Dissipation and non-thermal states in cryogenic cavities

We study the properties of photons in a cryogenic cavity, made by cryo-cooled mirrors surrounded by a room temperature environment. We model such a system as a multimode cavity coupled to two thermal reservoirs at different temperatures. Using a Lindblad master equation approach, we derive the photon distribution and the statistical properties of the cavity modes, finding an overall non-thermal state described by a mode-dependent effective temperature. We also calculate the dissipation rates arising from the interaction of the cavity field with the external environment and the mirrors, relating such rates to measurable macroscopic quantities. These results provide a simple theory to calculate the dissipative properties and the effective temperature of a cavity coupled to different thermal reservoirs, offering potential pathways for engineering dissipations and photon statistics in cavity settings.

💡 Research Summary

The paper presents a comprehensive theoretical study of photons in a cryogenic optical cavity whose mirrors are cooled to a low temperature (Tm) while the surrounding environment remains at room temperature (Te). The authors model the cavity as a set of independent harmonic modes, each coupled to two distinct thermal reservoirs: one representing the cryogenic mirrors and the other the external free‑space radiation. Using a Lindblad master‑equation framework, they derive the dissipative dynamics for each mode, introducing loss rates γν,m (mirror‑induced) and γν,e (free‑space‑induced). Detailed‑balance relations enforce γν,α⁺ = e⁻(ων/Tα)γν,α⁻, allowing the rates to be split into a temperature‑independent spectral factor γν,α and a Bose‑Einstein occupation factor nB(ων,Tα).

A key result is that the steady‑state photon distribution of each mode is thermal with an effective temperature T_eff(ων) that depends on the mode frequency. At low frequencies T_eff is a weighted average of Tm and Te, while at high frequencies it approaches the hotter reservoir temperature. The crossover is governed by the ratio γν,m/γν,e, highlighting that the presence of two baths drives the cavity out of equilibrium, in contrast to the usual single‑bath scenario where all modes thermalize to a common temperature.

The authors then derive microscopic expressions for the loss rates. For the mirror coupling they assume a dipole interaction Hc‑m = –∫ d(r)·E(r) and relate the correlation function of the mirror dipoles to the material conductivity σ(ων). This yields
γν,m =