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arXiv 1101.2659cond-mat.quant-gasquant-ph
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探讨孤立的强关联一维玻色气体的平衡弛豫过程

Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas

Stefan Trotzky, Yu-Ao Chen, Andreas Flesch, Ian P. McCulloch, Ulrich Schollwöck, Jens Eisert, Immanuel Bloch

摘要:

复杂的量子系统最终如何静止的问题是统计力学的核心。1957年E. T.杰恩斯提出了人们在平衡状态下应该期待的量子态,但没有暗示封闭的量子多体系统如何动态平衡。大量的理论和数值研究积累的证据表明,在特定条件下,量子多体模型可以松弛到局部或相对于某些可观测量的情况下,似乎整个系统已经松弛到最大熵状态。本文报道了在强关联条件下,超冷玻色子原子在光晶格中密度波的非平衡动力学的实验观测。使用光学超晶格,我们能够在一个众所周知的初始状态,高保真度的系统。然后,我们遵循系统的准局部密度,电流和凝聚力的动力学演化。基于含时密度矩阵重整化群方法的数值计算结果与实验数据吻合得很好。在很长一段时间内,所有三个局部观测值都显示出与全局最大熵状态预期的平衡值相兼容的快速弛豫。我们发现这种放松的准局域密度和电流最初遵循幂律的指数显着大于自由或硬核玻色子。对于中间时间,系统实现了作为动态量子模拟器的承诺,因为受控动态运行的时间比基于矩阵乘积状态的现有经典算法可以有效地跟踪的时间更长。

英文摘要:

The problem of how complex quantum systems eventually come to rest lies at the heart of statistical mechanics. The maximum entropy principle put forward in 1957 by E. T. Jaynes suggests what quantum states one should expect in equilibrium but does not hint as to how closed quantum many-body systems dynamically equilibrate. A number of theoretical and numerical studies accumulate evidence that under specific conditions quantum many-body models can relax to a situation that locally or with respect to certain observables appears as if the entire system had relaxed to a maximum entropy state. In this work, we report the experimental observation of the non-equilibrium dynamics of a density wave of ultracold bosonic atoms in an optical lattice in the regime of strong correlations. Using an optical superlattice, we are able to prepare the system in a well-known initial state with high fidelity. We then follow the dynamical evolution of the system in terms of quasi-local densities, currents, and coherences. Numerical studies based on the time-dependent density-matrix renormalization group method are in an excellent quantitative agreement with the experimental data. For very long times, all three local observables show a fast relaxation to equilibrium values compatible with those expected for a global maximum entropy state. We find this relaxation of the quasi-local densities and currents to initially follow a power-law with an exponent being significantly larger than for free or hardcore bosons. For intermediate times the system fulfills the promise of being a dynamical quantum simulator, in that the controlled dynamics runs for longer times than present classical algorithms based on matrix product states can efficiently keep track of.

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