# Time-reversed quantum trajectory analysis of micromaser correlation properties and fluctuation relations

## TL;DR

This paper develops a time-reversed quantum trajectory framework for the micromaser, linking it to fluctuation relations and correlation properties, extending existing theories with a renewal process approach.

## Contribution

It introduces a novel time-reversed quantum trajectory analysis for the micromaser, incorporating a general renewal process perspective and deriving fluctuation relations.

## Key findings

- Time-reversed trajectories naturally arise in micromaser correlation analysis.
- A fluctuation relation for trajectory probabilities is formulated.
- The approach extends master equation analysis with renewal process generalization.

## Abstract

The micromaser is examined with the aim of understanding certain of its properties based on a time-reversed quantum trajectory analysis. The background theory of master equations derived from a repeated interaction model perspective is briefly reviewed and extended by taking into account the more general renewal process description of the sequence of interactions of the system with incoming ancilla, and results compared with other recent (and not so recent) approaches that use this generalisation. The results are then specialised to the micromaser, and a quantum trajectory unravelling of the micromaser dynamics is formulated that enables time-reversed quantum trajectories, defined according to the Crooks approach, to, first, be shown to arise naturally in the analysis of micromaser and atomic beam correlations, and second used in the formulation of a fluctuation relation for the probabilities of trajectories and their time-reversed counterparts.