arXiv:2603.21927

Emergent thermal fluctuations and non-Hermitian phase transitions in open photon condensates

Moritz Janning, Roman Kramer, Michael Turaev, Sayak Ray, Johann Kroha

cond-mat.quant-gascond-mat.stat-mechquant-phSubmitted Mar 23, 2026• Announced Mar 24, 2026• 0 citations

Abstract

We investigate the nonequilibrium dynamics of an open photon Bose-Einstein condensate in a dye-filled microcavity using a Lindblad master-equation approach, treating the condensate and the noncondensed fluctuations on the same footing. The driven-dissipative condensate exhibits a long-lived, metastable plateau stabilized by a ghost attractor, a fixed point that lies outside the physical domain in configuration space, yet stalls the condensate dynamics for exceedingly long times before it dephases to zero [Phys. Rev. Lett. 135, 053402 (2025)]. Despite the nonequilibrium origin of this dynamical stabilization, the condensate exhibits quasithermal fluctuations in the plateau in that the relative order-parameter fluctuations scale as the inverse square root of the system size. A linear stability analysis further reveals the presence of exceptional points, resulting in multiple non-Hermitian phase transitions associated with the relaxation dynamics into and out of the metastable condensate.

Comments: 8 pages, 8 figures

Related papers

Stabilizing Open Photon Condensates by Ghost-Attractor Dynamics

Aya Abouelela, Michael Turaev, Roman Kramer +4 more

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.

arXiv:2503.16695Physical Review LettersJul 7, 20250 citations

Non-equilibrium dynamics in multi-mode and multi-cavity photon resonators

Aya Abouelela

This thesis explores the non-equilibrium dynamics of photons in optical micro-resonators, focusing on how coherence and collective behavior emerge in driven and dissipative systems. Starting from a microscopic description, we derive a Lindblad master equation under the assumptions of Markovian dynamics and fast molecular relaxation. By employing a cumulant expansion technique, we obtain a closed set of coupled dynamical equations for relevant observables, providing a method to analyze the system dynamics. A central aspect of this work is the explicit incorporation of U(1) symmetry-breaking fields to describe photon coherence. This formulation allows us to establish a distinction between coherent (condensed) and incoherent (thermal) photon populations, even at the level of a single-mode resonator. Within this framework, we study the temporal stability of the condensate and show that its persistence is governed by a key mechanism, the presence of a so-called ghost attractor. Although this fixed point lies outside the physical parameter space, its basin of attraction strongly influences the system dynamics, which results in stabilizing the condensate over an extended period of time before it eventually decays to zero. Additionally, we investigate the stability of the system by analyzing fluctuations around its fixed points. This analysis reveals the presence of exceptional points in the parameter space, signaling non-Hermitian phase transitions. These exceptional points separate the dynamics into two qualitatively different dynamical regimes, namely, a weakly-damped oscillatory regime, and a purely dissipative regime with bi-exponential decay. Finally, we investigate the possibility of generating quantum correlations and entanglement in a system of two coupled micro-resonators. Despite the presence of coherent dynamics and inter-cavity coupling, our results show that the photon states remain separable throughout the time evolution. This conclusion is supported by the evaluation of continuous-variable entanglement criteria for Gaussian states, which naturally arise within the cumulant expansion framework.

Sep 30, 20260 citations

Fluctuation dynamics of an open photon Bose-Einstein condensate

Fahri Emre Ozturk, Tim Lappe, Göran Hellmann +5 more

The dynamics of a Bose-Einstein condensate of photons is investigated experimentally and theoretically. An oscillatory behavior of the second-order photon number correlation function is observed in two-dimensional photon gases in a dye-filled optical microcavity and explained by a theoretical model derived from nonlinear rate equations. This behavior is traced back to the weakly driven-dissipative nature of the system, leading to a breaking of time-reversal symmetry.

