Derivation of the quantum-optical master equation based on coarse-graining of time

TL;DR

This paper presents a new derivation of the quantum-optical master equation using coarse-graining of time, providing clearer insights and addressing common assumptions about system-bath factorization.

Contribution

It offers a derivation that avoids complex concepts like quantum stochastic methods, clarifies the validity of the factorization assumption for spontaneous emission, and simplifies understanding of the master equation.

Findings

The derivation aligns with existing methods but is more accessible.

The factorization assumption is justified for spontaneous emission.

Provides a clearer conceptual framework for the master equation.

Abstract

This is a derivation of the quantum-optical master equation using coarse-graining of time, which brings new insights into a decades old technique. My derivation is quite similar to derivations using quantum stochastic methods or Kraus operators, though I go through the derivation without explicitly invoking any of these concepts, so it may be easier to follow as an introduction. I also address the major pitfall of nearly all microscopic derivations of the master equation, namely that they assume the state of the system and bath factorize for all times. I show why this assumption actually holds for spontaneous emission, and coincidentally turns out to be correct.