Infinite density for cold atoms in shallow optical lattices

Infinite densities are non-normalizable quasi-probability distributions that can describe the long-time properties of systems when ergodicity is broken and the equilibrium Boltzmann-Gibbs distribution fails. Their experimental observation has remained elusive so far. We here perform semiclassical Monte Carlo simulations of cold atoms in dissipative optical lattices with realistic parameters. We show that the momentum infinite density, as well as its scale invariance, should be observable in shallow potentials. We further evaluate the momentum autocorrelation function both in the stationary and nonstationary, aging regime.