Stochastic master equation for a probed system in a cavity

TL;DR

This paper derives a stochastic master equation for a quantum system in a cavity under indirect measurement, illustrating quantum jumps and dynamics freezing through analytical solutions.

Contribution

It provides a detailed, physics-based derivation of the stochastic master equation for cavity-probed quantum systems, linking parameters to observable dynamics.

Findings

Demonstrates quantum jumps in the system's evolution.

Shows measurement-induced freezing of internal dynamics.

Provides analytical solutions illustrating the theory.

Abstract

We present a detailed derivation of the stochastic master equation determining the time evolution of the state of a general quantum system, which is placed inside a cavity and subjected to indirect measurements by monitoring the state of electromagnetic radiation transmitted through the cavity. The derivation is based on the physics involved and the final result is stated in terms of the physical parameters of the setup. To illustrate the predictions contained in the equation, we solve it analytically for a specific system, and we demonstrate quantum jumps and freezing of the internal coherent dynamics of the system as a result of continued measurements.