We study the thermalization and the Bose-Einstein condensation of a paraxial, spectrally narrow beam of quantum light propagating in a lossless bulk Kerr medium. The spatiotemporal evolution of the quantum optical field is ruled by a Heisenberg equation analogous to the quantum nonlinear Schrödinger equation of dilute atomic Bose gases. Correspondingly, in the weak-nonlinearity regime, the phase-space density evolves according to the Boltzmann equation. Expressions for the thermalization time and for the temperature and the chemical potential of the eventual Bose-Einstein distribution are found. After discussing experimental issues, we introduce an optical setup allowing the evaporative cooling of a guided beam of light towards Bose-Einstein condensation. This might serve as a novel source of coherent light.
We study the thermalization and the Bose-Einstein condensation of a paraxial, spectrally narrow beam of quantum light propagating in a lossless bulk Kerr medium. The spatiotemporal evolution of the quantum optical field is ruled by a Heisenberg equation analogous to the quantum nonlinear Schrödinger equation of dilute atomic Bose gases. Correspondingly, in the weak-nonlinearity regime, the phase-space density evolves according to the Boltzmann equation. Expressions for the thermalization time and for the temperature and the chemical potential of the eventual Bose-Einstein distribution are found. After discussing experimental issues, we introduce an optical setup allowing the evaporative cooling of a guided beam of light towards Bose-Einstein condensation. This might serve as a novel source of coherent light.
The propagation of light in nonlinear media is well described by a 2D nonlinear Schrödinger equation (NLSE) within the paraxial approximation, which is equivalent to the GrossPitaevskii equation (GPE), the mean-field description for the dynamics of Bose-Einstein condensates (BECs). As a product of this similarity, we can establish the figure of a quantum fluid of light. Quantum fluids of light have been used for theoretical and experimental investigations of phenomena already studied and realised in BECs. In this thesis, we describe the mechanisms that make the conception of a quantum fluid of light possible for different experimental platforms. Furthermore, we present a study on the formation of self-bound droplets of light in hot atomic vapours, our chosen nonlinear medium, in an attempt to obtain a mapping between experimental parameters typically used in BEC experiments and those needed to observe the analogous phenomenon in atomic vapours. We investigate the static properties of the system, providing a phase diagram for the different and possible solutions for the optical regimes of interest. Finally, we systematically study droplet dynamics, focusing on the behaviour of the collective monopole excitation and the dynamic formation of these objects under realistic experimental conditions.
Making use of a generalized quantum theory of paraxial light propagation where the radiation-axis and the temporal coordinates play exchanged roles, we discuss the potential of bulk nonlinear optical media in cavityless configurations for quantum statistical mechanics studies of the conservative many-body dynamics of a gas of interacting photons. To illustrate the general features of this point of view, we investigate the response of the fluid of light to the quantum quenches in the photon-photon interaction constant experienced at the front and the back faces of a finite slab of weakly nonlinear material. Extending the standard Bogoliubov theory of dilute Bose-Einstein condensates, peculiar features are predicted for the statistical properties of the light emerging from the nonlinear medium.
Turbulence in the quantum (superfluid) regime, similarly to its classical counterpart, continues to attract a great deal of scientific inquiry due to the yet high number of unresolved problems. While turbulent states can be routinely created in degenerate atomic gases, there is no generic scheme to produce turbulence in fluids of light. Under paraxial propagation, light in bulk nonlinear media behaves as a two-dimensional superfluid, described by a nonlinear Schr\"odinger equation formally equivalent to the Gross-Pitaevskii model of a weakly interacting Bose gas, where photon-photon interactions are mediated by a third-order (Kerr) nonlinearity. Here we develop the theory describing the onset of a kinetic instability when two paraxial optical fluids with different streaming velocities interact via the optical nonlinearity. From numerical simulations of the nonlinear Schr\"odinger equation, we further characterize the onset of the instability and describe its saturation in the form of vortex nucleation and excitation of turbulence. The experimental observation of such effects is also discussed. The class of instabilities described here thus provide a natural route towards the investigation of quantum (superfluid) turbulence, structure formation, and out-of-equilibrium dynamics in superfluids of light.
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.
Abstract Coupled nonlinear Schrödinger equations for paraxial optics with two circular polarizations of light in a defocusing Kerr medium with anomalous dispersion coincide in form with the Gross–Pitaevskii equations for a binary Bose—Einstein condensate (BEC) of cold atoms in the phase separation regime. In this case, the helical symmetry of an optical waveguide corresponds to rotation of the transverse potential confining the BEC. The “centrifugal force” considerably affects the propagation of a light wave in such a system. Numerical experiments for a waveguide with an elliptical cross section have revealed characteristic structures consisting of quantized vortices and domain walls between two polarizations, which have not been observed earlier in optics.
Coupled nonlinear Schrödinger equations for paraxial optics with two circular polarizations of light in a defocusing Kerr medium with anomalous dispersion coincide in form with the Gross–Pitaevskii equations for a binary Bose—Einstein condensate (BEC) of cold atoms in the phase separation regime. In this case, the helical symmetry of an optical waveguide corresponds to rotation of the transverse potential confining the BEC. The “centrifugal force” considerably affects the propagation of a light wave in such a system. Numerical experiments for a waveguide with an elliptical cross section have revealed characteristic structures consisting of quantized vortices and domain walls between two polarizations, which have not been observed earlier in optics.