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
N1 - Publisher Copyright:
© 2016 American Physical Society.
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
U2 - 10.1103/PhysRevE.94.022151
DO - 10.1103/PhysRevE.94.022151
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
C2 - 27627290
SN - 2470-0045
VL - 94
JO - Physical Review E
JF - Physical Review E
IS - 2
M1 - 022151
ER -