Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions

TL;DR

This paper studies how two indistinguishable particles with different quantum statistics co-walk in one-dimensional lattices with interactions, revealing bound states, walk speeds, and analytical solutions that connect quantum statistics with observable dynamics.

Contribution

It provides analytical solutions and an effective model for two-particle quantum walks with interactions, highlighting the influence of quantum statistics on walk behavior.

Findings

Strong interactions lead to bound states and co-walking behavior.

Bosons have a walk speed three times that of fermions/HCBs.

Analytical solutions for scattering and bound states are derived.

Abstract

We investigate continuous-time quantum walks of two indistinguishable particles [bosons, fermions or hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are well consistent with the recent experimental observation of two-magnon dynamics [Nature 502, 76 (2013)]. The two interacting particles can undergo independent- and/or co-walking depending on both quantum statistics and interaction strength. Two strongly interacting particles may form a bound state and then co-walk like a single composite particle with statistics-dependent walk speed. Analytical solutions for the scattering and bound states, which appear in the two-particle quantum walks, are obtained by solving the eigenvalue problem in the two-particle Hilbert space. In the context of degenerate perturbation theory, an effective single-particle model for the quantum co-walking is analytically derived and the walk seep of bosons is found to be exactly three times of the ones of fermions/HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.