Collective modes of a photon Bose–Einstein condensate with thermo-optic interaction

Abstract

Although for photon Bose-Einstein condensates the main mechanism of the observed photonphoton interaction has already been identified to be of a thermo-optic nature, its influence on the condensate dynamics is still unknown. Here a mean-field description of this effect is derived, which consists of an open-dissipative Schrödinger equation for the condensate wave function coupled to a diffusion equation for the temperature of the dye solution. With this system at hand, the lowest-lying collective modes of a harmonically trapped photon Bose-Einstein condensate are calculated analytically via a linear stability analysis. As a result, the collective frequencies and, thus, the strength of the effective photon-photon interaction turn out to strongly depend on the thermal diffusion in the cavity mirrors. In particular, a breakdown of the Kohn theorem is predicted, i.e.the frequency of the centre-of-mass oscillation is reduced due to the thermo-optic photon-photon interaction.

Photon BEC with thermo-optic interaction at dimensional crossover

“…In a second step, it is now crucial to search for mechanisms to increase the effective photon-photon interaction. In this respect we already found in the former theoretical study [22] the intriguing result that the strength of the thermo-optic interaction increases quadratically with the lateral extension of the cavity mirrors. However, as this would be quite laborious to achieve experimentally, we explore here an alternative mechanism, which relies on increasing the effective photon-photon interaction strength by reducing the system dimension from 2D to 1D.…”

“…Furthermore, the duty cycle σ describes that the experiment operates with a pulsed pump laser, whereas our theoretical description works with a continuous pump for reaching the steady state. This modification is needed here, as the temperature necessitates several experimental cycles to achieve its steady state [22].…”

“…Here the resulting thermo-optic interaction strength is defined as [22] g T = σγτ B, (14) and is, thus, determined by various material properties of the dye solution. As a next step, we determine the energy functional corresponding to equation (13), which turns out to consist of three parts:…”

Cloud shape of a molecular Bose–Einstein condensate in a disordered trap: a case study of the dirty boson problem

“…As no obvious energy functional exists, we cannot rely upon the standard variational procedure of [79,80], which has been so successful in the realm of ultracold quantum gases. Instead, we follow [81,82], where a similar variational solution is worked out directly on the basis of the underlying equations of motion within a so-called cumulant approach. To this end, we use a Gaussian ansatz for the disorder-ensemble averaged condensate wave function ( ) , respectively, and integrate over the whole space.…”

Controlled two-mode emission from the interplay of driving and thermalization in a dye-filled photonic cavity

“…While the former process describes simple lasing [1], in the last decade the regime where thermalization is the dominant process, has been realized and equilibrium-like Bose condensation of photons was observed in various systems [2][3][4][5][6][7]. Also the temporal [8][9][10] and spatial [11] features of photon BECs driven out of equilibrium have been studied, as well as the demarcation of photon BECs from lasers [12][13][14][15][16], the grand-canonical statistics in photon BECs [17], the breakdown of equilibrium-like behavior [18] and the thermo-optic interaction effects [19]. Very recently, it was found both theoretically [20] and experimentally [7] that excited cavity modes start to emit coherently together with the ground mode, when the pump power and the photon loss are increased relative to the thermalizing coupling to the dye.…”