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:1609.01554 · Physical Review A

Phase-space views into dye-microcavity thermalized and condensed photons

Jakov Marelic, Benjamin T. Walker, Robert A. Nyman

Published Dec 5, 2016• 18 citations
arXivHTMLPDF

Abstract

We have observed momentum- and position-resolved spectra and images of the photoluminescence from thermalized and condensed dye-microcavity photons. The spectra yield the dispersion relation and the potential energy landscape for the photons. From this dispersion relation, below condensation threshold, we find that the effective mass is that of a bare cavity photon, not a polariton. Above threshold, we place an upper bound on the dimensionless two-dimensional interaction strength of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}\ensuremath{\lesssim}{10}^{\ensuremath{-}3}$, which is compatible with existing estimates. Both photon-photon and photon-molecule interactions are weak. The temperature is found to be independent of momentum, but dependent on pump spot size, indicating that the system is ergodic but not perfectly at thermal equilibrium. Condensation always happens first in the mode with lowest potential and lowest kinetic energy, although at very high pump powers multimode condensation occurs into other modes.

DOI
10.1103/physreva.94.063812

Related papers

Thermalization and Effective Interactions in Photon Condensates

Charly Beulenkamp

The experimental realization of a Bose-Einstein condensate of photons, first achieved in 2010 at Bonn University, allowed for new ways to probe the properties of condensates. For thermal light in free space the chemical potential is zero and condensation is not possible. By confining light to a microcavity, the transverse degrees of freedom behave as massive bosons which can have nonzero chemical potential. The gas of thermal photons can be brought to thermalize with a fluorescent dye though absorption and emission cycles. By pumping the dye molecules with a laser, the chemical potential can be increased and the photons will condense. \nWe have built a setup with which we can spatially and spectrally resolve the photon distribution in such a dye-filled microcavity. This allows us to study the shape and occupation of the low energy transverse modes of the cavity. We use this to investigate the thermalization process of the photon gas. A rate equation model is presented and qualitatively compared to experimental data. We find that the photon gas is not in thermal equilibrium.\nWe also investigate effective photon-photon interactions by measuring the spatial extent of the condensate. We find an effective interaction in the form of thermal lensing. As the thermal lensing depends on the interaction between the photon gas and the dye, we find that the model used for thermalization can also make good predictions about effective photon-photon interactions.

•Jan 1, 2018•0 citations

Interactions in dye-microcavity photon condensates and the prospects for their observation

Robert A. Nyman, Marzena Hanna Szymańska

We derive the equation of motion for a Bose-Einstein condensate of photons in a dye-microcavity system, starting from Maxwell's equations. Our theory takes into account mirror shape, Kerr-type intensity-dependent refractive index and incoherent pumping and loss. The resulting equation is remarkably similar to the Gross-Pitaevskii equation for exciton-polariton condensates, despite the different microscopic origins. We calculate the incoherent photoluminescence spectrum of the photon condensate, which shows the Bogoliubov-type excitations around the mean field at thermal equilibrium. Both open- and closed-system models are presented to account for, respectively dissipation and inhomogeneities. Considering realistic parameters and experimental resolution, we estimate that by observing the angle-resolved spectrum of incoherent photoluminescence it is possible to resolve dimensionless interaction parameters of order ${10}^{\ensuremath{-}5}$, two orders of magnitude below current estimates. Thus we expect that this technique will lead to accurate measurements of the interactions in photon condensates.

arXiv:1308.3588•Physical Review A•Mar 24, 2014•44 citations

Bose-Einstein condensation of photons

Jakov Marelic

A Bose-Einstein condensate can be made of photons. The photons are held at thermodynamic equilibrium in a dye-filled microcavity and pumped with a laser. Thermalisation can be demonstrated and above the threshold a Bose-Einstein condensate will form. A Mach-Zehnder interferometer is built and used to measure the spatial and temporal first-order coherence under various conditions. We build a momentum-resolved spectrometer and use it to obtain views into the phase-space distribution of the photon condensate. We put an upper bound on the value of the interaction strength parameter and find that the microcavity system is ergodic even when not at thermal equilibrium. We build a setup to stabilise the pump laser power with the aim to observe the λ-point of the condensate.

