TY - JOUR

T1 - Heavy-tailed phase-space distributions beyond Boltzmann-Gibbs

T2 - Confined laser-cooled atoms in a nonthermal state

AU - Dechant, Andreas

AU - Shafier, Shalom Tzvi

AU - Kessler, David A.

AU - Barkai, Eli

PY - 2016/8/31

Y1 - 2016/8/31

N2 - The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for nonthermal systems such as cold atoms in optical lattices, where the heat bath is replaced with the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy of the system still describes its stationary state statistics. We find that this is true for the center part of the phase-space density for deep lattices, where the Boltzmann-Gibbs density provides an approximate description. The relation between energy and statistics also persists for strong confinement and in the limit of high energies, where the system becomes underdamped. However, the phase-space density now exhibits heavy power-law tails. In all three cases we find expressions for the leading-order phase-space density and corrections which break the equivalence of probability and energy and violate energy equipartition. The nonequilibrium nature of the steady state is corroborated by explicit violations of detailed balance. We complement these analytical results with numerical simulations to map out the intricate structure of the phase-space density.

AB - The Boltzmann-Gibbs density, a central result of equilibrium statistical mechanics, relates the energy of a system in contact with a thermal bath to its equilibrium statistics. This relation is lost for nonthermal systems such as cold atoms in optical lattices, where the heat bath is replaced with the laser beams of the lattice. We investigate in detail the stationary phase-space probability for Sisyphus cooling under harmonic confinement. In particular, we elucidate whether the total energy of the system still describes its stationary state statistics. We find that this is true for the center part of the phase-space density for deep lattices, where the Boltzmann-Gibbs density provides an approximate description. The relation between energy and statistics also persists for strong confinement and in the limit of high energies, where the system becomes underdamped. However, the phase-space density now exhibits heavy power-law tails. In all three cases we find expressions for the leading-order phase-space density and corrections which break the equivalence of probability and energy and violate energy equipartition. The nonequilibrium nature of the steady state is corroborated by explicit violations of detailed balance. We complement these analytical results with numerical simulations to map out the intricate structure of the phase-space density.

UR - http://www.scopus.com/inward/record.url?scp=84989299165&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84989299165&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.94.022151

DO - 10.1103/PhysRevE.94.022151

M3 - Article

AN - SCOPUS:84989299165

VL - 94

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 2

M1 - 022151

ER -