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We explore the global and local condensate and superfluid (SF) fractions in asystem of a few hard core (HC) bosons (N=8 and N=40) trapped inside a combinedharmonic optical cubic lattice (CHOCL) at T=0 K. The condensate fraction (CF)is computed for individual lattice wells by separating the one-body densitymatrix (OBDM) of the whole system into components at the various lattice sites.Then each "lattice-site" component is diagonalized to find its eigenvalues. Theeigenvalues are obtained by a method presented earlier [Dubois and Glyde, Phys.Rev. A {\bf 63}, 023602 (2001)]. The effects of interference between thecondensates 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 ofPollock 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 withincreasing lattice wave vector $k$. In addition, the CF in a lattice well isenhanced by the interference with its neighbor wells beyond the result when theinterference is neglected. The global SF is depleted with a rise of therepulsion between the bosons, yet at very strong interaction superfluidity isstill present. The global CF remains almost constant with increasing HCrepulsion. A reduction in the lattice dimension, i.e. an increase in thelattice wave vector, increases the local CF in each lattice well, but reducesthe corresponding local SFF. At large HC repulsion, a coexisting SF-(vacuum)MIphase is established.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

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