Light thermalized at room temperature in an optically pumped, dye-filled microcavity resembles a model system of noninteracting Bose-Einstein condensation in the presence of dissipation. We have experimentally investigated some of the steady-state properties of this unusual state of light and found features which do not match the available theoretical descriptions. We have seen that the critical pump power for condensation depends on the pump beam geometry, being lower for smaller pump beams. Far below threshold, both intracavity photon number and thermalized photon cloud size depend on pump beam size, with optimal coupling when the pump beam matches the thermalized cloud size. We also note that the critical pump power for condensation depends on the cavity cutoff wavelength and longitudinal mode number, which suggests that energy-dependent thermalization and loss mechanisms are important.
Light thermalized at room temperature in an optically pumped, dye-filled microcavity resembles a model system of noninteracting Bose-Einstein condensation in the presence of dissipation. We have experimentally investigated some of the steady-state properties of this unusual state of light and found features which do not match the available theoretical descriptions. We have seen that the critical pump power for condensation depends on the pump beam geometry, being lower for smaller pump beams. Far below threshold, both intracavity photon number and thermalized photon cloud size depend on pump beam size, with optimal coupling when the pump beam matches the thermalized cloud size. We also note that the critical pump power for condensation depends on the cavity cutoff wavelength and longitudinal mode number, which suggests that energy-dependent thermalization and loss mechanisms are important.
A system of identical bosons can exhibit a state of matter in which the ground state is macroscopically occupied. This special state is called Bose-Einstein condensation, and was predicted by Satyendra Nath Bose and Albert Einstein in 1924. It took some time before physicists achieved this experimentally, but in 1995 it was done by Eric Cornell and Carl Wieman. Since photons are also bosonic particles, they should be able to achieve Bose-Einstein condensation in thermal equilibrium. However this is not as easy for photons as it is for atoms, since the number of photons depends on the temperature. But in 2010 the group of Martin Weitz in Bonn was able to produce a photon Bose-Einstein condensate. This was done using a dye-filled microcavity which is optically pumped. The same principles are used in our setup. Photons inside the cavity thermalize with a fluorescent dye through multiple absorption and emission cycles. The effectively two-dimensional photon gas is trapped by a harmonic potential induced by the shape of the cavity mirrors. This results in photons with eigenenergies of the quantum harmonic oscillator. The minimal energy is determined by the cutoff frequency, set by the cavity length. The thermalization of the photon gas depends on this cutoff frequency, and the total pump power. Jonathan Keeling and Peter Kirton developed a theoretical model describing this system and its thermalization, and simulated it in one dimension.\nWe simulate the same model, in two dimensions using radially averaged photon modes. Threshold for Bose-Einstein condensation is determined for different cutoff frequencies. Our results show good agreement with those of Keeling and Kirton, below, at and above threshold. Multimode condensation and gain clamping of the molecular excitation density are observed above threshold. Comparison with experimental data can only be done qualitatively since it currently is uncalibrated.
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.
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.
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.
Bose-Einstein condensation, the macroscopic ground state occupation of a system of bosonic particles below a critical temperature, has been observed in cold atomic gases and solid-state physics quasiparticles. In contrast, photons do not show this phase transition usually, because in Planck's blackbody radiation the particle number is not conserved and at low temperature the photons disappear in the walls of the system. Here we report on the realization of a photon Bose-Einstein condensate in a dye-filled optical microcavity, which acts as a "white-wall" photon box. The cavity mirrors provide a trapping potential and a non-vanishing effective photon mass, making the system formally equivalent to a two-dimensional gas of trapped massive bosons. Thermalization of the photon gas is reached in a number conserving way by multiple scattering off the dye molecules. Signatures for a BEC upon increased photon density are: a spectral distribution that shows Bose-Einstein distributed photon energies with a macroscopically populated peak on top of a broad thermal wing, the observed threshold of the phase transition showing the predicted absolute value and scaling with resonator geometry, and condensation appearing at the trap centre even for a spatially displaced pump spot.