Global and local condensate and superfluid fraction of a few hard core bosons in a cubic optical lattice plus external harmonic confinement

TL;DR

This study investigates how condensate and superfluid fractions behave locally and globally in a few hard core bosons within a cubic optical lattice with harmonic confinement, revealing opposing trends with lattice parameters and interaction strength.

Contribution

It introduces a detailed analysis of local and global condensate and superfluid fractions in a few-boson system, highlighting the effects of interference and strong interactions.

Findings

Global condensate fraction and superfluid fraction behave oppositely with increasing lattice wave vector.

Interference enhances the condensate fraction in lattice wells beyond non-interference results.

Strong interactions lead to a coexistence of superfluid and Mott insulator phases.

Abstract

We explore the global and local condensate and superfluid (SF) fractions in a system of a few hard core (HC) bosons (N=8 and N=40) trapped inside a combined harmonic optical cubic lattice (CHOCL) at T=0 K. The condensate fraction (CF) is computed for individual lattice wells by separating the one-body density matrix (OBDM) of the whole system into components at the various lattice sites. Then each "lattice-site" component is diagonalized to find its eigenvalues. The eigenvalues are obtained by a method presented earlier [Dubois and Glyde, Phys. Rev. A {\bf 63}, 023602 (2001)]. The effects of interference between the condensates in the lattice wells on the CF in one well is also investigated. The SF fraction (SFF) is calculated for N=40 by using the diffusion formula of Pollock and Ceperley [Pollock and Ceperley, Phys. Rev. B {\bf 36}, 8343 (1987)]. Our chief result is an opposing behavior of the global CF and SFF with increasing lattice wave vector $k$. In addition, the CF in a lattice well is enhanced by the interference with its neighbor wells beyond the result when the interference is neglected. The global SF is depleted with a rise of the repulsion between the bosons, yet at very strong interaction superfluidity is still present. The global CF remains almost constant with increasing HC repulsion. A reduction in the lattice dimension, i.e. an increase in the lattice wave vector, increases the local CF in each lattice well, but reduces the corresponding local SFF. At large HC repulsion, a coexisting SF-(vacuum)MI phase is established.