- Access by Xinjiang University
Quantum correlated steady states under competing collective and individual decay
Phys. Rev. A 114, 013720 – Published 24 July, 2026
DOI: https://doi.org/10.1103/cy7b-hsl3
Abstract
Collective dissipation can generate useful quantum correlations, while ubiquitous individual decay destroys them. We study the interplay between these two competing processes considering a driven system of many spins (“atoms”) undergoing both collective and individual dissipation (“radiation”). In the steady state and depending on drive, we find that the system exhibits a first-order phase transition and quantum bistability: its quantum state is a mixture of two many-body states associated with the two competing decay processes. Accordingly, one of these states closely resembles a correlated “coherently radiating spin state” (CRSS)—the solution of purely collective dissipation—exhibiting spin-squeezing entanglement. We predict dynamical switching between the two stable states, manifest as many-body quantum jumps in the various observables of spin and radiation. Macroscopically, the switching rate tends to vanish and the system can reside in a correlated CRSS for long times. This reveals how correlated dissipative physics emerges at the presence of decorrelating individual decay, opening a path for unlocking collective dissipation phenomena in realistic quantum platforms and applications. We discuss consequences for experiments in collective radiation.
Physics Subject Headings (PhySH)
Article Text
References (89)
- F. Reiter, T. L. Nguyen, J. P. Home, and S. F. Yelin, Cooperative breakdown of the oscillator blockade in the Dicke model, Phys. Rev. Lett. 125, 233602 (2020).
- B. Kraus, H. P. Büchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller, Preparation of entangled states by quantum Markov processes, Phys. Rev. A 78, 042307 (2008).
- J. Ma, X. Wang, C. P. Sun, and F. Nori, Quantum spin squeezing, Phys. Rep. 509, 89 (2011).
- F. Reiter, A. S. Sørensen, P. Zoller, and C. A. Muschik, Dissipative quantum error correction and application to quantum sensing with trapped ions, Nat. Commun. 8, 1822 (2017).
- Y. Suzuki, S. Endo, K. Fujii, and Y. Tokunaga, Quantum error mitigation as a universal error reduction technique: Applications from the NISQ to the fault-tolerant quantum computing eras, PRX Quantum 3, 010345 (2022).
- J. C. Hoke, M. Ippoliti, E. Rosenberg, et al., Measurement-induced entanglement and teleportation on a noisy quantum processor, Nature (London) 622, 481 (2023).
- M. Gross and S. Haroche, Superradiance: An essay on the theory of collective spontaneous emission, Phys. Rep. 93, 301 (1982).
- D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, Prospects for a millihertz-linewidth laser, Phys. Rev. Lett. 102, 163601 (2009).
- L. Henriet, J. S. Douglas, D. E. Chang, and A. Albrecht, Critical open-system dynamics in a one-dimensional optical-lattice clock, Phys. Rev. A 99, 023802 (2019).
- D. E. Chang, J. Ye, and M. D. Lukin, Controlling dipole-dipole frequency shifts in a lattice-based optical atomic clock, Phys. Rev. A 69, 023810 (2004).
- S. Ostermann, O. Rubies-Bigorda, V. Zhang, and S. F. Yelin, Breakdown of steady-state superradiance in extended driven atomic arrays, Phys. Rev. Res. 6, 023206 (2024).
- M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, Superradiance on the millihertz linewidth strontium clock transition, Sci. Adv. 2, e1601231 (2016).
- Y. Kaluzny, P. Goy, M. Gross, J. M. Raimond, and S. Haroche, Observation of self-induced Rabi oscillations in two-level atoms excited inside a resonant cavity: The ringing regime of superradiance, Phys. Rev. Lett. 51, 1175 (1983).
- A. Angerer, K. Streltsov, T. Astner, S. Putz, H. Sumiya, S. Onoda, J. Isoya, W. J. Munro, K. Nemoto, J. Schmiedmayer, and J. Majer, Superradiant emission from colour centres in diamond, Nat. Phys. 14, 1168 (2018).
- W. Kersten, N. de Zordo, E. S. Redchenko, N. Lagos, A. N. Kanagin, A. Angerer, W. J. Munro, K. Nemoto, I. E. Mazets, and J. Schmiedmayer, Self-induced superradiant masing, Nat. Phys. 22, 158 (2026).
- J. G. Bohnet, Z. Chen, J. M. Weiner, D. Meiser, M. J. Holland, and J. K. Thompson, A steady-state superradiant laser with less than one intracavity photon, Nature (London) 484, 78 (2012).
- G.-D. Lin and S. F. Yelin, Superradiance: An integrated approach to cooperative effects in various systems, in Advances In Atomic, Molecular, and Optical Physics, edited by P. Berman, E. Arimondo, and C. Lin (Academic Press, San Diego, 2012), Vol. 61, Chap. 6, pp. 295–329.
