State diagram for continuous quasi-one dimensional systems in optical lattices

TL;DR

This paper investigates the formation of Mott insulator domains in quasi-one-dimensional optical lattices with harmonic traps using continuous Hamiltonians, revealing how atom number and trap confinement influence domain connectivity and structure.

Contribution

It introduces a continuous Hamiltonian approach to study Mott domains in optical lattices, moving beyond the standard Bose-Hubbard approximation.

Findings

Optical potential depth needed decreases with more atoms.

Minimum potential depth occurs at one particle per well density.

Mott domains form via shell structures at higher densities.

Abstract

We studied the appearance of Mott insulator domains of hard sphere bosons on quasi one-dimensional optical lattices when an harmonic trap was superimposed along the main axis of the system. Instead of the standard approximation represented by the Bose-Hubbard model, we described those arrangements by continuous Hamiltonians that depended on the same parameters as the experimental setups. We found that for a given trap the optical potential depth, $V_0$, needed to create a single connected Mott domain decreased with the number of atoms loaded on the lattice. If the confinement was large enough, it reached a minimum when, in absence of any optical lattice, the atom density at the center of the trap was the equivalent of one particle per optical well. For larger densities, the creation of that single domain proceeded via an intermediate shell structure in which Mott domains alternated with superfluid ones.