State diagrams for harmonically trapped bosons in optical lattices

TL;DR

This paper uses quantum Monte Carlo simulations to map out zero-temperature phase diagrams of strongly correlated bosons in optical lattices with harmonic traps, analyzing phase coexistence and critical parameters relevant to experiments.

Contribution

It introduces a state diagram based on the characteristic density that accounts for inhomogeneity and trap effects, extending understanding beyond homogeneous systems.

Findings

Critical U/t for Mott domains depends on local filling.

Experimental data aligns with the simulated critical points.

Finite temperature effects are minimal in 2D but notable in 1D.

Abstract

We use quantum Monte Carlo simulations to obtain zero-temperature state diagrams for strongly correlated lattice bosons in one and two dimensions under the influence of a harmonic confining potential. Since harmonic traps generate a coexistence of superfluid and Mott insulating domains, we use local quantities such as the quantum fluctuations of the density and a local compressibility to identify the phases present in the inhomogeneous density profiles. We emphasize the use of the "characteristic density" to produce a state diagram that is relevant to experimental optical lattice systems, regardless of the number of bosons or trap curvature and of the validity of the local-density approximation. We show that the critical value of U/t at which Mott insulating domains appear in the trap depends on the filling in the system, and it is in general greater than the value in the homogeneous system. Recent experimental results by Spielman et al. [Phys. Rev. Lett. 100, 120402 (2008)] are analyzed in the context of our two-dimensional state diagram, and shown to exhibit a value for the critical point in good agreement with simulations. We also study the effects of finite, but low (T<t/2), temperatures. We find that in two dimensions they have little influence on our zero-temperature results, while their effect is more pronounced in one dimension.