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:2207.12070 · Physical Review A

Sunlight-pumped two-dimensional thermalized photon gas

Erik Busley, Leon Espert Miranda, Christian Kurtscheid, Frederik Wolf, Frank Vewinger, Julian Schmitt, Martin Weitz

Published May 5, 2023• 3 citations
arXivHTMLPDF

Abstract

The Liouville theorem states that the phase-space volume of an ensemble in a closed system remains constant. While gases of material particles can efficiently be cooled by sympathetic or laser cooling techniques, allowing for large phase-space compression upon suitable coupling to the environment, for light both the absence of an internal structure, as well as the nonconservation of photons upon contact with matter imposes fundamental limits for three-dimensional light-harvesting systems, such as fluorescence-based light concentrators. An advantageous physical situation can in principle be expected for dye-solution-filled microcavities with a mirror spacing in the wavelength range, where low-dimensional photon gases with nonvanishing and tunable chemical potential have been experimentally realized. Motivated by the goal to observe phase-space compression of sunlight by cooling the captured radiation to room temperature, in this work we theoretically show that in a lossless, harmonically confined system the phase-space volume scales as ${(\mathrm{\ensuremath{\Delta}}x\mathrm{\ensuremath{\Delta}}p/T)}^{d}=\mathrm{constant}$, where $\mathrm{\ensuremath{\Delta}}x$ and $\mathrm{\ensuremath{\Delta}}p$ denote the position and momentum spread and $d$ the dimensionality of the system ($d=1$ or 2). Experimentally, we realize a corresponding sunlight-pumped dye microcavity and demonstrate thermalization of scattered sunlight to a two-dimensional room temperature photon gas with nonvanishing chemical potential. Prospects of phase-space buildup of light by cooling, as can be feasible in systems with a two- or three-dimensional band gap, range from quantum state preparation in tailored potentials up to technical applications for more efficient collection of diffuse sunlight.

DOI
10.1103/physreva.107.052204

Related papers

Thermalization of a two-dimensional photon gas in a polymeric host matrix

Julian Schmitt, Tobias Damm, Frank Vewinger +2 more

We investigate thermodynamic properties of a two-dimensional photon gas confined by a dye-filled optical microcavity. A thermally equilibrated state of the photon gas is achieved by radiative coupling to a heat bath that is realized with dye molecules embedded in a polymer at room temperature. The chemical potential of the gas is freely adjustable. The optical microcavity consisting of two curved mirrors induces both a non-vanishing effective photon mass and a harmonic trapping potential for the photons. While previous experiments of our group have used liquid dye solutions, the measurements described here are based on dye molecules incorporated into a polymer host matrix. The solid state material allows a simplified operation of the experimental scheme. We furthermore describe studies of fluorescence properties of dye-doped polymers, and verify the applicability of Kennard–Stepanov theory in this system. In the future, dye-based solid state systems hold promise for the realization of single-mode light sources in thermal equilibrium based on Bose–Einstein condensation of photons, as well as for solar energy concentrators.

arXiv:1201.4658•New Journal of Physics•Jul 20, 2012•6 citations

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

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

Photon thermalization in an open and disordered scattering medium

Lorenzo Soncin, Romain Pierrat, Yannick De Wilde +2 more

Thermalization of light, where photons acquire a temperature and chemical potential analogous to a material gas, remains a striking yet experimentally elusive manifestation of quantum statistical physics. To date, it has been realized only in carefully engineered photonic environments that enforce repeated absorption-emission cycles. Here we show that such thermalization can emerge in a radically simpler setting: an open scattering medium. Using a pumped fluorescent dye solution doped with colloidal particles, we demonstrate that multiple scattering alone suffices to trap photons long enough to drive them to thermal equilibrium. The emitted radiation follows a Bose-Einstein distribution with a finite chemical potential, independently tunable via optical pumping, while its temperature is set by the host medium. A clear spectroscopic signature of thermalization is observed as a plateau at the sample temperature over a finite spectral range. Our results establish disordered scattering media as a generic platform for photon thermalization, extending this fundamental phenomenon beyond resonant cavities and opening new routes towards cavity-free photonic thermodynamics and thermal light sources operating under ambient conditions.

