# A continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer

## TL;DR

This paper presents an analytic, continuous-variable approach to understanding the spectral properties and quantum states of a two-component Bose-Hubbard dimer, capturing localization transitions and spectral collapse phenomena.

## Contribution

It introduces a fully-analytic semiclassical method for analyzing the transition regimes, providing explicit descriptions of eigenstates and spectra near critical points.

## Key findings

- Analytic description of low-energy eigenstates and spectra.
- Confirmation of spectral collapse during localization transition.
- Good agreement between semiclassical predictions and numerical results.

## Abstract

A bosonic gas formed by two interacting species trapped in a double-well potential features macroscopic localization effects when the interspecies interaction becomes sufficiently strong. A repulsive interaction spatially separates the species into different wells while an attractive interaction confines both species in the same well. We perform a fully-analytic study of the transitions from the weak- to the strong-interaction regime by exploiting the semiclassical method in which boson populations are represented in terms of continuous variables. We find an explict description of low-energy eigenstates and spectrum in terms of the model parameters which includes the neighborhood of the transition point. To test the effectiveness of the continuous-variable method we compare its predictions with the exact results found numerically. Numerical calculations confirm the spectral collapse evidenced by this method when the space localization takes place.