arXiv:1908.00883Physical Review AOct 2, 201912 citations

Observation of a non-Hermitian phase transition in an optical quantum gas

Fahri Emre Öztürk, Tim Lappe, Göran Hellmann +5 more

Quantum gases of light, such as photon or polariton condensates in optical microcavities, are collective quantum systems enabling a tailoring of dissipation from, for example, cavity loss. This characteristic makes them a tool to study dissipative phases, an emerging subject in quantum many-body physics. We experimentally demonstrate a non-Hermitian phase transition of a photon Bose-Einstein condensate to a dissipative phase characterized by a biexponential decay of the condensate's second-order coherence. The phase transition occurs because of the emergence of an exceptional point in the quantum gas. Although Bose-Einstein condensation is usually connected to lasing by a smooth crossover, the observed phase transition separates the biexponential phase from both lasing and an intermediate, oscillatory condensate regime. Our approach can be used to study a wide class of dissipative quantum phases in topological or lattice systems.

arXiv:2010.15829ScienceApr 1, 202192 citations

From lasers to photon Bose–Einstein condensates: a unified description via an open-dissipative Bose–Einstein distribution

Joshua Krauß, Enrico Stein, Axel Pelster

Abstract Photon condensation was first experimentally realized in 2010 within a dye-filled microcavity at room temperature. Since then, interest in the field has increased significantly, as a photon Bose-Einstein condensate (BEC) represents a prototypical driven-dissipative system. Here, we investigate how its inherent open nature influences the condensation process both quantitatively and qualitatively. To this end, we consider a mean-field model, which can be derived microscopically from a Lindblad master equation. The underlying rate equations depend on various external parameters such as emission and absorption rates of the dye molecules as well as the cavity photon loss rate. In steady state, we obtain an open-dissipative Bose-Einstein distribution for the mode occupations. The chemical potential of this distribution depends on the occupations of the dye molecules in both their ground and excited state and must therefore be determined self-consistently. We find that the resulting photon distribution is strongly influenced by the driven-dissipative parameters. Based on this result, we identify the main differences between a photonic BEC, an atomic BEC, and a laser.

arXiv:2510.05917The European Physical Journal Special TopicsMar 9, 20261 citation

Non-Markovian Dynamics of Open Bose-Einstein Condensates

Tim Lappe

Quantum many-body systems coupling photonic and matter degrees of freedom are ideal for the realization of driven open quantum dynamics at the intersection of quantum optics and condensed matter. They offer the possibility to address unresolved issues regarding a variety of non-equilibrium phenomena. In such open systems, the substructure of the reservoir then introduces further timescales that may enter into competition with rapid system processes, raising long-standing questions about the influence of non-Markovian effects on dynamics and equilibration out of equilibrium. \n \nThe central result of this thesis is a general pseudo-particle technique that can be applied to a large class of models of interacting light and matter and allows for realistic and efficient simulations of the full non-equilibrium dynamics of these systems. Since organic molecules, as used in experiments with photon condensates, which provide the main area of application for this thesis, possess an electronic transition coupled to vibrational phonon modes, we construct a representation where an auxiliary boson is assigned to each vibrational state of the molecule. An operator constraint then enforces single occupation across all of these states. We emphasize that we implement the operator constraint exactly and that we are the first to apply a faithful auxiliary-boson representation to open quantum systems. \n \nAs a contribution to bridging the gap between well-understood equilibrium and less explored non-equilibrium phenomena, we investigate photon condensates as they are driven away from equilibrium. The earliest signs of the non-equilibrium character of the driven-dissipative photon gas do not manifest in the spectrally resolved intensity distribution but in the time dependence of the intensity fluctuations. The energy flow through the system renders it {non-Hermitian} and induces a novel driven-dissipative transition in the second-order correlations characterized by the appearance of exceptional points. If only the static intensity spectrum is monitored, this transition remains unnoticed, as does the fact that the system is not truly in equilibrium. Non-Markovian effects due to the non-separability of system and reservoir timescales are shown to become important far away from equilibrium. Furthermore, we derive a novel photon-condensate Gross-Pitaevskii equation, which is capable of describing photo-molecular coherence. Such effects cannot be captured by existing theories and hence serve as a validation of our auxiliary-boson method. These results provide a building block to understanding the properties of the photon condensates in stationary operation where they act as fluctuating light sources. In the future, lattice systems of coupled photon condensates may lead to the appearance of novel driven-dissipative phases of light.

Mar 8, 20216 citations