Lemos Gabriela Barreto, Toscano Fabricio
Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jul;84(1 Pt 2):016220. doi: 10.1103/PhysRevE.84.016220. Epub 2011 Jul 25.
We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long time scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt-echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert-space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert-space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime.
我们研究了通过退相类型相互作用与具有混沌经典动力学的任意环境耦合的量子系统中的退相干。在优先能量本征基下写出的中心系统约化态的相干性是量子洛施密特回波，在强耦合 regime 中，它们在长时间尺度上的特征是围绕一个恒定平均值的涨落。我们表明，由于环境的混沌动力学，洛施密特回波涨落的平均值和宽度与我们定义为环境有效希尔伯特空间维度的量成反比，该量通常小于整个可用希尔伯特空间的维度。然而，在半经典 regime 中，这个有效希尔伯特空间维度通常很大，在这种情况下，即使是具有少数自由度的混沌环境也会产生无复苏的退相干。此外，我们表明在这个 regime 中，环境会使中心系统平衡到其约化密度矩阵的时间平均值，这对应于优先能量本征基下的对角态。对于两个未耦合、初始纠缠的中心系统与具有混沌经典动力学的相同局部量子环境相互作用的情况，我们表明在半经典极限下，平衡态任意接近可分离态。我们通过数值模拟证实了我们的结果，其中环境由混沌 regime 中的量子踢转子建模。
