一维晶格中的多粒子量子行走和Fisher信息
Multi-particle quantum walks and Fisher information in one-dimensional lattices
摘要：
最近的单粒子和双粒子的量子行走（QWs）实验表明，在一维（1D）晶格中存在微妙的量子力学相关行走。然而，相互作用和量子统计在这种行走中的作用在多体水平上却鲜为人知。本文利用时间演化的分块抽取算法和多体微扰理论，严格研究了一维晶格中三种不可分辨玻色子和费米子的量子阱、Bloch振荡和量子Fisher信息。我们发现，这种强关联的多体量子阱不仅产生了散射态、二体和三体束缚态的依赖于物理和相互作用的弹道输运，而且还提供了一种量子增强的引力精确测量。结果表明，与费米子的行走相比，三玻色子的量子阱表现出更丰富的协同行走动力学和竞争Bloch振荡，在特征时间$t_0$以下呈现出令人惊讶的时间标度$t^3$，并且对于$t>t_0$饱和到$t^2$的基本极限.
英文摘要：
Recent experiments on quantum walks (QWs) of a single and two particles demonstrated subtle quantum statistics-dependent walks in one-dimensional (1D) lattices. However the roles of interaction and quantum statistics in such a kind of walks are little known at a many-body level. In this letter, using time-evolving block decimation algorithm and many-body perturbation theory we rigorously study QWs, Bloch oscillations and quantum Fisher informations (FIs) for three indistinguishable bosons and fermions in 1D lattices. We show that such strongly correlated many-body QWs not only give rise to statistics-and-interaction-dependent ballistic transports of scattering states, two- and three-body bound states, but also present a quantum enhanced precision measurement of the gravitational force. It turns out that in contrast to the walks of the fermions, the QWs of three bosons exhibit richer dynamics of co-walkings and competitive Bloch oscillations, which remarkably present a surprising time scaling $t^3$ of FI below a characteristic time $t_0$ and saturate to the fundamental limit of $t^2$ for $t>t_0$.
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