Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2502.14986 · Physical Review Letters

Time-Periodic Driving of a Bath-Coupled Open Quantum Gas of Light

Andris Erglis, Alexander Sazhin, Frank Vewinger, Martin Weitz, Stefan Yoshi Buhmann, Julian Schmitt

Published Jun 10, 2025• 4 citations
arXivHTMLPDF

Abstract

We study the frequency-resolved density response of a photon Bose-Einstein condensate coupled to a bath of dye molecules by time-periodic driving. By monitoring the photon number dynamics for different drive frequencies, we obtain the spectral response of the condensate in a phase-sensitive way. We find that as the photon number increases, the response of the coupled condensate-bath system transitions from overdamped to resonant behavior, indicating a transition from closed to open system dynamics. Our spectroscopy method paves the way for studies of collective excitations in complex driven-dissipative systems.

DOI
10.1103/922g-1fng

Related papers

Dynamics and correlations of a Bose–Einstein condensate of photons

Julian Schmitt

Abstract The Tutorial reports recent experimental advances in studies of the dynamics as well as the number and phase correlations of a Bose–Einstein condensed photon gas confined in a high-finesse dye-filled microcavity. Repeated absorption–emission-processes of photons on dye molecules here establish a thermal coupling of the photonic quantum gas to both a heat bath and a particle reservoir comprised of dye molecules. In this way, for the first time Bose–Einstein condensation under grand-canonical statistical ensemble conditions becomes experimentally accessible. The work presented in this Tutorial was one of the four shortlisted finalists of the 2017 DPG SAMOP dissertation prize.

arXiv:1807.08747•Journal of Physics B Atomic Molecular and Optical Physics•Jul 17, 2018•24 citations

Observation of nonlinear response and Onsager regression in a photon Bose-Einstein condensate

Alexander Sazhin, V. N. Gladilin, Andris Erglis +5 more

The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the single-time averages. This provides a powerful framework for the investigation of the intrinsic microscopic behaviour of physical systems by studying their macroscopic response to a controlled external perturbation. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath. This confirms the regression theorem for a quantum gas, and, moreover, demonstrates it in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored. For strong perturbations, we observe nonlinear relaxation dynamics which our microscopic theory relates to the equilibrium fluctuations, thereby extending the regression theorem beyond the regime of linear response.

arXiv:2403.04705•Nature Communications•Jun 3, 2024•7 citations

Many-body phenomena in a Bose-Einstein condensate of light

Arie‐Willem de Leeuw

In this thesis we study Bose-Einstein condensation of photons. In Chapter 1 we describe the current experimental set-up and we explain the two important features of the Bose-Einstein condensate of light: dissipation through the interaction with the external reservoir of dye molecules and driving by the external pumping. In Chapter 2 we use the Schwinger-Keldysh formalism to describe the complete time evolution of the light. We show that the finite-lifetime effects of the photons due to the interaction with the dye can be characterized by a single dimensionless parameter, that depends on the power of the external laser pumping the dye. We also determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases. In Chapter 3 we demonstrate that the finite-lifetime effects on the spatial first-order correlation functions of the condensed light are negligible, but are important for the temporal first-order correlations. Furthermore, we show that in the normal state the first-order correlations of the photons are suppressed by the interaction with the dye. In Chapter 4 we develop a model to describe the effect of interactions on the number fluctuations in Bose-Einstein condensates. We find good agreement between the observed number fluctuations in the light Bose-Einstein condensate and the results of our model for different interaction strenghts. In Chapter 5 we propose an experiment to observe phase diffusion in the Bose-Einstein condensate of photons and we predict the outcome of individual measurements. In our model we incorporate quantum and thermal fluctuations as well as the finite-lifetime effects. In Chapter 6 we investigate the light in the presence of a periodic potential and we study the transition from a superfluid to a Mott-insulator. We demonstrate that in this system the true Mott-insulating state is longer present due the interactions with the dye molecules. Finally, in Chapter 7 we consider Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities. We demonstrate that in this system there is also a single dimensionless damping parameter that depends on the external pumping. We propose to use the experimental freedom to investigate the superfluidity of the photons via the excitation of scissors modes. We determine the frequency and damping of these scissors modes. We also calculate the density-density correlations of the excited light fluid and we show that this contains a signature of the dynamical Casimir effect.

