Thermo-optical interactions in a dye-microcavity photon Bose–Einstein condensate

Abstract

Superfluidity and Bose-Einstein condensation are usually considered as two closely related phenomena. Indeed, in most macroscopic quantum systems, like liquid helium, ultracold atomic Bose gases, and exciton-polaritons, condensation and superfluidity occur in parallel. In photon Bose-Einstein condensates realized in the dye microcavity system, thermalization does not occur by direct interaction of the condensate particles as in the above described systems, i.e. photon-photon interactions, but by absorption and re-emission processes on the dye molecules, which act as a heat reservoir. Currently, there is no experimental evidence for superfluidity in the dye microcavity system, though effective photon interactions have been observed from thermo-optic effects in the dye medium. In this work, we theoretically investigate the implications of effective thermo-optic photon interactions, a temporally delayed and spatially non-local effect, on the photon condensate, and derive the resulting Bogoliubov excitation spectrum. The calculations suggest a linear photon dispersion at low momenta, fulfilling the Landau's criterion of superfluidity. We envision that the temporally delayed and long-range nature of the thermo-optic photon interaction offer perspectives for novel quantum fluid phenomena.

Classical field model for arrays of photon condensates

“…Eq. (5) does not contain interaction energy, which is quite negligible in current experiments [37], except for a slow thermo-optical nonlinearity [38], inclusion of which would be a straightforward extension of our model. With Eq.…”

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

“…A minimal mean-field description of the thermo-optic interaction consists of two equations [22][23][24]. One is a nonlinear Schrödinger equation that accounts for the evolution of the electric field inside the cavity, which is assumed to be linearly polarised.…”

Anisotropic Superfluidity in a Weakly Interacting Condensate of Quasi‐2D Photons

“…However, it is evident that the Thomas-Fermi approximation is hardly applicable because of the essential weakness of the photon-photon interaction. For a dye-photon cavity, the interactions are governed by the thermo-optical effects [2,11] and, additionally, the χ (3) Kerr-type non-linearity. [12] Theoretical calculations from the correlation data [13] and the master-equation model [14] provide rather low estimates for the dimensionless 2D interaction parameter [15]g ≈ 10 −7 − 10 −4 .…”

“…changing the cavity width from local (for cavities with L ≈ 1 µm) to highly non-local forms (for thick cavities with L ≈ 10 µm), [11] and is temporally very much delayed due to the slow timescales of heating, taking up to ≈ 1 ms to act.…”

“…It is worth noting that all corrections to due the coordinate dependence of the effective mass enter the Equations (9), (11), and (12) via T = q 2 /2m ph 0 which grows with q and, while the shift ofμ is negligible due to the factor (L 1 /L 0 ) 2 , the corrections to V 0 and V 1 cannot be neglected. Here, we assume that the modulation of the condensate profile by the periodic change in the cavity width is weak, which means that V 0 should be small compared toμ.…”