Multiparticle Quantum Walks and Fisher Information in One-Dimensional Lattices

Recent experiments on quantum walks (QWs) of a single and two particles demonstrated subtle statistics-dependent in one-dimensional (1D) lattices. However the roles interaction statistics such kind are little known at many-body level. In this letter, using time-evolving block decimation algorithm perturbation theory we rigorously study QWs, Bloch oscillations Fisher informations (FIs) for three indistinguishable bosons fermions 1D We show that strongly correlated QWs not only give rise to statistics-and-interaction-dependent ballistic transports scattering states, two- three-body bound but also present enhanced precision measurement gravitational force. It turns out contrast fermions, exhibit richer dynamics co-walkings competitive oscillations, which remarkably surprising time scaling $t^3$ FI below characteristic $t_0$ saturate fundamental limit $t^2$ $t>t_0$.