Exact Diagonalization Study of Bose-Condensed Gas with Finite-Range Gaussian Interaction

TL;DR

This study uses exact diagonalization to analyze how finite-range Gaussian interactions influence the ground state, condensation, and collective excitations of a quasi-two-dimensional Bose gas, providing insights relevant for experimental setups.

Contribution

It presents the first detailed exact diagonalization analysis of finite-range Gaussian interactions in a quasi-2D Bose gas, highlighting their effects on condensation and collective modes.

Findings

Finite-range interactions increase the degree of condensation.

Finite-range effects modify the breathing mode excitation.

Results are relevant for realistic experimental conditions.

Abstract

We investigate a system of $N$ spinless bosons confined in quasi-two-dimensional harmonic trap with repulsive two-body finite-range Gaussian interaction potential of large $s$-wave scattering length. Exact diagonalization of the Hamiltonian matrix is carried out to obtain the $N$-body ground state as well as low-lying excited states, using Davidson algorithm in beyond lowest-Landau-level approximation. We examine the finite-range effects of the interaction potential on the many-body ground state energy as also the degree of condensation of the Bose-condensed gas. The results obtained indicate that the finite-range Gaussian interaction potential enhances the degree of condensation compared to the zero-range interaction potential. We further analyze the effect of finite-range interaction potential on the breathing mode collective excitation. Our theoretical results may be relevant for experiments currently conducted on quasi-two-dimensional Bose gas with more realistic interaction potential.