Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices

TLDR

The study investigates the properties of ultra‑cold bosonic atoms in one-, two-, and three‑dimensional optical lattices using large‑scale quantum Monte Carlo simulations of the Bose–Hubbard model under parabolic confinement. Simulations were performed on the Bose–Hubbard model with parabolic confinement potentials to explore local phase structures and momentum‑distribution signatures. The simulations reveal that local phase structures can be identified through a well‑defined local compressibility, that extended Mott plateaux are indicated by the shape of the coherent component of the momentum distribution, that additional fine structures in the momentum distribution are unrelated to local phases, and that while parabolic confinement suppresses quantum criticality and critical slowing down, flat confinement potentials enable observable quantum critical behavior and facilitate experimental detection of the Mott transition.

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.