- J. Pellegrino, R. Bourgain, S. Jennewein, Y. R. P. Sortais, A. Browaeys, S. D. Jenkins, and J. Ruostekoski, Observation of suppression of light scattering induced by dipole-dipole interactions in a cold-atom ensemble, Phys. Rev. Lett. 113, 133602 (2014).
- W. Kersten, N. de Zordo, O. Diekmann, T. Reiter, M. Zens, A. N. Kanagin, S. Rotter, J. Schmiedmayer, and A. Angerer, Triggered superradiance and spin inversion storage in a hybrid quantum system, Phys. Rev. Lett. 131, 043601 (2023).
- D. D. Grimes, S. L. Coy, T. J. Barnum, Y. Zhou, S. F. Yelin, and R. W. Field, Direct single-shot observation of millimeter-wave superradiance in Rydberg-Rydberg transitions, Phys. Rev. A 95, 043818 (2017).
- G. Ferioli, A. Glicenstein, I. Ferrier-Barbut, and A. Browaeys, A non-equilibrium superradiant phase transition in free space, Nat. Phys. 19, 1345 (2023).
- S. J. Masson and A. Asenjo-Garcia, Universality of Dicke superradiance in arrays of quantum emitters, Nat. Commun. 13, 2285 (2022).
- A. Ishizaki and G. R. Fleming, Quantum coherence in photosynthetic light harvesting, Annu. Rev. Condens. Matter Phys. 3, 333 (2012).
- A. González-Tudela, V. Paulisch, D. E. Chang, H. Kimble, and J. I. Cirac, Deterministic generation of arbitrary photonic states assisted by dissipation, Phys. Rev. Lett. 115, 163603 (2015).
- Z. Wang, T. Jaako, P. Kirton, and P. Rabl, Supercorrelated radiance in nonlinear photonic waveguides, Phys. Rev. Lett. 124, 213601 (2020).
- D. Rivero, C. A. Pessoa Jr., G. H. De França, R. C. Teixeira, S. Slama, and P. W. Courteille, Quantum resonant optical bistability with a narrow atomic transition: Bistability phase diagram in the bad cavity regime, New J. Phys. 25, 093053 (2023).
- C. Hotter, L. Ostermann, and H. Ritsch, Cavity sub- and superradiance for transversely driven atomic ensembles, Phys. Rev. Res. 5, 013056 (2023).
- E. Y. Song et al., A dissipation-induced superradiant transition in a strontium cavity-QED system, Sci. Adv. 11, eadu5799 (2025).
- R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).
- P. D. Drummond and H. J. Carmichael, Volterra cycles and the cooperative fluorescence critical point, Opt. Commun. 27, 160 (1978).
- H. J. Carmichael, Analytical and numerical results for the steady state in cooperative resonance fluorescence, J. Phys. B 13, 3551 (1980).
- E. M. Kessler, G. Giedke, A. Imamoglu, S. F. Yelin, M. D. Lukin, and J. I. Cirac, Dissipative phase transition in a central spin system, Phys. Rev. A 86, 012116 (2012).
- C. Sánchez Muñoz, B. Buča, J. Tindall, A. González-Tudela, D. Jaksch, and D. Porras, Symmetries and conservation laws in quantum trajectories: Dissipative freezing, Phys. Rev. A 100, 042113 (2019).
- D. Barberena, R. J. Lewis-Swan, J. K. Thompson, and A. M. Rey, Driven-dissipative quantum dynamics in ultra-long-lived dipoles in an optical cavity, Phys. Rev. A 99, 053411 (2019).
- O. Somech and E. Shahmoon, Quantum entangled states of a classically radiating macroscopic spin, PRX Quantum 5, 010349 (2024).
- A. Gonzalez-Tudela and D. Porras, Mesoscopic entanglement induced by spontaneous emission in solid-state quantum optics, Phys. Rev. Lett. 110, 080502 (2013).
- T. E. Lee, C.-K. Chan, and S. F. Yelin, Dissipative phase transitions: Independent versus collective decay and spin squeezing, Phys. Rev. A 90, 052109 (2014).
- C. Qu and A. M. Rey, Spin squeezing and many-body dipolar dynamics in optical lattice clocks, Phys. Rev. A 100, 041602(R) (2019).
- O. Somech, Y. Shimshi, and E. Shahmoon, Heisenberg-Langevin approach to driven superradiance, Phys. Rev. A 108, 023725 (2023).
- I. Bloch, Ultracold quantum gases in optical lattices, Nat. Phys. 1, 23 (2005).
- D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays, Science 354, 1021 (2016).
