Bose-Einstein condensation of photons in an ideal atomic gas

Abstract

We study peculiarities of Bose-Einstein condensation of photons that are in thermodynamic equilibrium with atoms of noninteracting gases. General equations of the thermodynamic equilibrium of the system under study are obtained. We examine solutions of these equations in the case of high temperatures, when the atomic components of the system can be considered as nondegenerated ideal gases of atoms, and the photonic component can form a state with the Bose condensate. Transcendental equation for transition temperature and expression for the density of condensed photons in the considered system are derived. We also obtain analytical solutions of the equation for the critical temperature in a number of particular cases. The existence of two regimes of Bose condensation of photons, which differ significantly in nature of transition temperature dependence on the total density of photons pumped into the system, is revealed. In one case, this dependence is a traditional fractional-power law, and in another one it is the logarithmic law. Applying numerical methods, we determine boundaries of existence and implementation conditions for different regimes of condensation depending on the physical parameters of the system under study. We also show that for a large range of physical systems that are in equilibrium with photons (from ultracold gases of alkali metals to certain types of ideal plasma), the condensation of photons should occur according to the logarithmic regime.Comment: 12 pages, 3 figure

Schwinger-Keldysh theory for Bose-Einstein condensation of photons in a dye-filled optical microcavity

“…[22], and conditions for BEC of photons that are in thermal equilibrium with atoms of dilute gases were derived in Ref. [23].…”

One-dimensional Bose-Einstein condensation of photons in a microtube

“…In equilibrium this quantity is linearly proportional to the number of atoms and is given by N at 1 + g 12 exp ωat− ω0 T −1 , where g 12 is the ratio between degeneracy of the atomic ground state and the first excited state, see for details Refs. [7,8].…”

“…[3,6,8,22]) and in different contexts for D = 3 (see e.g. [7,23,24]), but never in one dimension. Therefore, * alex.kruchkov@epfl.ch there's a need to complete the study for photons with the one-dimensional degree of freedom.…”

Thermalization and Bose–Einstein condensation of a photon gas in a multimode hybrid atom-membrane optomechanical microcavity

“…Some of these studies have concentrated on the modeling of the photon BEC from the point of view of equilibrium statistical mechanics [15,[21][22][23][24][25], and some other theoretical works have explored such topics as the emergence of phase coherence in photon BEC resulting from photon-photon interaction through an intermediate medium [26], phase diffusion in a BEC of light in a dye-filled optical microcavity [27], quantum modeling of the nonequilibrium BEC of photons and polaritons in planar microcavity devices [28], and the crossover from photon condensation to laser-like states [29,30]. BEC and laser operation have similar features because both of them involve a spontaneous phase-symmetry breaking and a transition to a macroscopically occupied quantum state.…”