Transitions in the ergodicity of subrecoil-laser-cooled gases

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.

5 pages, 1 figure, 4 pages of supplementary material

References in corpus (10)

• Lévy walks
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Pesin-Type Identity for Weak Chaos
• Phase Diagram in Stored-Energy-Driven Lévy Flight
• Statistics of the longest interval in renewal processes
• Statistics of occupation time and connection to local properties of non-homogeneous random walks
• Regularized Boltzmann-Gibbs statistics for a Brownian particle in a non-confining field
• Renewal processes and fluctuation analysis of molecular motor stepping
• Thermodynamics of a Brownian particle in a non-confining potential
• A work fluctuation theorem for a Brownian particle in a non confining potentia

Cited by in corpus (5)

• Anomalous statistics of laser-cooled atoms in dissipative optical lattices
• Infinite ergodic theory for three heterogeneous stochastic models with application to subrecoil laser cooling
• Gas of sub-recoiled laser cooled atoms described by infinite ergodic theory
• Brownian particles in periodic potentials: coarse-graining versus fine structure
• Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder