An algebraic approach to the study of weakly excited states for a condensate in a ring geometry

TL;DR

This paper develops an algebraic method using Inönü-Wigner contraction to analyze low-energy states of a two-mode Bose-Einstein condensate in a ring, providing accurate results across various interaction regimes.

Contribution

It introduces an algebraic approach with Inönü-Wigner contraction to study weakly excited states in a two-mode condensate, improving upon traditional semiclassical methods.

Findings

Results closely match numerical solutions.

Approach is effective across different tunneling regimes.

Provides analytical insights into condensate spectra.

Abstract

We determine the low-energy spectrum and the eigenstates for a two-bosonic mode nonlinear model by applying the In\"{o}n\"{u}-Wigner contraction method to the Hamiltonian algebra. This model is known to well represent a Bose-Einstein condensate rotating in a thin torus endowed with two angular-momentum modes as well as a condensate in a double-well potential characterized by two space modes. We consider such a model in the presence of both an attractive and a repulsive boson interaction and investigate regimes corresponding to different values of the inter-mode tunneling parameter. We show that the results ensuing from our approach are in many cases extremely satisfactory. To this end we compare our results with the ground state obtained both numerically and within a standard semiclassical approximation based on su(2) coherent states.