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 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 (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.
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.
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.
We develop a nonequilibrium model of condensation and lasing of photons in a dye filled microcavity. We examine in detail the nature of the thermalization process induced by absorption and emission of photons by the dye molecules, and investigate when the photons are able to reach a thermal equilibrium Bose-Einstein distribution. At low temperatures, or large cavity losses, the absorption and emission rates are too small to allow the photons to reach thermal equilibrium and the behavior becomes more like that of a conventional laser.
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.
Bose-Einstein condensation is a state of matter for which massive bosons develop a macroscopic occupation of the ground state. After the theoretical discovery by Bose and Einstein, it took approximately 70 years to be experimentally realized using Rubidium-87 atoms. Ever since, many different species have been shown to Bose condense. The key in these experiments is cooling down atoms temperatures below 200 nK, while maintaining a large density. Despite all these species, it was thought that photons could not Bose condense. This changed in 2010 when the first Bose-Einstein condensate of photons (phBEC) was achieved. In a table top experiment photons are confined to a dye-filled microcavity where under the right conditions a thermalized photon gas is achieved. Using our setup, we quantitatively show from both the spectral and spatial distribution of photons in the microcavity that a macroscopic occupation of the ground state is achieved, i.e. a condensate of photons. The achievement of phBEC in a dye-filled microcavity has led to a renewed interest in the density distribution of the ideal Bose gas in a two-dimensional harmonic oscillator. We present measurements of the radial profile of photons inside the microcavity below and above the critical point for phBEC with a large signal-to-noise ratio. We obtain good agreement with theoretical profiles obtained using exact summation of eigenstates. An interesting open question is, whether the photons in the condensate are interacting or non-interacting and as a consequence, whether the condensate is also a superfluid or only forms a macroscopically occupied ground state, as predicted by Einstein. When increasing the photon density, we observe an increase in the radius of the condensate which we attribute to effective repulsive interactions. For several dye concentrations we accurately determine the radius of the condensate as a function of the number of condensate photons, and derive from the measurements an effective interaction strength. In many systems ranging from condensed matter physics and particle physics to cosmology, phase transitions and spontaneous symmetry breaking play a crucial role. The information of a polarized condensate from an unpolarized thermal cloud constitutes a directly observable prototype of spontaneous symmetry breaking. For every single-shot of the pump laser, we determine the Stokes parameters of the photons inside the microcavity which fully characterizes the polarization state of the sample. By varying experimental parameters, we investigate if the polarization is randomly chosen from shot-to-shot of the experiment. The dye-filled microcavity is a beautiful tool to achieve phBEC. However, it cannot provide the periodic potential required to achieve quantum phase transitions, such as the Mott insulator that have been so successfully exploited in the field of ultra-cold atoms. We use a local density approach to simulate large-area photonic crystal cavities. Clever interplay with both the electronic and photonic bandgap of these cavities has the potential of achieving phBEC in a periodic potential. We show that when the hole radius varies quadratically as a function of position, the eigenmodes of the photonic crystal can be described by the corresponding eigenmodes of the quantum harmonic oscillator.