•Oct 1, 2017•0 citations

Photon Bose-Einstein Condensation in a Dye-Filled Microcavity

Karindra Perrier

Bose-Einstein condensation (BEC) is the transition to a macroscopic occupation of the ground state of a system of bosonic particles. In 1995 the first experimental realization of BEC was achieved by condensing a dilute atomic gas [1,2]. It was long thought only massive particles could undergo BEC. However, in 2010 it was shown that photon BEC was achieved in an optical dye-filled microcavity [3]. In 2015, we became the second group to successfully repeat these experiments.\n\nBEC is a phase transition and thus it occurs at thermal equilibrium. To achieve a thermal photon gas the cavity is filled with a fluorescent dye solution. The dye molecules thermalize the photons by means of repeated absorption-emission cycles. We optically pump the cavity. With the pump we determine the number of photons absorbed by the dye, consequently defining a nonvanishing chemical potential. This ensures a conserved photon number. The photons are trapped by the harmonic potential induced by the concave cavity mirrors. Due to the cutoff energy determined by the cavity length, the trapped photons have a dispersion similar to that of a massive particle in a quantum harmonic oscillator. The cavity length is tuned such that the free spectral range is larger than the bandwidth of the dye. Therefore, only one longitudinal mode fits inside the cavity, making the photon gas effectively two-dimensional. We end up with a thermalized two-dimensional photon gas that has the eigenenergies of a quantum harmonic oscillator. The Bose-Einstein distribution function predicts a critical photon number. Pumping the thermal photon gas beyond this critical number will lead to photon BEC.\n\nWe measure the spectral- and spatial distributions of our two-dimensional photon gas. In both distributions we observe photon BEC. Results show the characteristics of a phase transition: the appearance of a sharp peak on top of the thermal cloud that coincides with a converging chemical potential to zero. Both the spectral- and spatial distribution are in agreement with the theoretical distribution of photons with an effective mass in a quantum harmonic oscillator. Expansion of the condensate has been measured. This could indicate nonlinear optical effects such as thermal lensing or repulsive photon-photon interactions.

•May 31, 2016•0 citations

Thermalization and condensation dynamics of a photon Bose-Einstein condensate

Jan Klaers

W present time-resolved studies of the thermalization and condensation process of a two-dimensional photon gas in an optical microcavity. In our experiment, a two-dimensional photon gas is confined in a high finesse microresonator containing a dye medium. If this system is operated in a regime in which reabsorption of cavity photons by the dye medium dominates over photon loss, e.g. by mirror transmission, a thermalization process of the photon gas to the temperature of the resonator (room temperature) takes place. In earlier work, we have experimentally observed both the thermalization process and, at sufficiently high photon densities, a condensation in the resonator ground mode. In recent experiments, we have studied the thermalization and condensation dynamics of the system after excitation with a short laser pulse. The timescale on which the photon gas becomes thermal (Bose-Einstein distribution) is found to be in the picosecond to nanosecond regime and is tunable by various system parameters e.g. by the dye concentration. Upon spatially displacing the pump spot from the optical axis, a transient laser-like oscillation of higher order cavity modes can be observed. These laser-like oscillations decay after several hundred picoseconds when the majority of photons have relaxed to the resonator ground state.

Journal of Physical Chemistry & Biophysics•Oct 28, 2014•0 citations

Photon condensation from thermal sources and the limits of heat engines

Luísa Toledo Tude, Emily Haughton, Paul R. Eastham

The trapping and cooling of photon gases in microcavities has been used to create Bose-Einstein condensates. We investigate the conditions required for condensation in dye-filled microcavities, with photon populations created either by driving a transition of the dye, or by coupling the cavity modes to a thermal photon reservoir such as sunlight. We find that the threshold pump temperature, above which condensation appears, is determined by the second law of thermodynamics. The minimum achievable threshold is that of a reversible three-level heat engine, which we show arises in the dye-pumped case, and for pumping of the modes of a two-level cavity. For a many-level cavity condensation occurs at a similar but higher temperature. Our results show that photon condensates can be produced by pumping with incoherent thermal sources, opening possibilities for coherent light generation, energy harvesting, and experimental studies of quantum heat engines.

arXiv:2507.19128•Physical Review A•Dec 10, 2025•0 citations
We have observed momentum- and position-resolved spectra and images of the photoluminescence from thermalized and condensed dye-microcavity photons. The spectra yield the dispersion relation and the potential energy landscape for the photons. From this dispersion relation, below condensation threshold, we find that the effective mass is that of a bare cavity photon, not a polariton. Above threshold, we place an upper bound on the dimensionless two-dimensional interaction strength of g\ifmmode~\else˜\fi\ensuremath≲10\ensuremath−3\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}\ensuremath{\lesssim}{10}^{\ensuremath{-}3}g\ifmmode~\else˜\fi​\ensuremath≲10\ensuremath−3, which is compatible with existing estimates. Both photon-photon and photon-molecule interactions are weak. The temperature is found to be independent of momentum, but dependent on pump spot size, indicating that the system is ergodic but not perfectly at thermal equilibrium. Condensation always happens first in the mode with lowest potential and lowest kinetic energy, although at very high pump powers multimode condensation occurs into other modes.
The experimental realization of a Bose-Einstein condensate of photons, first achieved in 2010 at Bonn University, allowed for new ways to probe the properties of condensates. For thermal light in free space the chemical potential is zero and condensation is not possible. By confining light to a microcavity, the transverse degrees of freedom behave as massive bosons which can have nonzero chemical potential. The gas of thermal photons can be brought to thermalize with a fluorescent dye though absorption and emission cycles. By pumping the dye molecules with a laser, the chemical potential can be increased and the photons will condense. \nWe have built a setup with which we can spatially and spectrally resolve the photon distribution in such a dye-filled microcavity. This allows us to study the shape and occupation of the low energy transverse modes of the cavity. We use this to investigate the thermalization process of the photon gas. A rate equation model is presented and qualitatively compared to experimental data. We find that the photon gas is not in thermal equilibrium.\nWe also investigate effective photon-photon interactions by measuring the spatial extent of the condensate. We find an effective interaction in the form of thermal lensing. As the thermal lensing depends on the interaction between the photon gas and the dye, we find that the model used for thermalization can also make good predictions about effective photon-photon interactions.
We derive the equation of motion for a Bose-Einstein condensate of photons in a dye-microcavity system, starting from Maxwell's equations. Our theory takes into account mirror shape, Kerr-type intensity-dependent refractive index and incoherent pumping and loss. The resulting equation is remarkably similar to the Gross-Pitaevskii equation for exciton-polariton condensates, despite the different microscopic origins. We calculate the incoherent photoluminescence spectrum of the photon condensate, which shows the Bogoliubov-type excitations around the mean field at thermal equilibrium. Both open- and closed-system models are presented to account for, respectively dissipation and inhomogeneities. Considering realistic parameters and experimental resolution, we estimate that by observing the angle-resolved spectrum of incoherent photoluminescence it is possible to resolve dimensionless interaction parameters of order ${10}^{\ensuremath{-}5}$, two orders of magnitude below current estimates. Thus we expect that this technique will lead to accurate measurements of the interactions in photon condensates.
