An approximation scheme and non-Hermitian re-normalization for description of atom-field system evolution

TL;DR

This paper introduces an approximation scheme and a non-Hermitian re-normalization method to analyze the time evolution of a two-level atom interacting with a quantum field, providing simplified formulas and deriving optical Bloch equations.

Contribution

It presents a systematic approximation for the evolution of atom-field systems at any time, incorporating a novel non-Hermitian re-normalization technique.

Findings

Derived simplified evolution formulas for atom-field interactions.

Successfully recovered optical Bloch equations using the new framework.

Provided insights into non-asymptotic quantum system dynamics.

Abstract

Interactions between a source of light and atoms are ubiquitous in nature. The study of them is interesting on the fundamental level as well as for applications. They are in the core of Quantum Information Processing tasks and in Quantum Thermodynamics protocols. However, even for two-level atom interacting with field in rotating wave approximation there exists no exact solution. This touches as basic problem in quantum field theory, where we can only calculate the transitions in the time asymptotic limits (i.e. minus and plus infinity), while we are not able to trace the evolution. In this paper we want to get more insight into the time evolution of a total system of a two-level atom and a continuous-mode quantum field. We propose an approximation, which we are able to apply systematically to each order of Dyson expansion, resulting in greatly simplified formula for the evolution of the combined system at any time. Our tools include a proposed novel, {\it non-Hermitian} re-normalization method. As a sanity check, by applying our framework, we derive the known optical Bloch equations.