- M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, Atom-by-atom assembly of defect-free one-dimensional cold atom arrays, Science 354, 1024 (2016).
- J. Rui, D. Wei, A. Rubio-Abadal, S. Hollerith, J. Zeiher, D. M. Stamper-Kurn, C. Gross, and I. Bloch, A subradiant optical mirror formed by a single structured atomic layer, Nature (London) 583, 369 (2020).
- R. J. Bettles, S. A. Gardiner, and C. S. Adams, Enhanced optical cross section via collective coupling of atomic dipoles in a 2D array, Phys. Rev. Lett. 116, 103602 (2016).
- E. Shahmoon, D. S. Wild, M. D. Lukin, and S. F. Yelin, Cooperative resonances in light scattering from two-dimensional atomic arrays, Phys. Rev. Lett. 118, 113601 (2017).
- A. Asenjo-Garcia, M. Moreno-Cardoner, A. Albrecht, H. J. Kimble, and D. E. Chang, Exponential improvement in photon storage fidelities using subradiance and “selective radiance” in atomic arrays, Phys. Rev. X 7, 031024 (2017).
- A. Grankin, P. O. Guimond, D. V. Vasilyev, B. Vermersch, and P. Zoller, Free-space photonic quantum link and chiral quantum optics, Phys. Rev. A 98, 043825 (2018).
- A. Cidrim, T. S. do Espirito Santo, J. Schachenmayer, R. Kaiser, and R. Bachelard, Photon blockade with ground-state neutral atoms, Phys. Rev. Lett. 125, 073601 (2020).
- C. D. Parmee and J. Ruostekoski, Bistable optical transmission through arrays of atoms in free space, Phys. Rev. A 103, 033706 (2021).
- F. Robicheaux and D. A. Suresh, Beyond lowest order mean-field theory for light interacting with atom arrays, Phys. Rev. A 104, 023702 (2021).
- D. Fernández-Fernández and A. González-Tudela, Tunable directional emission and collective dissipation with quantum metasurfaces, Phys. Rev. Lett. 128, 113601 (2022).
- S. P. Pedersen, L. Zhang, and T. Pohl, Quantum nonlinear metasurfaces from dual arrays of ultracold atoms, Phys. Rev. Res. 5, L012047 (2023).
- Y. Solomons, R. Ben-Maimon, and E. Shahmoon, Universal approach for quantum interfaces with atomic arrays, arXiv:2302.04913.
- Z. Yan, J. Ho, Y.-H. Lu, S. J. Masson, A. Asenjo-Garcia, and D. M. Stamper-Kurn, Superradiant and subradiant cavity scattering by atom arrays, Phys. Rev. Lett. 131, 253603 (2023).
- K. Hammerer, A. S. Sørensen, and E. S. Polzik, Quantum interface between light and atomic ensembles, Rev. Mod. Phys. 82, 1041 (2010).
- S. L. Bromley, B. Zhu, M. Bishof, X. Zhang, T. Bothwell, J. Schachenmayer, T. L. Nicholson, R. Kaiser, S. F. Yelin, M. D. Lukin, A. M. Rey, and J. Ye, Collective atomic scattering and motional effects in a dense coherent medium, Nat. Commun. 7, 11039 (2016).
- W. Guerin, M. O. Araújo, and R. Kaiser, Subradiance in a large cloud of cold atoms, Phys. Rev. Lett. 116, 083601 (2016).
- B. Olmos, D. Yu, and I. Lesanovsky, Steady-state properties of a driven atomic ensemble with nonlocal dissipation, Phys. Rev. A 89, 023616 (2014).
- D. Goncalves, L. Bombieri, G. Ferioli, S. Pancaldi, I. Ferrier-Barbut, A. Browaeys, E. Shahmoon, and D. E. Chang, Driven-dissipative phase separation in free-space atomic ensembles, PRX Quantum 6, 020303 (2025).
- S. Agarwal, E. Chaparro, D. Barberena, A. P. Orioli, G. Ferioli, S. Pancaldi, I. Ferrier-Barbut, A. Browaeys, and A. M. Rey, Directional superradiance in a driven ultracold atomic gas in free-space, PRX Quantum 5, 040335 (2024).
- K. Tucker, D. Barberena, R. J. Lewis-Swan, J. K. Thompson, J. G. Restrepo, and A. M. Rey, Facilitating spin squeezing generated by collective dynamics with single-particle decoherence, Phys. Rev. A 102, 051701(R) (2020).
- S. J. Masson, I. Ferrier-Barbut, L. A. Orozco, A. Browaeys, and A. Asenjo-Garcia, Many-body signatures of collective decay in atomic chains, Phys. Rev. Lett. 125, 263601 (2020).
