 3, 023062 (2021).
  76. A. Le Boité, M.-J. Hwang, H. Nha, and M. B. Plenio, Fate of photon blockade in the deep strong-coupling regime, Phys. Rev. A 94, 033827 (2016).
  77. J. M. Fink, A. Dombi, A. Vukics, A. Wallraff, and P. Domokos, Observation of the photon-blockade breakdown phase transition, Phys. Rev. X 7, 011012 (2017).

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PRX Quantum 7, 020349– Published 3 June, 2026
  • Received 2 December 2025
  • Accepted 7 April 2026
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