Ultracold bosons in one-dimensional harmonic and multi-well traps: a Quantum Monte Carlo vs a correlated pair approach

TL;DR

This paper compares Quantum Monte Carlo simulations with analytical correlated pair wave functions to study the behavior of 1D bosonic systems in harmonic and multi-well traps across different interaction regimes, revealing on-site effects beyond mean-field approximations.

Contribution

It introduces an analytical correlated-pair wave function approach for larger atom numbers in 1D bosonic systems, validated against Quantum Monte Carlo results, and extends analysis to multi-well potentials.

Findings

Quantum Monte Carlo results agree well with analytical functions.

On-site effects beyond mean-field are captured by the analytical approach.

The method efficiently describes single-particle behavior in multi-well traps.

Abstract

We study the crossover of a finite one-dimensional (1D) bosonic ensemble from weak to strong interactions in harmonic traps and multi-well potentials. Although these systems are very common in experimental setups and have been studied theoretically, an analytical description is lacking. We perform Diffusion Quantum Monte Carlo calculations which we show to be in good agreement with results from analytical functions that we construct to describe these systems. For the harmonic trap we use the correlated-pair wave function which we introduced in [1] considering here much larger atom numbers, going beyond the few-body ensembles studied in \cite{brouzos}. We also investigate double and triple wells, changing correspondingly the uncorrelated part of the Ansatz to describe efficiently the single-particle behaviour. On-site effects beyond mean-field and standard Bose-Hubbard calculations that appear in densities being captured by our analytical functions are explored.