The steady state quantum statistics of a non-Markovian atom laser

TL;DR

This paper provides a quantum mechanical analysis of an atom laser model, revealing conditions for steady state formation and calculating the output energy flux, with implications for understanding non-Markovian quantum systems.

Contribution

It introduces a non-Markovian quantum model of an atom laser without relying on Born or Markov approximations, analyzing bound states and steady-state conditions.

Findings

Bound state existence depends on gravity presence.

No steady state in the absence of gravity due to bound states.

Calculated steady-state output energy flux.

Abstract

We present a fully quantum mechanical treatment of a single-mode atomic cavity with a pumping mechanism and an output coupling to a continuum of external modes. This system is a schematic description of an atom laser. In the dilute limit where atom-atom interactions are negligible, we have been able to solve this model without making the Born and Markov approximations. When coupling into free space, it is shown that for reasonable parameters there is a bound state which does not disperse, which means that there is no steady state. This bound state does not exist when gravity is included, and in that case the system reaches a steady state. We develop equations of motion for the two-time correlation in the presence of pumping and gravity in the output modes. We then calculate the steady-state output energy flux from the laser.