Photons in a dye filled microcavity have been proven to form Bose-Einstein condensates both theoretically and experimentally. The system may also be placed in a fundamentally non- equilibrium state where multiple modes are condensed. This thesis theoretically examines some of the deviations from traditional Bose-Einstein condensate models which have been observed and which may be expected in future experiments. Unusual and potentially unseen condensed states are predicted, along with the unexpected non-critical slowing down of system evolution when in these states. A rigorous derivation of a master equation from a microscopic Hamiltonian is given in chapter two. This is used to study the multimode phases of the condensate in chapter three along with transitions between them. The temporal evolution of the condensate in various phases and close to phase boundaries is presented in chapter four. Dramatic improvements in the simulation of photonic condensates are also discussed in chapter four. These improvements also offer a conceptual shift in the theoretical description of photonic condensates which allows new insights to be made. The fifth chapter establishes a foundation of coupled rate equations which may be used to model the higher order coherences of photons and molecules in future work. Finally the transport of photons across non-standard cavities is modelled, providing guidance for future experiments and possible applications of photonic condensates.
Photons in a dye filled microcavity have been proven to form Bose-Einstein condensates both theoretically and experimentally. The system may also be placed in a fundamentally non- equilibrium state where multiple modes are condensed. This thesis theoretically examines some of the deviations from traditional Bose-Einstein condensate models which have been observed and which may be expected in future experiments. Unusual and potentially unseen condensed states are predicted, along with the unexpected non-critical slowing down of system evolution when in these states. A rigorous derivation of a master equation from a microscopic Hamiltonian is given in chapter two. This is used to study the multimode phases of the condensate in chapter three along with transitions between them. The temporal evolution of the condensate in various phases and close to phase boundaries is presented in chapter four. Dramatic improvements in the simulation of photonic condensates are also discussed in chapter four. These improvements also offer a conceptual shift in the theoretical description of photonic condensates which allows new insights to be made. The fifth chapter establishes a foundation of coupled rate equations which may be used to model the higher order coherences of photons and molecules in future work. Finally the transport of photons across non-standard cavities is modelled, providing guidance for future experiments and possible applications of photonic condensates.
In this thesis we study Bose-Einstein condensation of photons. In Chapter 1 we describe the current experimental set-up and we explain the two important features of the Bose-Einstein condensate of light: dissipation through the interaction with the external reservoir of dye molecules and driving by the external pumping. In Chapter 2 we use the Schwinger-Keldysh formalism to describe the complete time evolution of the light. We show that the finite-lifetime effects of the photons due to the interaction with the dye can be characterized by a single dimensionless parameter, that depends on the power of the external laser pumping the dye. We also determine spectral functions and collective modes of the photon gas in both the normal and the Bose-Einstein condensed phases. In Chapter 3 we demonstrate that the finite-lifetime effects on the spatial first-order correlation functions of the condensed light are negligible, but are important for the temporal first-order correlations. Furthermore, we show that in the normal state the first-order correlations of the photons are suppressed by the interaction with the dye. In Chapter 4 we develop a model to describe the effect of interactions on the number fluctuations in Bose-Einstein condensates. We find good agreement between the observed number fluctuations in the light Bose-Einstein condensate and the results of our model for different interaction strenghts. In Chapter 5 we propose an experiment to observe phase diffusion in the Bose-Einstein condensate of photons and we predict the outcome of individual measurements. In our model we incorporate quantum and thermal fluctuations as well as the finite-lifetime effects. In Chapter 6 we investigate the light in the presence of a periodic potential and we study the transition from a superfluid to a Mott-insulator. We demonstrate that in this system the true Mott-insulating state is longer present due the interactions with the dye molecules. Finally, in Chapter 7 we consider Bose-Einstein condensation of light in nano-fabricated semiconductor microcavities. We demonstrate that in this system there is also a single dimensionless damping parameter that depends on the external pumping. We propose to use the experimental freedom to investigate the superfluidity of the photons via the excitation of scissors modes. We determine the frequency and damping of these scissors modes. We also calculate the density-density correlations of the excited light fluid and we show that this contains a signature of the dynamical Casimir effect.
A theory of Bose-Einstein condensation of light in a dye-filled optical microcavity is presented. The theory is based on the hierarchical maximum entropy principle and allows one to investigate the fluctuating behavior of the photon gas in the microcavity for all numbers of photons, dye molecules, and excitations at all temperatures, including the whole critical region. The master equation describing the interaction between photons and dye molecules in the microcavity is derived and the equivalence between the hierarchical maximum entropy principle and the master equation approach is shown. The cases of a fixed mean total photon number and a fixed total excitation number are considered, and a much sharper, nonparabolic onset of a macroscopic Bose-Einstein condensation of light in the latter case is demonstrated. The theory does not use the grand canonical approximation, takes into account the photon polarization degeneracy, and exactly describes the microscopic, mesoscopic, and macroscopic Bose-Einstein condensation of light. Under certain conditions, it predicts sub-Poissonian statistics of the photon condensate and the polarized photon condensate, and a universal relation takes place between the degrees of second-order coherence for these condensates. In the macroscopic case, there appear a sharp jump in the degrees of second-order coherence, a sharp jump and kink in the reduced standard deviations of the fluctuating numbers of photons in the polarized and whole condensates, and a sharp peak, a cusp, of the Mandel parameter for the whole condensate in the critical region. The possibility of nonclassical light generation in the microcavity with the photon Bose-Einstein condensate is predicted.
