- Open Access
Stabilizing Open Photon Condensates by Ghost-Attractor Dynamics
Phys. Rev. Lett. 135, 053402 – Published 29 July, 2025
DOI: https://doi.org/10.1103/hcsq-dwcg
Abstract
We study the temporal, driven-dissipative dynamics of open photon Bose-Einstein condensates (BEC) in a dye-filled microcavity, taking the condensate amplitude and the noncondensed fluctuations into account on the same footing by means of a cumulant expansion within the Lindblad formalism. The fluctuations fundamentally alter the dynamics in that the BEC always dephases to zero for a sufficiently long time. However, a ghost attractor, although outside of the physically accessible configuration space, attracts the dynamics and leads to a plateaulike stabilization of the BEC for an exponentially long time, consistent with experiments. We also show that the photon BEC and the lasing state are separated by a true phase transition, since they are characterized by different fixed points. The ghost-attractor nonequilibrium stabilization mechanism is an alternative to prethermalization and may possibly be realized on other dynamical platforms as well.
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References (44)
- I. Carusotto and C. Ciuti, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013).
- J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Bose–Einstein condensation of photons in an optical microcavity, Nature (London) 468, 545 (2010).
- J. Marelic and R. A. Nyman, Experimental evidence for inhomogeneous pumping and energy-dependent effects in photon Bose-Einstein condensation, Phys. Rev. A 91, 033813 (2015).
- S. Greveling, K. L. Perrier, and D. van Oosten, Density distribution of a Bose-Einstein condensate of photons in a dye-filled microcavity, Phys. Rev. A 98, 013810 (2018).
- J. Bloch, I. Carusotto, and M. Wouters, Non-equilibrium Bose–Einstein condensation in photonic systems, Nat. Rev. Phys. 4, 470 (2022).
- R. A. Nyman and B. T. Walker, Bose-Einstein condensation of photons from the thermodynamic limit to small photon numbers, J. Mod. Opt. 65, 754 (2018).
- K. Karkihalli Umesh, J. Schulz, J. Schmitt, M. Weitz, G. von Freymann, and F. Vewinger, Dimensional cross-over in a quantum gas of light, Nat. Phys. 20, 1810 (2024).
- B. T. Walker, L. C. Flatten, H. J. Hesten, F. Mintert, D. Hunger, A. A. Trichet, J. M. Smith, and R. A. Nyman, Driven-dissipative non-equilibrium Bose-Einstein condensation of less than ten photons, Nat. Phys. 14, 1173 (2018).
- J. Schmitt, T. Damm, D. Dung, C. Wahl, F. Vewinger, J. Klaers, and M. Weitz, Spontaneous symmetry breaking and phase coherence of a photon Bose-Einstein condensate coupled to a reservoir, Phys. Rev. Lett. 116, 033604 (2016).
- E. Busley, L. E. Miranda, A. Redmann, C. Kurtscheid, K. K. Umesh, F. Vewinger, M. Weitz, and J. Schmitt, Compressibility and the equation of state of an optical quantum gas in a box, Science 375, 1403 (2022).
- F. E. Öztürk, F. Vewinger, M. Weitz, and J. Schmitt, Fluctuation-dissipation relation for a Bose-Einstein condensate of photons, Phys. Rev. Lett. 130, 033602 (2023).
- F. E. Öztürk, T. Lappe, G. Hellmann, J. Schmitt, J. Klaers, F. Vewinger, J. Kroha, and M. Weitz, Observation of a non-Hermitian phase transition in an optical quantum gas, Science 372, 88 (2021).
- M. Pieczarka, M. Gębski, A. N. Piasecka, J. A. Lott, A. Pelster, M. Wasiak, and T. Czyszanowski, Bose–Einstein condensation of photons in a vertical-cavity surface-emitting laser, Nat. Photonics 18, 1090 (2024).
- J. Schmitt, T. Damm, D. Dung, F. Vewinger, J. Klaers, and M. Weitz, Observation of grand-canonical number statistics in a photon Bose-Einstein condensate, Phys. Rev. Lett. 112, 030401 (2014).
- J. Marelic, B. T. Walker, and R. A. Nyman, Phase-space views into dye-microcavity thermalized and condensed photons, Phys. Rev. A 94, 063812 (2016).
- Y. Tang, H. S. Dhar, R. F. Oulton, R. A. Nyman, and F. Mintert, Breakdown of temporal coherence in photon condensates, Phys. Rev. Lett. 132, 173601 (2024).
- F. E. Ozturk, T. Lappe, G. Hellmann, J. Schmitt, J. Klaers, F. Vewinger, J. Kroha, and M. Weitz, Fluctuation dynamics of an open photon Bose-Einstein condensate, Phys. Rev. A 100, 043803 (2019).
