Modulation-induced long-range magnon bound states in one-dimensional optical lattices

TL;DR

This paper demonstrates how periodic modulation in optical lattices can induce long-range magnon bound states, expanding the understanding of multi-particle interactions in Floquet systems.

Contribution

It introduces a Floquet-Bloch band theory for two magnons under modulation and predicts novel long-range bound states with relative distances of two or more sites.

Findings

Discovery of modulation-induced long-range magnon bound states

Analytical derivation of an effective Hamiltonian for these states

Proposal to detect bound states via quantum walks

Abstract

Ultracold two-level atoms in optical lattices offer an excellent experimental platform to explore magnon excitations [Fukuhara et al 2013 Nat. Phys. 9, 235; Fukuhara et al 2013 Nature 502, 76]. Here, we investigate how gradient magnetic field and periodically modulated tunneling strength affect the two-magnon excitations in these ultracold atomic systems. In the resonant condition where the driving frequency matches and smooths the potential bias, the system gains translational invariance in both space and time in the rotating frame, and thus we can develop a Floquet-Bloch band theory for two magnons. We find a new kind of bound states with relative distance no less than two sites, apart from the conventional bound states with relative distance at one site, which indicates the modulation-induced long-range interaction. We analytically derive an effective Hamiltonian via the many-body perturbation theory for a deeper understanding of such novel bound states and explore the interplay between these two types of bound states. Moreover, we propose to probe modulation-induced bound states via quantum walks. Our study not only provides a scheme to form long-range magnon bound states, but also lays a cornerstone for engineering exotic quantum states in multi-particle Floquet systems.