Photon counting beyond the rotating-wave approximation

TL;DR

This paper develops a method to extract photon counting statistics from quantum Langevin equations, enabling analysis of radiation in open quantum systems beyond the rotating-wave approximation, and shows that an effective Lindblad approach remains useful.

Contribution

It introduces a way to obtain photon counting statistics from quantum Langevin equations, extending the Lindblad framework beyond the rotating-wave approximation.

Findings

Photon counting statistics can be derived from quantum Langevin equations.

An effective Lindblad equation captures key radiation statistics outside the rotating-wave limit.

The method is demonstrated on a damped harmonic oscillator at finite temperature.

Abstract

Open quantum systems are often described by a Lindblad master equation, which relies on a set of approximations, most importantly the rotating-wave approximation which is only valid for weak damping. In the Lindblad setting, dissipative processes are described through jump operators, distinguishing between absorption and emission of photons. This enables the simple identification of emitted photons which provides a straightforward way to obtain the radiation statistics. Outside the rotating-wave limit, the Lindblad approach does not work. Open quantum systems can then be described by, e.g., the quantum Langevin equation. However, in this framework the number of emitted photons is not easily accessible. In this work, we point out how to obtain the photon counting statistics from a quantum Langevin equation and provide an expression for the photon current operator, for arbitrary systems coupled to linear environments. As an example, we employ the method to study the radiation statistics of a damped harmonic oscillator at finite temperature beyond the rotating-wave approximation. We show that even outside the rotating-wave limit, the most important contribution to the radiation statistics can be captured by an effective Lindblad equation, thus extending the range of possible applications of the Lindblad framework.