Spatial correlations of trapped 1d bosons in an optical lattice

TL;DR

This paper studies how trapped 1D bosonic atoms in an optical lattice exhibit spatial correlations, using numerical methods to distinguish superfluid and insulating phases and confirming the local density approximation.

Contribution

It demonstrates that a rescaled one-particle density matrix can characterize phases and confirms the local density approach for weak interactions in trapped systems.

Findings

Rescaled one-particle density matrix distinguishes superfluid and insulator states.

Local density approximation is valid for weak interactions in trapped systems.

Superfluid-insulator transition observed via interference peak width.

Abstract

We investigate a quasi-one dimensional system of trapped cold bosonic atoms in an optical lattice by using the density matrix renormalization group to study the Bose-Hubbard model at T=0 for experimentally realistic numbers of lattice sites. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. For typical parabolic traps we also confirm the widely used local density approach for describing correlations in the limit of weak interaction. Finally, we note that the superfluid to Mott-insulating transition is seen most directly in the half width of the interference peak.