Multi-particle quantum walks and Fisher information in one-dimensional lattices

TL;DR

This paper investigates many-body quantum walks of three indistinguishable bosons and fermions in 1D lattices, revealing how quantum statistics and interactions influence transport, bound states, and quantum Fisher information for precision measurements.

Contribution

It provides a rigorous analysis of many-body quantum walks, Bloch oscillations, and Fisher information, highlighting the effects of quantum statistics and interactions in 1D lattices.

Findings

Statistics-dependent ballistic transport observed.

Rich dynamics of co-walkings for bosons.

Quantum Fisher information scales as t^3 below t_0 and saturates to t^2.

Abstract

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 $t>t_0$.