Quantum statistics of a single-atom Scovil-Schulz-DuBois heat engine

TL;DR

This paper analyzes the quantum statistical behavior of a single-atom heat engine, revealing how hot bath temperature influences lasing and introducing a four-level model to eliminate double-threshold effects.

Contribution

It derives a quantum laser equation for the single-atom heat engine and proposes a four-level model to prevent double-threshold behavior.

Findings

Lasing occurs with increased hot bath temperature due to population inversion.

High hot bath temperature enhances atomic decay, weakening lasing gain.

A four-level model removes the double-threshold phenomenon, simplifying lasing conditions.

Abstract

We study the statistics of the lasing output from a single atom quantum heat engine, which was originally proposed by Scovil and Schulz-DuBois (SSDB). In this heat engine model, a single three-level atom is strongly coupled with an optical cavity, and contacted with a hot and a cold heat bath together. We derive a fully quantum laser equation for this heat engine model, and obtain the photon number distribution for both below and above the lasing threshold. With the increase of the hot bath temperature, the population is inverted and lasing light comes out. However, we notice that if the hot bath temperature keeps increasing, the atomic decay rate is also enhanced, which weakens the lasing gain. As a result, another critical point appears at a very high temperature of the hot bath, after which the output light become thermal radiation again. To avoid this double-threshold behavior, we introduce a four-level heat engine model, where the atomic decay rate does not depend on the hot bath temperature. In this case, the lasing threshold is much easier to achieve, and the double-threshold behavior disappears.