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

摘要

We investigate continuous-time quantum walks of two indistinguishableparticles [bosons, fermions or hard-core bosons (HCBs)] in one-dimensionallattices with nearest-neighbor interactions. The results for two HCBs are wellconsistent 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 interactionstrength. Two strongly interacting particles may form a bound state and thenco-walk like a single composite particle with statistics-dependent walk speed.Analytical solutions for the scattering and bound states, which appear in thetwo-particle quantum walks, are obtained by solving the eigenvalue problem inthe two-particle Hilbert space. In the context of degenerate perturbationtheory, an effective single-particle model for the quantum co-walking isanalytically derived and the walk seep of bosons is found to be exactly threetimes of the ones of fermions/HCBs. Our result paves the way for experimentallyexploring quantum statistics via two-particle quantum walks.