Description of ultracold atoms in a one-dimensional geometry of a harmonic trap with a realistic interaction

TL;DR

This paper calculates the ground state energy of two ultracold atoms in a one-dimensional harmonic trap with realistic interactions, comparing numerical and analytical methods to assess their validity.

Contribution

It introduces a detailed analysis of the ground state energy dependence on interaction strength using both numerical and analytical approaches, including the oscillator representation method.

Findings

Numerical investigation of pseudopotential method validity.

Assessment of oscillator representation method for combined potentials.

Identification of interaction regimes where methods are accurate.

Abstract

We compute the ground state energy of two atoms in a one-dimensional geometry of a harmonic optical trap. We obtain a dependence of the energy on a one-dimensional scattering length, which corresponds to various strengths of the interaction potential of a gaussian type. The calculation is performed by numerical and analytical methods. For the analytical method we choose the oscillator representation method (OR), which has been successfully applied to computations of bound states of various few-body systems. The main results of this paper are: 1) numerical investigation of the validity range of the previously used pseudopotential method; 2) investigation of the validity range of the OR for a superposition of parabolic and gaussian potentials.