Deviations from Boltzmann-Gibbs Statistics in Confined Optical Lattices
Deviations from Boltzmann-Gibbs Statistics in Confined Optical Lattices
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DOI：
10.1103/physrevlett.115.173006
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发表时间：
2015-10-23
影响因子：
8.6
通讯作者：
Barkai, Eli
中科院分区：
文献类型：
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作者：
Dechant, Andreas;Kessler, David A.;Barkai, Eli
研究了附加简谐禁闭的西西弗冷却晶格中冷原子的半经典相空间几率分布。我们提出了这个非平衡定态是否满足能量和概率等价的问题。这个等价性是玻尔兹曼-吉布斯统计和广义恒温统计的基础，也是用温度描述的前提。在大能量下，P(x，p)只依赖于哈密顿量H(x，p)，问题的答案是肯定的。与Boltzmann-Gibbs态不同，大能量尾巴是幂定律P(x，p)。H(x，p)(-1/D)，其中D与光学晶格的深度有关。然而，在中等能量下，P(x，p)不能表示为哈密顿量的函数，能量和概率之间的等价性被打破。其结果是，平均势能和动能不同，没有明确定义的温度。玻尔兹曼-吉布斯态只有在深光学晶格的极限下才能恢复。对于相对于阻尼项的强约束，我们得到了定常相空间分布的显式表达式。
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.