### Abstract

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 language | English (US) |
---|---|

Article number | 062301 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 90 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*90*(6), [062301]. https://doi.org/10.1103/PhysRevA.90.062301

}

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 90, no. 6, 062301. https://doi.org/10.1103/PhysRevA.90.062301

**Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions.** / Qin, Xizhou; Ke, Yongguan; Guan, Xiwen; Li, Zhibing; Andrei, Natan; Lee, Chaohong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Statistics-dependent quantum co-walking of two particles in one-dimensional lattices with nearest-neighbor interactions

AU - Qin, Xizhou

AU - Ke, Yongguan

AU - Guan, Xiwen

AU - Li, Zhibing

AU - Andrei, Natan

AU - Lee, Chaohong

PY - 2014/12/1

Y1 - 2014/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84914133118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84914133118&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.90.062301

DO - 10.1103/PhysRevA.90.062301

M3 - Article

AN - SCOPUS:84914133118

VL - 90

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 6

M1 - 062301

ER -