Hartree-Fock Analogue Theory of Thermo-Optic Interaction

TL;DR

This paper develops a quantum mechanical theory of thermo-optic photon-photon interactions in dye-filled microcavities, going beyond mean-field models to enable precise measurement of interaction strength.

Contribution

It introduces a self-consistent quantum model of thermo-optic interactions, deriving an approximate Hamiltonian applicable to experimental regimes.

Findings

Quantum theory predicts interaction effects in photon condensates.

Perturbative analysis applied to harmonic and box potentials.

Potential for precise measurement of photon-photon interaction strength.

Abstract

Thermo-optic interaction significantly differs from the usual particle-particle interactions in physics, as it is retarded in time. A prominent platform for realising this kind of interaction are photon Bose-Einstein condensates, which are created in dye-filled microcavities. The dye solution continually absorbs and re-emits these photons, causing the photon gas to thermalise and to form a Bose-Einstein condensate. Because of a non-ideal quantum efficiency, these cycles heat the dye solution, creating a medium that provides an effective thermo-optic photon-photon interaction. So far, only a mean-field description of this process exists. This paper goes beyond by working out a quantum mechanical description of the effective thermo-optic photon-photon interaction. To this end, the self-consistent modelling of the temperature diffusion builds the backbone of the modelling. Furthermore, the manyfold experimental timescales allow for deriving an approximate Hamiltonian. The resulting quantum theory is applied in the perturbative regime to both a harmonic and a box potential for investigating its prospect for precise measurements of the effective photon-photon interaction strength.