- M. Xu, D. A. Tieri, and M. J. Holland, Simulating open quantum systems by applying SU(4) to quantum master equations, Phys. Rev. A 87, 062101 (2013).
- F. Damanet, D. Braun, and J. Martin, Cooperative spontaneous emission from indistinguishable atoms in arbitrary motional quantum states, Phys. Rev. A 94, 033838 (2016).
- N. Shammah, N. Lambert, F. Nori, and S. De Liberato, Superradiance with local phase-breaking effects, Phys. Rev. A 96, 023863 (2017).
- Y. Zhang, Y.-X. Zhang, and K. Mølmer, Monte-Carlo simulations of superradiant lasing, New J. Phys. 20, 112001 (2018).
- D. Roberts and A. A. Clerk, Exact solution of the infinite-range dissipative transverse-field Ising model, Phys. Rev. Lett. 131, 190403 (2023).
- 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).
- J. R. Johansson, P. D. Nation, and F. Nori, QuTiP 2: A Python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184, 1234 (2013).
- D. Nigro, On the uniqueness of the steady-state solution of the Lindblad–Gorini–Kossakowski–Sudarshan equation, J. Stat. Mech. (2019) 043202.
- K. Binder and D. P. Landau, Finite-size scaling at first-order phase transitions, Phys. Rev. B 30, 1477 (1984).
- F. Minganti, A. Biella, N. Bartolo, and C. Ciuti, Spectral theory of Liouvillians for dissipative phase transitions, Phys. Rev. A 98, 042118 (2018).
- F. Vicentini, F. Minganti, R. Rota, G. Orso, and C. Ciuti, Critical slowing down in driven-dissipative Bose-Hubbard lattices, Phys. Rev. A 97, 013853 (2018).
- K. Ptaszyński and M. Esposito, Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling, Phys. Rev. E 110, 044134 (2024).
- T. E. Lee, H. Häffner, and M. C. Cross, Collective quantum jumps of Rydberg atoms, Phys. Rev. Lett. 108, 023602 (2012).
- R. M. Wilson, K. W. Mahmud, A. Hu, A. V. Gorshkov, M. Hafezi, and M. Foss-Feig, Collective phases of strongly interacting cavity photons, Phys. Rev. A 94, 033801 (2016).
- J. Gelhausen and M. Buchhold, Dissipative Dicke model with collective atomic decay: Bistability, noise-driven activation, and the nonthermal first-order superradiance transition, Phys. Rev. A 97, 023807 (2018).
- P. Brookes, G. Tancredi, A. D. Patterson, J. Rahamim, M. Esposito, T. K. Mavrogordatos, P. J. Leek, E. Ginossar, and M. H. Szymanska, Critical slowing down in circuit quantum electrodynamics, Sci. Adv. 7, eabe9492 (2021).
- F. Minganti, V. Savona, and A. Biella, Dissipative phase transitions in -photon driven quantum nonlinear resonators, Quantum 7, 1170 (2023).
- B. Gábor, D. Nagy, A. Vukics, and P. Domokos, Quantum bistability in the hyperfine ground state of atoms, Phys. Rev. Res. 5, L042038 (2023).
- K. Mølmer, Y. Castin, and J. Dalibard, Monte Carlo wave-function method in quantum optics, J. Opt. Soc. Am. B 10, 524 (1993).
- H. J. Carmichael, Breakdown of photon blockade: A dissipative quantum phase transition in zero dimensions, Phys. Rev. X 5, 031028 (2015).
- C. Savage and H. Carmichael, Single atom optical bistability, IEEE J. Quantum Electron. 24, 1495 (1988).
- G. Ferioli, A. Glicenstein, F. Robicheaux, R. T. Sutherland, A. Browaeys, and I. Ferrier-Barbut, Laser-driven superradiant ensembles of two-level atoms near Dicke regime, Phys. Rev. Lett. 127, 243602 (2021).
- W.-K. Mok, A. Poddar, E. Sierra, C. C. Rusconi, J. Preskill, and A. Asenjo-Garcia, Universal scaling laws for correlated decay of many-body quantum systems, arXiv:2406.00722.
- N. Leppenen and E. Shahmoon, Quantum correlated steady states under competing collective and individual decay [Dataset], Zenodo, 2026, https://doi.org/10.5281/zenodo.21358207.
- Y. Solomons and E. Shahmoon, Multichannel waveguide QED with atomic arrays in free space, Phys. Rev. A 107, 033709 (2023).
- M. W. Hirsch, R. L. Devaney, and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra (Elsevier Science & Technology, San Diego, 1974).
- A. Cabot, L. S. Muhle, F. Carollo, and I. Lesanovsky, Quantum trajectories of dissipative time crystals, Phys. Rev. A 108, L041303 (2023).