arXiv:2606.01997•Jun 1, 2026•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

Bose-Einstein Condensation of Photons and Grand-Canonical Condensate Fluctuations

Jan Klaers, Martin Weitz

We review recent experiments on the Bose-Einstein condensation of photons in a dye-filled optical microresonator. The most well-known example of a photon gas, photons in blackbody radiation, does not show Bose-Einstein condensation. Instead of massively populating the cavity ground mode, photons vanish in the cavity walls when they are cooled down. The situation is different in an ultrashort optical cavity imprinting a low-frequency cutoff on the photon energy spectrum that is well above the thermal energy. The latter allows for a thermalization process in which both temperature and photon number can be tuned independently of each other or, correspondingly, for a nonvanishing photon chemical potential. We here describe experiments demonstrating the fluorescence-induced thermalization and Bose-Einstein condensation of a two-dimensional photon gas in the dye microcavity. Moreover, recent measurements on the photon statistics of the condensate, showing Bose-Einstein condensation in the grand-canonical ensemble limit, will be reviewed. Introduction Quantum statistical effects become relevant when a gas of particles is cooled, or its density is increased, to the point where the associated de Broglie wavepackets spatially overlap. For particles with integer spin (bosons), the phenomenon of Bose-Einstein condensation (BEC) then leads to macroscopic occupation of a single quantum state at finite temperatures [1]. Bose-Einstein condensation in the gaseous case was first achieved in 1995 by laser and subsequent evaporative cooling of a dilute cloud of alkali atoms [2, 3, 4], as detailed in Chapter 3 of this volume. The condensate atoms can be described by a macroscopic singleparticle wavefunction, similar to the case of liquid helium [1]. Bose-Einstein condensation has also been observed for exciton-polaritons, which are hybrid states of matter and light [5, 6, 7] (see Chapter 4), magnons [8] (see Chapter 25), and other physical systems. Other than material particles, photons usually do not show Bose-Einstein condensation [9]. In blackbody radiation, the most common Bose gas, photons at low temperature disappear, instead of condensing to a macroscopically occupied ground-state mode. In this system, photons have a vanishing chemical potential, meaning that the number of photons is determined by the available thermal energy and cannot be tuned independently from temperature.

