Deviations from Boltzmann-Gibbs equilibrium in confined optical lattices

Cold atoms in dissipative optical lattices have long been known to exhibit anomalous kinetics due to an effective nonlinear friction force. Here we show that confining the spatial motion of the atoms will lead to an anomalous non-Boltzmann-Gibbs equilibrium state, with a power law tail at large energies. Only in the limit of deep optical lattices, do we regain the Boltzmann-Gibbs state. For strong confinement relative to the damping, we find an explicit expression for the equilibrium phase-space distribution, which generally differs from the canonical Boltzmann-Gibbs state at all energies. Both in the low and high energy limits, the equilibrium distribution is a function of the system's Hamiltonian. At intermediate energies, however, the distribution is not a function of energy only and equipartition is violated.