Two-particle States in One-dimensional Coupled Bose-Hubbard Models
- URL: http://arxiv.org/abs/2201.05536v1
- Date: Fri, 14 Jan 2022 16:14:34 GMT
- Title: Two-particle States in One-dimensional Coupled Bose-Hubbard Models
- Authors: Yabo Li, Dominik Schneble, Tzu-Chieh Wei
- Abstract summary: We study one-dimensional Bose-Hubbard models and solve for the wave functions and energies of two-particle eigenstates.
We find that the two-particle spectrum of the system with generic interactions comprises in general four different continua and three doublon dispersions.
- Score: 1.5727276506140881
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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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