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arXiv · 1409.0306

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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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.

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Xizhou Qin, Yongguan Ke, Xiwen Guan, Zhibing Li, Natan Andrei, Chaohong Lee. 2014-11-11. Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions. https://doi.org/10.1103/physreva.90.062301

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