The time evolution of an atom coupled to a thermal radiation field

TL;DR

This paper models the time evolution of an atom coupled to a thermal radiation field using a harmonic oscillator and scalar field, revealing how the atom thermalizes through emission and absorption processes.

Contribution

It introduces a simplified model employing dressed states to analyze atomic thermalization dynamics in a thermal radiation environment.

Findings

Atomic occupation numbers depend on emission and absorption probabilities.

The atom thermalizes with the field within a time scale inversely proportional to the coupling constant.

The model provides explicit expressions for the time evolution of the atom's state.

Abstract

We study the time evolution of an atom suddenly coupled to a thermal radiation field. As a simplified model of the atom-electromagnetic field system we use a system composed by a harmonic oscillator linearly coupled to a scalar field in the framework of the recently introduced dressed coordinates and dressed states. We show that the time evolution of the thermal expectation values for the occupation number operators depend exclusively on the probabilities associated with the emission and absorption of field quanta. In particular, the time evolution of the number operator associated with the atom is given in terms of the probability of remaining in the first excited state and the decay probabilities from this state by emission of field quanta of frequencies $\omega_k$. Also, it is showed that independent of the initial state of the atom, it thermalizes with the thermal radiation field in a time scale of the order of the inverse coupling constant.