Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices

TL;DR

This paper uses large-scale quantum Monte Carlo simulations to analyze confined bosonic atoms in optical lattices, revealing how local phase structures and Mott plateaux can be detected and how confinement shape affects quantum criticality.

Contribution

It introduces a method to identify local phase structures via local compressibility and shows how confinement shape influences quantum critical behavior and experimental detection of the Mott transition.

Findings

Local compressibility quantifies local phase structures.

Extended Mott plateaux are indicated by the momentum distribution shape.

Flat confinement potentials enable observation of quantum criticality.

Abstract

We study properties of ultra-cold bosonic atoms in one, two and three dimensional optical lattices by large scale quantum Monte Carlo simulations of the Bose Hubbard model in parabolic confinement potentials. Local phase structures of the atoms are shown to be accessible via a well defined local compressibility, quantifying a global response of the system to a local perturbation. An indicator for the presence of extended Mott plateaux is shown to stem from the shape of the coherent component of the momentum distribution function, amenable to experimental detection. Additional fine structures in the momentum distribution are found to appear unrelated to the local phase structure, disproving previous claims. We discuss limitations of local potential approximations for confined Bose gases, and the absence of quantum criticality and critical slowing down in parabolic confinement potentials, thus accounting for the fast dynamics in establishing phase coherence in current experiments. In contrast, we find that flat confinement potentials allow quantum critical behavior to be observed already on moderately sized optical lattices. Our results furthermore demonstrate, that the experimental detection of the Mott transition would be significantly eased in flat confinement potentials.