Deviations from Boltzmann-Gibbs Statistics in Confined Optical Lattices

Area of Science:

• Atomic physics
• Quantum mechanics
• Statistical mechanics

Background:

• Cold atoms in optical lattices are crucial for quantum simulations.
• Sisyphus cooling creates nonequilibrium steady states.
• Thermostatic statistics rely on energy-probability equivalence.

Purpose of the Study:

• To investigate the semiclassical phase-space distribution of cold atoms in a Sisyphus cooling lattice with harmonic confinement.
• To determine if the nonequilibrium steady state satisfies the equivalence of energy and probability.

Main Methods:

• Analysis of the semiclassical phase-space probability distribution P(x,p).
• Investigation of the dependence of P(x,p) on the Hamiltonian H(x,p).
• Derivation of an explicit expression for the stationary phase-space distribution under strong confinement.

Main Results:

• At high energies, P(x,p) depends on H(x,p), satisfying energy-probability equivalence with power-law tails.
• At intermediate energies, this equivalence breaks down, leading to differing average kinetic and potential energies.
• A well-defined temperature cannot be assigned in this regime.

Conclusions:

• The equivalence of energy and probability is not universally satisfied in this driven system.
• The Boltzmann-Gibbs state is only recovered in the limit of deep optical lattices.
• The study provides insights into the statistical properties of driven quantum systems.