arXiv:1611.10286•Cambridge University Press eBooks•Oct 4, 2018•2 citations
The Liouville theorem states that the phase-space volume of an ensemble in a closed system remains constant. While gases of material particles can efficiently be cooled by sympathetic or laser cooling techniques, allowing for large phase-space compression upon suitable coupling to the environment, for light both the absence of an internal structure, as well as the nonconservation of photons upon contact with matter imposes fundamental limits for three-dimensional light-harvesting systems, such as fluorescence-based light concentrators. An advantageous physical situation can in principle be expected for dye-solution-filled microcavities with a mirror spacing in the wavelength range, where low-dimensional photon gases with nonvanishing and tunable chemical potential have been experimentally realized. Motivated by the goal to observe phase-space compression of sunlight by cooling the captured radiation to room temperature, in this work we theoretically show that in a lossless, harmonically confined system the phase-space volume scales as (\ensuremathΔx\ensuremathΔp/T)d=constant{(\mathrm{\ensuremath{\Delta}}x\mathrm{\ensuremath{\Delta}}p/T)}^{d}=\mathrm{constant}(\ensuremathΔx\ensuremathΔp/T)d=constant, where \ensuremathΔx\mathrm{\ensuremath{\Delta}}x\ensuremathΔx and \ensuremathΔp\mathrm{\ensuremath{\Delta}}p\ensuremathΔp denote the position and momentum spread and ddd the dimensionality of the system (d=1d=1d=1 or 2). Experimentally, we realize a corresponding sunlight-pumped dye microcavity and demonstrate thermalization of scattered sunlight to a two-dimensional room temperature photon gas with nonvanishing chemical potential. Prospects of phase-space buildup of light by cooling, as can be feasible in systems with a two- or three-dimensional band gap, range from quantum state preparation in tailored potentials up to technical applications for more efficient collection of diffuse sunlight.
We investigate thermodynamic properties of a two-dimensional photon gas confined by a dye-filled optical microcavity. A thermally equilibrated state of the photon gas is achieved by radiative coupling to a heat bath that is realized with dye molecules embedded in a polymer at room temperature. The chemical potential of the gas is freely adjustable. The optical microcavity consisting of two curved mirrors induces both a non-vanishing effective photon mass and a harmonic trapping potential for the photons. While previous experiments of our group have used liquid dye solutions, the measurements described here are based on dye molecules incorporated into a polymer host matrix. The solid state material allows a simplified operation of the experimental scheme. We furthermore describe studies of fluorescence properties of dye-doped polymers, and verify the applicability of Kennard–Stepanov theory in this system. In the future, dye-based solid state systems hold promise for the realization of single-mode light sources in thermal equilibrium based on Bose–Einstein condensation of photons, as well as for solar energy concentrators.
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.
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.
Thermalization of light, where photons acquire a temperature and chemical potential analogous to a material gas, remains a striking yet experimentally elusive manifestation of quantum statistical physics. To date, it has been realized only in carefully engineered photonic environments that enforce repeated absorption-emission cycles. Here we show that such thermalization can emerge in a radically simpler setting: an open scattering medium. Using a pumped fluorescent dye solution doped with colloidal particles, we demonstrate that multiple scattering alone suffices to trap photons long enough to drive them to thermal equilibrium. The emitted radiation follows a Bose-Einstein distribution with a finite chemical potential, independently tunable via optical pumping, while its temperature is set by the host medium. A clear spectroscopic signature of thermalization is observed as a plateau at the sample temperature over a finite spectral range. Our results establish disordered scattering media as a generic platform for photon thermalization, extending this fundamental phenomenon beyond resonant cavities and opening new routes towards cavity-free photonic thermodynamics and thermal light sources operating under ambient conditions.
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.
We review recent experiments on the Bose-Einstein condensation of photons in a dye-filled optical microresonator. The most well-known example of a photon gas, photons in blackbody radiation, does not show Bose-Einstein condensation. Instead of massively populating the cavity ground mode, photons vanish in the cavity walls when they are cooled down. The situation is different in an ultrashort optical cavity imprinting a low-frequency cutoff on the photon energy spectrum that is well above the thermal energy. The latter allows for a thermalization process in which both temperature and photon number can be tuned independently of each other or, correspondingly, for a nonvanishing photon chemical potential. We here describe experiments demonstrating the fluorescence-induced thermalization and Bose-Einstein condensation of a two-dimensional photon gas in the dye microcavity. Moreover, recent measurements on the photon statistics of the condensate, showing Bose-Einstein condensation in the grand-canonical ensemble limit, will be reviewed. Introduction Quantum statistical effects become relevant when a gas of particles is cooled, or its density is increased, to the point where the associated de Broglie wavepackets spatially overlap. For particles with integer spin (bosons), the phenomenon of Bose-Einstein condensation (BEC) then leads to macroscopic occupation of a single quantum state at finite temperatures [1]. Bose-Einstein condensation in the gaseous case was first achieved in 1995 by laser and subsequent evaporative cooling of a dilute cloud of alkali atoms [2, 3, 4], as detailed in Chapter 3 of this volume. The condensate atoms can be described by a macroscopic singleparticle wavefunction, similar to the case of liquid helium [1]. Bose-Einstein condensation has also been observed for exciton-polaritons, which are hybrid states of matter and light [5, 6, 7] (see Chapter 4), magnons [8] (see Chapter 25), and other physical systems. Other than material particles, photons usually do not show Bose-Einstein condensation [9]. In blackbody radiation, the most common Bose gas, photons at low temperature disappear, instead of condensing to a macroscopically occupied ground-state mode. In this system, photons have a vanishing chemical potential, meaning that the number of photons is determined by the available thermal energy and cannot be tuned independently from temperature.