Variational approach for interacting ultra-cold atoms in arbitrary one-dimensional confinement

TL;DR

This paper introduces a variational method for modeling interacting ultra-cold atoms in one-dimensional traps, extending beyond traditional approaches by accommodating arbitrary confinement and comparing results with exact solutions.

Contribution

It proposes an alternative variational ansatz for the pair-correlation wave-function that works without decoupling center-of-mass motion, applicable to bosons and fermionic mixtures.

Findings

The method accurately predicts many-body properties across various particle numbers and interactions.

Results agree well with exact diagonalization in diverse trapping potentials.

The approach extends the analytical toolkit for one-dimensional quantum gases.

Abstract

Standard analytical construction of the many-body wave function of interacting particles in one dimension, beyond mean-field theory, is based on the Jastrow approach. The many-body interacting ground state is build up from the ground state of the non-interacting system and the product of solutions of the corresponding interacting two-body problem. However, this is possible only if the center-of-mass motion is decoupled from the mutual interactions. In our work, based on the general constraints given by contact nature of the atom-atom interactions, we present an alternative approach to the standard construction of the \textit{pair-correlation} wave-function. Within the proposed ansatz, we study the many-body properties of trapped bosons as well as fermionic mixtures and we compare these predictions with the exact diagonalization approach in a wide range of particle numbers, interaction strengths, and different trapping potentials.