This chapter reviews recent work on the Bose–Einstein condensation of photons in a dye microcavity environment. The chapter is organized as follows. Section 6.2 describes the fluorescence induced thermalization mechanism of the photon gas. Section 6.3 discusses the statistical theory of the trapped photon gas. Section 6.4 reviews experiments on the thermalization process. Section 6.5 presents the corresponding results on Bose–Einstein condensation, and Section 6.6 concludes. A fluorescence induced thermalization process leads to a thermal photon gas at room temperature with freely adjustable chemical potential.
This chapter reviews recent work on the Bose–Einstein condensation of photons in a dye microcavity environment. The chapter is organized as follows. Section 6.2 describes the fluorescence induced thermalization mechanism of the photon gas. Section 6.3 discusses the statistical theory of the trapped photon gas. Section 6.4 reviews experiments on the thermalization process. Section 6.5 presents the corresponding results on Bose–Einstein condensation, and Section 6.6 concludes. A fluorescence induced thermalization process leads to a thermal photon gas at room temperature with freely adjustable chemical potential.
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 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.
Photons can come to thermal equilibrium at room temperature by scattering multiple times from a fluorescent dye. By confining the light and dye in a microcavity, a minimum energy is set and the photons can then show Bose–Einstein condensation. We present here the physical principles underlying photon thermalization and condensation, and review the literature on the subject. We then explore the ‘small’ regime where very few photons are needed for condensation. We compare thermal equilibrium results to a rate-equation model of microlasers, which includes spontaneous emission into the cavity, and we note that small systems result in ambiguity in the definition of threshold.
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.
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.