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.
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.
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.
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.
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.
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 has in the last two decades been observed in cold atomic gases and in solid-state physics quasiparticles, exciton-polaritons and magnons, respectively. The perhaps most widely known example of a bosonic gas, photons in blackbody radiation, however exhibits no Bose-Einstein condensation, because the particle number is not conserved and at low temperatures the photons disappear in the system’s walls instead of massively occupying the cavity ground mode. This is not the case in a small optical cavity, with a low-frequency cutoff imprinting a spectrum of photon energies restricted to values well above the thermal energy. The here reported experiments are based on a microscopic optical cavity filled with dye solution at room temperature. Recent experiments of our group observing Bose-Einstein condensation of photons in such a setup are described. Moreover, we discuss some possible applications of photon condensates to realize quantum manybody states in periodic photonic lattices and photonic Josephson devices.
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.