Two-particle states in one-dimensional coupled Bose-Hubbard models

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 interspecies interactions. 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 ω between two species of bosons, and their energies vary with ω 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.