Transitions in the ergodicity of subrecoil-laser-cooled gases

TL;DR

This paper explores how subrecoil laser cooling leads to non-ergodic behavior in atomic gases, characterized by a transition from ergodic to non-ergodic states due to power-law trapping times, described using infinite ergodic theory.

Contribution

It introduces a new statistical-mechanical framework based on infinite ergodic theory to describe non-ergodic properties in laser-cooled gases, highlighting a sharp transition in observable ergodicity.

Findings

Energy exhibits a discontinuous ergodic transition.

Transition controlled by fluorescence rate.

Observable ergodicity depends on integrability with respect to invariant density.

Abstract

With subrecoil-laser-cooled atoms one may reach nano-Kelvin temperatures while the ergodic properties of these systems do not follow usual statistical laws. Instead, due to an ingenious trapping mechanism in momentum space, power-law-distributed sojourn times are found for the cooled particles. Here, we show how this gives rise to a statistical-mechanical framework based on infinite ergodic theory, which replaces ordinary ergodic statistical physics of a thermal gas of atoms. In particular, the energy of the system exhibits a sharp discontinuous transition in its ergodic properties. Physically this is controlled by the fluorescence rate, but more profoundly it is a manifestation of a transition for any observable, from being an integrable to becoming a non-integrable observable, with respect to the infinite (non-normalised) invariant density.