Fluctuations and dissipation in a Bose-Einstein condensed photon gas

Abstract

Bose-Einstein condensation, superfluidity and superconductivity are all related phenomena where particles behave as collective quantum systems. The behavior of such systems is treated using quantum statistics and their properties such as energy distribution or coherence are used to describe the system at a macroscopic level. These quantities are affected not only by the intrinsic features of the particles that constitute the quantum gas, but also by the interaction of these particles with their environment. The effect of a coupling of the quantum gas with its surroundings can be as drastic as completely changing its coherence properties or it might lead to a slight deviation from an equilibrium energy distribution. In this thesis, we investigate the effects caused by coupling a quantum gas of light with its environment. <br /> Quantum gases of light are realized in optical microcavities filled with a medium the photons couple to. If a strong coupling between the light and the medium is realized, the gas comprises mixed states of matter and light such as polaritons. Phenomena like lasing, Bose-Einstein condensation and superfluidity can be observed in such systems. In the opposite case, when the coupling of medium and photons is weak, no coherent coupling is established and the gas consists of pure photons. The latter situation can be experimentally realized in high quality optical microcavities filled with photo-excitable dye molecules. In this system it was shown that if the lifetime of the photons in the cavity are sufficiently long, they thermalize at the temperature of the dye solution. And if the density of the photons is increased beyond a critical point, a Bose-Einstein condensate of photons forms. <br /> A distinct feature of a condensate of photons in the dye-microcavity system compared to atom or polariton condensates is that the dye molecules act as a reservoir of particles, as well as energy. The photon gas exchanges particles with excited dye molecules and the coupling between the two is of statistical nature. It has been shown that Bose-Einstein condensation can coexist with unusually large particle number fluctuations in the so called grand-canonical statistical ensemble regime. In the first part of this thesis, we experimentally investigate the fluctuation-dissipation relation in a Bose-Einstein condensate of photons realized in the dye-microcavity. In equilibrium, thermally driven fluctuations are closely connected to how the system dissipates its excess energy or particles. This relation is so general that it has been observed in a variety of systems ranging from Brownian particles to quantum gases of atoms. However, its validity in Bose-Einstein condensates has not been shown. Despite being intrinsically in thermal equilibrium, fluctuations usually completely diminish in a Bose-Einstein condensate soon after the condensation threshold. We measure the second-order coherence of the photon Bose-Einstein condensate to search for the expected ratio of statistical number fluctuations and compressibility following the fluctuation-dissipation theorem. <br /> Another intriguing aspect of the photon condensate is introduced due to the imperfect reflectivity of the cavity mirrors. In the second part of this thesis we show that this openness can lead to the existence of new states of the condensate. Physical models often consider systems that are completely isolated from their environment, such as a gas of particles closed in a box. Real-life situations often deviate from these idealized scenarios and the system loses energy or particles to its surroundings. In contemporary physics, systems which are dissipatively coupled to the environment are actively studied in a broad range of research fields ranging from optics to biophysics. Here, we investigate the open-system dynamics of a photon condensate in grand-canonical ensemble conditions. We identify non-Hermitian phases of the system that are observed by abrupt changes in the dynamics of the condensate’s second-order coherence.