Counting statistics of energy transport across squeezed thermal reservoirs

TL;DR

This paper develops a formalism to analyze the full counting statistics of energy exchange between multiple squeezed thermal reservoirs and a cavity, revealing effects of noncommutativity and conditions for fluctuation theorems.

Contribution

It introduces a general formalism based on the two-point measurement scheme for energy transport in systems coupled to squeezed thermal reservoirs, including analytical results for specific cases.

Findings

Short time statistics are affected by noncommutativity, potentially leading to negative probabilities.

No general transient fluctuation theorem exists for single reservoir energy transport.

Steady-state fluctuation theorem with a non-universal affinity is valid for two reservoirs.

Abstract

A general formalism for computing the full counting statistics of energy exchanged between 'N' squeezed thermal photon reservoirs weakly coupled to a cavity with 'M' photon modes is presented. The formalism is based on the two-point measurement scheme and is applied to two simple special cases, the relaxation dynamics of a single mode cavity in contact with a single squeezed thermal photon reservoir and the steady-state energy transport between two squeezed thermal photon reservoirs coupled to a single cavity mode. Using analytical results, it is found that the short time statistics is significantly affected by noncommutivity of the initial energy measurements with the reservoirs squeezed states, and may lead to negative probabilities if not accounted properly. Furthermore, it is found that for the single reservoir setup, generically there is no transient or steady-state fluctuation theorems for energy transport. In contrast, for the two reservoir case, although there is no generic transient fluctuation theorem, steady-state fluctuation theorem with a non-universal affinity is found to be valid. Statistics of energy currents are further discussed.