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

Xizhou Qin, Yongguan Ke, Xiwen Guan, Zhibing Li, Natan Andrei, Chaohong Lee

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    51 Citations (Scopus)


    We investigate continuous-time quantum walks of two indistinguishable particles [two bosons, or two fermions, or two hard-core bosons (HCBs)] in one-dimensional lattices with nearest-neighbor interactions. The results for two HCBs are consistent with the recent experimental observation of two-magnon dynamics [Fukuhara, Nature (London) 502, 76 (2013)NATUAS0028-083610.1038/nature12541]. The two interacting particles can undergo independent walking 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 a 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 speed of bosons is found to be exactly three times that of fermions and HCBs. Our result paves the way for experimentally exploring quantum statistics via two-particle quantum walks.

    Original languageEnglish
    Article number062301
    JournalPhysical Review A - Atomic, Molecular, and Optical Physics
    Issue number6
    Publication statusPublished - 1 Dec 2014


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