Through trapping light in a dye-filled optical microcavity, one can engineer a gapped band structure for photons, causing them to behave as massive bosons moving in two dimensions. Repeated absorption and emission by the dye can lead to a thermal distribution and Bose- Einstein condensation. In this thesis, I study photonic condensates beyond the equilibrium thermodynamic Bose-Einstein condensation limit in three ways. First, I describe a method for fine control of the trapping potential for light allowing for future study of thermalised light in box potentials and 1D potentials as well as others, expected to show quasi-condensation and possibly superfluid behaviour, rather than ideal Bose-Einstein condensation. Second, I show how this fabrication technique has been used to define tight trapping potentials with only a few thermally accessible energy levels. In these systems, dominance of the ground- state population and build-up of coherence occur at photon numbers less than ten, raising interesting questions about how to define condensation. I discuss these questions through the relevant chapter. Third, pulsed-pump experiments show interesting temporal dynamics including jitter in the formation time of a condensate after a pump pulse due to the stochastic nature of the emission processes involved. I show how the non-stationary two-time correlation function g(2)(t1, t2) is a powerful tool for characterising these temporal dynamics and I interpret the results in a more general framework of the evolution of a probability density function through an effective free energy landscape, driven by drift terms and stochastic forces.
In this bachelor’s thesis we study multi-mode effects on the Bose-Einstein condensation (BEC) of photons in a dye-filled microcavity. The repulsive effective interaction of the photons should increase the conden- sate size. We show how the condensate radius of the ground state and an excited state depend on this effective interaction of the photons. We show that the spatial form of the excited state can also decrease the radius of the ground state. For this effect to occur, we expect a sufficiently large effective interaction. Comparing our model with experimental data gives us an effective interaction of g ̃ = (5.2 ± 2.3) × 10−5. However, one should interpret this result with care, because better measurements of the photon occupa- tion numbers are needed before we can reach solid conclusions.\nWe further investigate rate equations for the BEC of photons to understand the stationary photon occupation numbers. We find approximated solutions to these rate equations to find the dependence of the photon occupation numbers on the pump rate which excites the dye molecules in the condensate. Despite those approximations we estimate critical parameters for which either lasing or saturation of the photon numbers is expected. We conclude that the rate of decay from the cavity and emission rates of the dye is very important. From comparing the model with experiment we can conclude that the approximations are well enough to capture the right trend of real data. However, in the limit of large photon numbers, the approximations aren’t good enough anymore and a more accurate approach will be necessary.
This thesis explores non-equilibrium phenomena in quantum many-body systems, with a focus on correlated electron systems and photon Bose-Einstein condensates. The first part develops the theoretical foundation, beginning with the Lindblad master equation and the construction of non-equilibrium quantum field theory. The two-particle irreducible effective action formalism is introduced, from which the Kadanoff-Baym equations for real-time evolution and the Dyson equation for steady-states are derived. The theoretical groundwork continues with a treatment of strongly correlated electron systems, where non-equilibrium dynamical mean-field theory (DMFT), auxiliary particles, and the non-crossing approximation (NCA) are introduced. These techniques, together with the Lindblad and Kadanoff-Baym approaches, are used throughout the subsequent chapters. The second part presents the main research projects of this thesis. The first two projects are concerned with the fate of the heavy fermion state under irradiation of light. To accurately incorporate light-matter interactions in this case, dipole transitions must be included. In the first project a periodically driven system is considered, where the light can be treated semiclassically. A Floquet DMFT+NCA framework is developed, revealing the mechanisms and conditions under which the heavy fermion state is most strongly suppressed. The second project analyzes a THz spectroscopy experiment performed on CeCu6. In this case a semi-classical treatment of the light field is no longer sufficient, and a full two-time evolution of all the non-equilibrium Green functions is necessary. This approach reveals the microscopic mechanisms underlying the collapse and revival of the Kondo state observed in the experiment. The next project investigates a recent experiment regarding an observation of a non-Hermitian phase transition in EuO. The equilibrium properties of EuO are first analyzed, and then an exciton model is constructed that gives rise to the non-Hermitian phase transition, in good agreement with experimental observations. In the final project, a photon Bose-Einstein condensate in a dye-filled microcavity is studied. A stabilization mechanism, distinct from thermalization, is revealed which admits a condensate phase for orders of magnitude longer than the experimentally relevant timescales.
Abstract Photon condensation was first experimentally realized in 2010 within a dye-filled microcavity at room temperature. Since then, interest in the field has increased significantly, as a photon Bose-Einstein condensate (BEC) represents a prototypical driven-dissipative system. Here, we investigate how its inherent open nature influences the condensation process both quantitatively and qualitatively. To this end, we consider a mean-field model, which can be derived microscopically from a Lindblad master equation. The underlying rate equations depend on various external parameters such as emission and absorption rates of the dye molecules as well as the cavity photon loss rate. In steady state, we obtain an open-dissipative Bose-Einstein distribution for the mode occupations. The chemical potential of this distribution depends on the occupations of the dye molecules in both their ground and excited state and must therefore be determined self-consistently. We find that the resulting photon distribution is strongly influenced by the driven-dissipative parameters. Based on this result, we identify the main differences between a photonic BEC, an atomic BEC, and a laser.