Two-particle States in One-dimensional Coupled Bose-Hubbard Models

TL;DR

This paper analyzes two-particle eigenstates in coupled 1D Bose-Hubbard models, revealing complex spectra, doublon states, and their dependence on coupling and interactions, with implications for cold atom experiments and quantum simulations.

Contribution

It introduces an intuitive construction for two-particle states in coupled Bose-Hubbard models, extending understanding beyond Bethe Ansatz solutions and detailing the spectrum and dynamics of doublons.

Findings

Two-particle spectrum includes four continua and three doublon dispersions.

Doublon existence and energies depend on inter-species coupling strength.

Dynamics vary significantly with coupling, affecting long-time behavior and entanglement.

Abstract

We study dynamically coupled one-dimensional Bose-Hubbard models and solve for the wave functions and energies of two-particle eigenstates. Even though the wave functions do not directly follow the form of a Bethe Ansatz, we describe an intuitive construction to express them as combinations of Choy-Haldane states for models with intra- and inter-species interaction. We find that the two-particle spectrum of the system with generic interactions comprises in general four different continua and three doublon dispersions. The existence of doublons depends on the coupling strength $\Omega$ between two species of bosons, and their energies vary with $\Omega$ and interaction strengths. We give details on one specific limit, i.e., with infinite interaction, and derive the spectrum for all types of two-particle states and their spatial and entanglement properties. We demonstrate the difference in time evolution under different coupling strengths, and examine the relation between the long-time behavior of the system and the doublon dispersion. These dynamics can in principle be observed in cold atoms and might also be simulated by digital quantum computers.