•Jun 22, 2016•0 citations

Giant critical response in a driven-dissipative quantum gas

Ross C. Schofield, Daniel Lim, Himadri S. Dhar +6 more

Systems close to a phase transition turn weak perturbations into large responses. At equilibrium, this amplification is closely linked to criticality: fluctuations grow, dynamics slow, and a common soft mode controls the response. Whether this correspondence survives in driven-dissipative quantum systems, sustained by continuous pumping and loss away from thermal equilibrium, remains an open question. Here we show experimentally that it does. In a room-temperature semiconductor photon Bose-Einstein condensate, the critical slowing of spontaneous intensity fluctuations and the amplification of weak pump perturbations are measured independently. Both peak at the same condensate population, $\bar{n}_c = 1250$, where the dimensionless slowing factor and susceptibility reach the same value, $\bar{n}_c/2 = 625$. A single weakly damped collective photon-reservoir mode governs both effects. This fluctuation-response correspondence in a finite open quantum gas establishes critical susceptibility as a measurable dynamical signature of condensation, with peak gain set by system size.

cond-mat.quant-gasCross-listedarXiv:2605.11230•May 13, 2026•0 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:1908.00883•Physical Review A•Oct 2, 2019•12 citations

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, 2021•6 citations
We study the frequency-resolved density response of a photon Bose-Einstein condensate coupled to a bath of dye molecules by time-periodic driving. By monitoring the photon number dynamics for different drive frequencies, we obtain the spectral response of the condensate in a phase-sensitive way. We find that as the photon number increases, the response of the coupled condensate-bath system transitions from overdamped to resonant behavior, indicating a transition from closed to open system dynamics. Our spectroscopy method paves the way for studies of collective excitations in complex driven-dissipative systems.
Abstract The Tutorial reports recent experimental advances in studies of the dynamics as well as the number and phase correlations of a Bose–Einstein condensed photon gas confined in a high-finesse dye-filled microcavity. Repeated absorption–emission-processes of photons on dye molecules here establish a thermal coupling of the photonic quantum gas to both a heat bath and a particle reservoir comprised of dye molecules. In this way, for the first time Bose–Einstein condensation under grand-canonical statistical ensemble conditions becomes experimentally accessible. The work presented in this Tutorial was one of the four shortlisted finalists of the 2017 DPG SAMOP dissertation prize.
The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the single-time averages. This provides a powerful framework for the investigation of the intrinsic microscopic behaviour of physical systems by studying their macroscopic response to a controlled external perturbation. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath. This confirms the regression theorem for a quantum gas, and, moreover, demonstrates it in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored. For strong perturbations, we observe nonlinear relaxation dynamics which our microscopic theory relates to the equilibrium fluctuations, thereby extending the regression theorem beyond the regime of linear response.
In this thesis we study Bose-Einstein condensation of photons. In Chapter 1 we describe the current experimental set-up and we explain the two important features of the Bose-Einstein condensate of light: dissipation through the interaction with the external reservoir of dye molecules and driving by the external pumping. In Chapter 2 we use the Schwinger-Keldysh formalism to describe the complete time evolution of the light. We show that the finite-lifetime effects of the photons due to the interaction with the dye can be characterized by a single dimensionless parameter, that depends on the power of the external laser pumping the dye. We also determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases. In Chapter 3 we demonstrate that the finite-lifetime effects on the spatial first-order correlation functions of the condensed light are negligible, but are important for the temporal first-order correlations. Furthermore, we show that in the normal state the first-order correlations of the photons are suppressed by the interaction with the dye. In Chapter 4 we develop a model to describe the effect of interactions on the number fluctuations in Bose-Einstein condensates. We find good agreement between the observed number fluctuations in the light Bose-Einstein condensate and the results of our model for different interaction strenghts. In Chapter 5 we propose an experiment to observe phase diffusion in the Bose-Einstein condensate of photons and we predict the outcome of individual measurements. In our model we incorporate quantum and thermal fluctuations as well as the finite-lifetime effects. In Chapter 6 we investigate the light in the presence of a periodic potential and we study the transition from a superfluid to a Mott-insulator. We demonstrate that in this system the true Mott-insulating state is longer present due the interactions with the dye molecules. Finally, in Chapter 7 we consider Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities. We demonstrate that in this system there is also a single dimensionless damping parameter that depends on the external pumping. We propose to use the experimental freedom to investigate the superfluidity of the photons via the excitation of scissors modes. We determine the frequency and damping of these scissors modes. We also calculate the density-density correlations of the excited light fluid and we show that this contains a signature of the dynamical Casimir effect.
Systems close to a phase transition turn weak perturbations into large responses. At equilibrium, this amplification is closely linked to criticality: fluctuations grow, dynamics slow, and a common soft mode controls the response. Whether this correspondence survives in driven-dissipative quantum systems, sustained by continuous pumping and loss away from thermal equilibrium, remains an open question. Here we show experimentally that it does. In a room-temperature semiconductor photon Bose-Einstein condensate, the critical slowing of spontaneous intensity fluctuations and the amplification of weak pump perturbations are measured independently. Both peak at the same condensate population, nˉc=1250\bar{n}_c = 1250nˉc​=1250, where the dimensionless slowing factor and susceptibility reach the same value, nˉc/2=625\bar{n}_c/2 = 625nˉc​/2=625. A single weakly damped collective photon-reservoir mode governs both effects. This fluctuation-response correspondence in a finite open quantum gas establishes critical susceptibility as a measurable dynamical signature of condensation, with peak gain set by system size.
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.