Spin-1 Quantum Walks

TL;DR

This paper provides an exact solution for the dynamics of two interacting spin-1 bosons in a quantum walk, revealing how spin-dependent interactions influence propagation, mixing, and correlation growth.

Contribution

It introduces an exact analytical solution for two spin-1 bosons in a quantum walk, highlighting the relationship between real-space propagation and spin mixing dynamics.

Findings

Two characteristic frequencies govern spin-mixing dynamics.

Long-range spin correlations depend on interaction sign and initial state.

Spin-dependent interactions couple real-space and spin-space dynamics.

Abstract

We study the quantum walks of two interacting spin-1 bosons. We derive an exact solution for the time-dependent wave function that describes the two-particle dynamics governed by the one-dimensional spin-1 Bose-Hubbard model. We show that propagation dynamics in real space and mixing dynamics in spin space are correlated via the spin-dependent interaction in this system. The spin-mixing dynamics has two characteristic frequencies in the limit of large spin-dependent interactions. One of the characteristic frequencies is determined by the energy difference between two bound states, and the other frequency relates to the cotunneling process of a pair of spin-1 bosons. Furthermore, we numerically analyze the growth of the spin correlations in quantum walks. We find that long-range spin correlations emerge showing a clear dependence on the sign of the spin-dependent interaction and the initial state.