- V. N. Gladilin and M. Wouters, Classical field model for arrays of photon condensates, Phys. Rev. A 101, 043814 (2020).
- V. N. Gladilin and M. Wouters, Vortices in nonequilibrium photon condensates, Phys. Rev. Lett. 125, 215301 (2020).
- P. Kirton and J. Keeling, Nonequilibrium model of photon condensation, Phys. Rev. Lett. 111, 100404 (2013).
- P. Kirton and J. Keeling, Thermalization and breakdown of thermalization in photon condensates, Phys. Rev. A 91, 033826 (2015).
- M. Radonjić, W. Kopylov, A. Balaź, and A. Pelster, Interplay of coherent and dissipative dynamics in condensates of light, New J. Phys. 20, 055014 (2018).
- B. T. Walker, H. J. Hesten, H. S. Dhar, R. A. Nyman, and F. Mintert, Noncritical slowing down of photonic condensation, Phys. Rev. Lett. 123, 203602 (2019).
- T. Bode, M. Kajan, F. Meirinhos, and J. Kroha, Non-Markovian dynamics of open quantum systems via auxiliary particles with exact operator constraint, Phys. Rev. Res. 6, 013220 (2024).
- P. Fowler-Wright, B. W. Lovett, and J. Keeling, Efficient many-body non-Markovian dynamics of organic polaritons, Phys. Rev. Lett. 129, 173001 (2022).
- S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity) (Westview Press, Cambridge, MA, 2001), Vol. 1.
- S. H. Strogatz and R. M. Westervelt, Predicted power laws for delayed switching of charge-density waves, Phys. Rev. B 40, 10501 (1989).
- D. Koch, A. Nandan, G. Ramesan, I. Tyukin, A. Gorban, and A. Koseska, Ghost channels and ghost cycles guiding long transients in dynamical systems, Phys. Rev. Lett. 133, 047202 (2024).
- E. U. Condon, Nuclear motions associated with electron transitions in diatomic molecules, Phys. Rev. 32, 858 (1928).
- H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2007).
- A. J. Moilanen, K. B. Arnardóttir, J. Keeling, and P. Törmä, Mode switching dynamics in organic polariton lasing, Phys. Rev. B 106, 195403 (2022).
- J. Keeling and S. Kéna-Cohen, Bose–Einstein condensation of exciton-polaritons in organic microcavities, Annu. Rev. Phys. Chem. 71, 435 (2020).
- J. C. L. Carreño, C. Sánchez Muñoz, E. del Valle, and F. P. Laussy, Excitation with quantum light. II. Exciting a two-level system, Phys. Rev. A 94, 063826 (2016).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/hcsq-dwcg for the detailed calculation of fixed points and their linear stability analysis and representative dynamics at lower pumping with fewer photon numbers.
- J. Schmitt, M. Weitz, and J. Klaers, Absorption and emission spectral data of room- temperature rhodamine 6G dye solution and some typical dye microcavity parameters, Zenodo, 10.5281/zenodo.10852936 (2024).
- M. Moeckel and S. Kehrein, Interaction quench in the Hubbard model, Phys. Rev. Lett. 100, 175702 (2008).
- M. Kollar, F. A. Wolf, and M. Eckstein, Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems, Phys. Rev. B 84, 054304 (2011).
- B. Bertini, F. H. L. Essler, S. Groha, and N. J. Robinson, Prethermalization and thermalization in models with weak integrability breaking, Phys. Rev. Lett. 115, 180601 (2015).
- K. Mallayya, M. Rigol, and W. De Roeck, Prethermalization and thermalization in isolated quantum systems, Phys. Rev. X 9, 021027 (2019).
- S. Ray, J. R. Anglin, and A. Vardi, Prethermalization with negative specific heat, Phys. Rev. E 102, 052107 (2020).
- R. Hanai, A. Edelman, Y. Ohashi, and P. B. Littlewood, Non-Hermitian phase transition from a polariton Bose-Einstein condensate to a photon laser, Phys. Rev. Lett. 122, 185301 (2019).
- A. V. Bezvershenko, C.-M. Halati, A. Sheikhan, C. Kollath, and A. Rosch, Dicke transition in open many-body systems determined by fluctuation effects, Phys. Rev. Lett. 127, 173606 (2021).
- T. Wu, S. Ray, and J. Kroha, Temporal bistability in the dissipative Dicke-Bose-Hubbard system, Ann. Phys. (Berlin) 536, 2300505 (2024).
- A. Abouelela, M. Turaev, R. Kramer, M. Janning, M. Kajan, S. Ray, and J. Kroha, Figure data for Stabilizing open photon condensates by ghost-attractor dynamics, Zenodo, 10.5281/zenodo.15830145 (2025).