TY - JOUR

T1 - Deviations from Boltzmann-Gibbs statistics in confined optical lattices

AU - Dechant, Andreas

AU - Kessler, David A.

AU - Barkai, Eli

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/10/23

Y1 - 2015/10/23

N2 - We investigate the semiclassical phase-space probability distribution P(x,p) of cold atoms in a Sisyphus cooling lattice with an additional harmonic confinement. We pose the question of whether this nonequilibrium steady state satisfies the equivalence of energy and probability. This equivalence is the foundation of Boltzmann-Gibbs and generalized thermostatic statistics, and a prerequisite for the description in terms of a temperature. At large energies, P(x,p) depends only on the Hamiltonian H(x,p) and the answer to the question is yes. In distinction to the Boltzmann-Gibbs state, the large-energy tails are power laws P(x,p)∞H(x,p)-1/D, where D is related to the depth of the optical lattice. At intermediate energies, however, P(x,p) cannot be expressed as a function of the Hamiltonian and the equivalence between energy and probability breaks down. As a consequence the average potential and kinetic energy differ and no well-defined temperature can be assigned. The Boltzmann-Gibbs state is regained only in the limit of deep optical lattices. For strong confinement relative to the damping, we derive an explicit expression for the stationary phase-space distribution.

AB - We investigate the semiclassical phase-space probability distribution P(x,p) of cold atoms in a Sisyphus cooling lattice with an additional harmonic confinement. We pose the question of whether this nonequilibrium steady state satisfies the equivalence of energy and probability. This equivalence is the foundation of Boltzmann-Gibbs and generalized thermostatic statistics, and a prerequisite for the description in terms of a temperature. At large energies, P(x,p) depends only on the Hamiltonian H(x,p) and the answer to the question is yes. In distinction to the Boltzmann-Gibbs state, the large-energy tails are power laws P(x,p)∞H(x,p)-1/D, where D is related to the depth of the optical lattice. At intermediate energies, however, P(x,p) cannot be expressed as a function of the Hamiltonian and the equivalence between energy and probability breaks down. As a consequence the average potential and kinetic energy differ and no well-defined temperature can be assigned. The Boltzmann-Gibbs state is regained only in the limit of deep optical lattices. For strong confinement relative to the damping, we derive an explicit expression for the stationary phase-space distribution.

UR - http://www.scopus.com/inward/record.url?scp=84945416382&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.115.173006

DO - 10.1103/PhysRevLett.115.173006

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C2 - 26551114

AN - SCOPUS:84945416382

SN - 0031-9007

VL - 115

JO - Physical Review Letters

JF - Physical Review Letters

IS - 17

M1 - 173006

ER -