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arXiv · 2201.05536

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

Yabo Li·Dominik Schneble·Tzu-Chieh Wei
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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.

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Yabo Li, Dominik Schneble, Tzu-Chieh Wei. 2022-01-14. Two-particle States in One-dimensional Coupled Bose-Hubbard Models. https://doi.org/10.1103/physreva.105.053310

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