A Bose-Einstein condensate can be made of photons. The photons are held at thermodynamic equilibrium in a dye-filled microcavity and pumped with a laser. Thermalisation can be demonstrated and above the threshold a Bose-Einstein condensate will form. A Mach-Zehnder interferometer is built and used to measure the spatial and temporal first-order coherence under various conditions. We build a momentum-resolved spectrometer and use it to obtain views into the phase-space distribution of the photon condensate. We put an upper bound on the value of the interaction strength parameter and find that the microcavity system is ergodic even when not at thermal equilibrium. We build a setup to stabilise the pump laser power with the aim to observe the λ-point of the condensate.
Bose-Einstein condensation (BEC) is the transition to a macroscopic occupation of the ground state of a system of bosonic particles. In 1995 the first experimental realization of BEC was achieved by condensing a dilute atomic gas [1,2]. It was long thought only massive particles could undergo BEC. However, in 2010 it was shown that photon BEC was achieved in an optical dye-filled microcavity [3]. In 2015, we became the second group to successfully repeat these experiments.\n\nBEC is a phase transition and thus it occurs at thermal equilibrium. To achieve a thermal photon gas the cavity is filled with a fluorescent dye solution. The dye molecules thermalize the photons by means of repeated absorption-emission cycles. We optically pump the cavity. With the pump we determine the number of photons absorbed by the dye, consequently defining a nonvanishing chemical potential. This ensures a conserved photon number. The photons are trapped by the harmonic potential induced by the concave cavity mirrors. Due to the cutoff energy determined by the cavity length, the trapped photons have a dispersion similar to that of a massive particle in a quantum harmonic oscillator. The cavity length is tuned such that the free spectral range is larger than the bandwidth of the dye. Therefore, only one longitudinal mode fits inside the cavity, making the photon gas effectively two-dimensional. We end up with a thermalized two-dimensional photon gas that has the eigenenergies of a quantum harmonic oscillator. The Bose-Einstein distribution function predicts a critical photon number. Pumping the thermal photon gas beyond this critical number will lead to photon BEC.\n\nWe measure the spectral- and spatial distributions of our two-dimensional photon gas. In both distributions we observe photon BEC. Results show the characteristics of a phase transition: the appearance of a sharp peak on top of the thermal cloud that coincides with a converging chemical potential to zero. Both the spectral- and spatial distribution are in agreement with the theoretical distribution of photons with an effective mass in a quantum harmonic oscillator. Expansion of the condensate has been measured. This could indicate nonlinear optical effects such as thermal lensing or repulsive photon-photon interactions.
W present time-resolved studies of the thermalization and condensation process of a two-dimensional photon gas in an optical microcavity. In our experiment, a two-dimensional photon gas is confined in a high finesse microresonator containing a dye medium. If this system is operated in a regime in which reabsorption of cavity photons by the dye medium dominates over photon loss, e.g. by mirror transmission, a thermalization process of the photon gas to the temperature of the resonator (room temperature) takes place. In earlier work, we have experimentally observed both the thermalization process and, at sufficiently high photon densities, a condensation in the resonator ground mode. In recent experiments, we have studied the thermalization and condensation dynamics of the system after excitation with a short laser pulse. The timescale on which the photon gas becomes thermal (Bose-Einstein distribution) is found to be in the picosecond to nanosecond regime and is tunable by various system parameters e.g. by the dye concentration. Upon spatially displacing the pump spot from the optical axis, a transient laser-like oscillation of higher order cavity modes can be observed. These laser-like oscillations decay after several hundred picoseconds when the majority of photons have relaxed to the resonator ground state.
The trapping and cooling of photon gases in microcavities has been used to create Bose-Einstein condensates. We investigate the conditions required for condensation in dye-filled microcavities, with photon populations created either by driving a transition of the dye, or by coupling the cavity modes to a thermal photon reservoir such as sunlight. We find that the threshold pump temperature, above which condensation appears, is determined by the second law of thermodynamics. The minimum achievable threshold is that of a reversible three-level heat engine, which we show arises in the dye-pumped case, and for pumping of the modes of a two-level cavity. For a many-level cavity condensation occurs at a similar but higher temperature. Our results show that photon condensates can be produced by pumping with incoherent thermal sources, opening possibilities for coherent light generation, energy harvesting, and experimental studies of quantum heat engines.