Eur. Phys. J. D (2012) 66: 267
https://doi.org/10.1140/epjd/e2012-30371-2

Regular Article

Global and local condensate and superfluid fractions of a few hard core bosons in a combined harmonic optical cubic lattice in continuous space

Al-Balqa Applied University, Faculty of Engineering Technology, Applied Sciences Department, 11134 Amman, Jordan

^a e-mail: asakhel@hotmail.com

Received: 13 June 2012
Published online: 18 October 2012

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) in continuous space at T = 0 K. The local 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 [J.L. DuBois, H.R. Glyde, Phys. Rev. A 63, 023602 (2001)]. The effects of overlap 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 only by using the diffusion formula of Pollock and Ceperley [Phys. Rev. B 36, 8343 (1987)]. Our chief result is an opposing behavior of the global and local CF and SFF with increasing lattice wave vector k. In addition, the CF in a lattice well is enhanced by the overlap with its neighbor wells beyond the result when the overlap 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.