Invariant states of quantum birth and death chains

TL;DR

This paper provides a sufficient condition for certain quantum birth and death chains to have invariant states, with applications to quantum masers and the Jaynes-Cummings model involving randomness and non-diagonal states.

Contribution

It introduces a new criterion for invariant states in quantum birth and death chains and applies it to complex quantum systems like generalized masers.

Findings

Invariant states exist under the given condition.

Application to generalized one-atom masers.

Application to Jaynes-Cummings maser with randomness.

Abstract

A sufficient condition is given for a class of quantum birth and death chains on the non-negative integers to possess invariant states. The result is applied to generalised one-atom masers and to the Jaynes-Cummings one-atom maser with random interaction time and not necessarily diagonal atomic states.