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Communications in Theoretical Physics

Phase Transition and Superfluid of Photons and Photon Pairs in a Two-Dimensional Optical Microcavity

Jian‐Jun Zhang, Jianhui Yuan, Junpei Zhang, Ze Cheng

Published Nov 1, 2012• 0 citations
Publisher

Abstract

We analyze the ground-state properties and the excitation spectrum of Bose—Einstein condensates of photons and PPs in a two-dimensional optical microcavity. First, using the variational method, we discuss the ground-state phase transition of the two-component system. We also investigate the energy gap between the ground state and the first excited state. Moreover, by investigating the excitation spectrum, we also illustrate how the superfluid behavior of photons and PPs can be associated with the phase transition of the system.

DOI
10.1088/0253-6102/58/5/10

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We analyze the ground-state properties and the excitation spectrum of Bose—Einstein condensates of photons and PPs in a two-dimensional optical microcavity. First, using the variational method, we discuss the ground-state phase transition of the two-component system. We also investigate the energy gap between the ground state and the first excited state. Moreover, by investigating the excitation spectrum, we also illustrate how the superfluid behavior of photons and PPs can be associated with the phase transition of the system.
The condensate density profile of trapped two-dimensional gas of photons in an optical microcavity, filled by a dye solution, is analyzed taking into account a coordinate-dependent effective mass of cavity photons and photon–photon coupling parameter. The profiles for the densities of the superfluid and normal phases of trapped photons in the different regions of the system at the fixed temperature are analyzed. The radial dependencies of local mean-field phase transition temperature Tc0(r) and local Kosterlitz–Thouless transition temperature Tc(r) for trapped microcavity photons are obtained. The coordinate dependence of cavity photon effective mass and photon–photon coupling parameter is important for the mirrors of smaller radius with the high trapping frequency, which provides Bose–Einstein condensation and superfluidity for smaller critical number of photons at the same temperature. We discuss a possibility of an experimental study of the density profiles for the normal and superfluid components in the system under consideration.
We investigate the Bose-Einstein condensation of photons and photon pairs in a two-dimension optical microcavity. We find that in the paraxial approximation, the mixed gas of photons and photon pairs is formally equivalent to a two dimension system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phase. We also discuss the quantum phase transition of the system and obtain the critical point analytically. Moreover, we find that the quantum phase transition of the system can be interpreted as second harmonic generation.
We study ground-state phase diagrams and excitation spectra of Bose-Bose mixtures in an optical lattice by applying the Gutzwiller approximation to the two-component Bose-Hubbard model. A case of equal hoppings and equal intra-component interactions for both components is considered. Due to the existence of inter-component interaction, there appear several quantum phases, such as the superfluid, paired superfluid, and counterflow superfluid phases. We find that the transition from superfluid (SF) to Mott insulator (MI) with even filling factors can be of the first order for a wide range of the chemical potential. We calculate the excitation spectra as a useful probe to identify the quantum phases and the SF-to-MI transitions. In the excitation spectra of the SF phase, there are two gapless modes and a few gapful modes, which respectively correspond to phase and amplitude fluctuations of the order parameters. At the SF-to-MI transition point, we show that the energy gaps of certain amplitude modes reach zero for the second-order transition while they remain finite for the first-order one. Since the excitation spectrum can be measured by the Bragg scattering, we calculate the dynamical structure factor by using the linear response theory. We consider three types of density fluctuations, and show that the density fluctuations are coupled to different excitation branches in different quantum phases.
The excitation spectrum for symmetric two-component Bose-Einstein condensate (BECs) in optical lattices is obtained, with emphasis on its quantitative dependence on intercomponent interaction parameter. The resulting two branches of the excitation spectrum have a linear spectrum asymptotically in the low momentum limit, which is expected as a behavior of superfluid. The critical superfluid velocity, depending on the intercomponent interaction parameter, is then obtained, which is quite different from the result obtained in other reference. A requirement of real excitation spectrum also results in a condition on the interaction parameters, which coincides with the phase separation condition. Hence in real spectrum excitation, it is proposed that there should be two branches of superfluid with different critical superfluid velocities, while in the complex spectrum it is predicted that there should be phase separation in the two-branch superfluid system. The excitation spectrum for an asymmetric two-component BEC system is also presented and analyzed.
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.
We study the Bose–Einstein condensation of parallel light in a two-dimensional nonlinear optical cavity, where the massive photons are converted into photon molecules (p-molecules). We extend the classical-field method to provide a description of the two-component system, and we also derive a coupled density equation which can be used to describe the conversion relation between photons and p-molecules. Furthermore, we obtain the chemical potential of the system, and we also find that the system can transform from the mixed photon and p-molecule condensate phase into a pure p-molecule condensate phase. Additionally, we investigate the collective excitation of the system. We also discuss the problem how the spontaneous decay of an atom is influenced by both the phase transition and collective excitation of the coupling system.