Bose-Einstein condensation (BEC) is a state of matter where bosons macroscopically\noccupy the ground state of a system. In 2010 the group of Martin Weitz achieved a\ntwo-dimensional Bose-Einstein condensation of photons by using a dye-filled micro-\ncavity. In 2015 our research group also achieved a photon BEC using a similar\nsetup. Although one expects the photons to be non-interacting, the radius of the\ncondensate has been shown to grow as a function of photon density. This implies\nrepulse photon-photon interactions. This leads us to question what the strength of\nthe interactions is.\nTo investigate the interaction strength we take single shot images of the photon gas,\nwhile varying the photon density in the cavity. From each image we determine the\nnumber of condensate photons and the radius of the condensate. Subsequently we de-\ntermine the interaction strength to be g = (6.6 +/- 0.7)E-3 and g = (8 +/- 1)E-2\nusing a dye concentration of 1.5 mM and 6.0 mM respectively. This implies that the\ninteraction strength increases for increasing dye concentration. The source of the\ninteractions is not yet understood and should be investigated further.\nWe also determine the polarization state of the photon gas. In order to do so we\nbuild an experimental setup which can measure all four Stokes parameters simulta-\nneously. Since the phase transition into Bose-Einstein condensation is an example of\nspontaneous symmetry breaking, one would expect the condensate to have a differ-\nent polarization each time it is created. We show that this is not the case and that\nevery newly created BEC has the same polarization state, i.e. linearly polarized in\nthe horizontal direction. We show this symmetry breaking is not affected by the dye\nconcentration, photon density inside the cavity or the cavity mirrors. It is however\ncaused by the intra-cavity polarization of the pump beam. We show that we can\nrotate the direction of the polarization by rotating the intra-cavity polarization of\nthe pump beam.
Bose-Einstein condensation (BEC) is a state of matter where bosons macroscopically\noccupy the ground state of a system. In 2010 the group of Martin Weitz achieved a\ntwo-dimensional Bose-Einstein condensation of photons by using a dye-filled micro-\ncavity. In 2015 our research group also achieved a photon BEC using a similar\nsetup. Although one expects the photons to be non-interacting, the radius of the\ncondensate has been shown to grow as a function of photon density. This implies\nrepulse photon-photon interactions. This leads us to question what the strength of\nthe interactions is.\nTo investigate the interaction strength we take single shot images of the photon gas,\nwhile varying the photon density in the cavity. From each image we determine the\nnumber of condensate photons and the radius of the condensate. Subsequently we de-\ntermine the interaction strength to be g = (6.6 +/- 0.7)E-3 and g = (8 +/- 1)E-2\nusing a dye concentration of 1.5 mM and 6.0 mM respectively. This implies that the\ninteraction strength increases for increasing dye concentration. The source of the\ninteractions is not yet understood and should be investigated further.\nWe also determine the polarization state of the photon gas. In order to do so we\nbuild an experimental setup which can measure all four Stokes parameters simulta-\nneously. Since the phase transition into Bose-Einstein condensation is an example of\nspontaneous symmetry breaking, one would expect the condensate to have a differ-\nent polarization each time it is created. We show that this is not the case and that\nevery newly created BEC has the same polarization state, i.e. linearly polarized in\nthe horizontal direction. We show this symmetry breaking is not affected by the dye\nconcentration, photon density inside the cavity or the cavity mirrors. It is however\ncaused by the intra-cavity polarization of the pump beam. We show that we can\nrotate the direction of the polarization by rotating the intra-cavity polarization of\nthe pump beam.
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.
A Bose-Einstein condensate is a state of matter where bosonic particles macroscopically occupy the ground state of a system. It was predicted as early as 1924 by Satyendra Nath Bose \\& Albert Einstein. Although this state of matter was deemed possible, it was only experimentally achieved relatively recently. In 1995 by Eric Cornell, Carl Wieman \\& Wolfgang Ketterle. This Bose-Einstein condensate was made using massive bosonic particles. But all bosons should be able to under go Bose-Einstein condensation so why not the most common one of them all, the photon?\n\nThis question was mostly waved away with a quick reference to the fact that photons adhere to Planck's law. For Bose-Einstein condensation one should be able to tune the temperature and particle number independently. It was thus thought that photons could not be made to condense. This all changed when Martin Weitz showed that he could tune both the temperature and particle number of photons independently by confining them to a white-wall box filled with a medium.\n\n\nIn 2010 they became the first group to achieve a Bose-Einstein condensate of photons. They used an optical dye filled microcavity to make a two-dimensional photon gas Bose-Einstein condense. In 2015 we became the second group in the world to replicate these results. \n\nOne of the characteristics of a photon Bose-Einstein condensate that has not yet been researched is its polarization. As Bose-Einstein condensation is an example of spontaneous symmetry breaking. One could expect each condensate to pick a well defined but random polarization. However, slight anisotropy could also force each condensate to pick the same polarization. To answer these questions we build an experimental setup which can measure all four Stokes parameters at the same time. \n\nWe find that the polarization of every condensate was the same. The polarization of the condensate shows a clear distinction from the polarization of the thermal cloud. We find that the thermal cloud is unpolarized while the condensate is a superposition of multiple polarization states with a strong linear contribution.
We experimentally study Bose-Einstein condensation of photons (phBEC) in a dye-filled microcavity. Through multiple absorption and emission cycles the photons inside the microcavity thermalize to the rovibronic temperature of the dye solution. Raising the photon density of the thermalized photon gas beyond the critical photon density yields a macroscopic occupation of the ground state, i.e. phBEC. For increasing density, we observe an increase of the condensate radius 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 an effective interaction strength parameter g~. For all concentrations we find g~∼10−2, one order larger than previously reported.
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 measure the polarization of a photon gas in a dye-filled microcavity. The polarization is obtained by a single-shot measurement of the Stokes parameters. We find that the polarization of both the thermal cloud and the Bose-Einstein condensate of photons (phBEC) does not differ from shot to shot. In the case of the phBEC, we find that the polarization correlates with the polarization of the pump pulse. The polarization of the thermal cloud is independent of parameters varied in the experiment and is governed by a hidden anisotropy in the system.
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.