Article

# Correlation functions of cold bosons in an optical lattice

Physical Review A (Impact Factor: 3.04). 07/2004; DOI: 10.1103/PhysRevA.70.063622

Source: arXiv

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**ABSTRACT:**We explore condensate and superfluid depletion in a system of a small number of hard core bosons (N=8 and N=40) trapped inside a combined harmonic optical cubic lattice (HOCL). The condensate fraction is computed for chosen individual lattice sites by separating the one-body density matrix (OBDM) of the whole system into its 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 in Ref.[1]. The effects of interference between the condensate at a lattice site and the surrounding condensates at all-neighbor lattice sites is also investigated. The superfluid fraction is calculated for N=40 by using the diffusion formula of Pollock and Ceperley [2]. Our chief result is that the condensate at a lattice site is enhanced by the interference with its neighbors beyond the result when the interference is neglected. The superfluid is depleted with a rise of the repulsion between the bosons, yet at very strong interaction superfluidity is still present. Further, the effects of lattice spacing have also been studied and it was found that a reduction in the lattice dimension, i.e. an increase in the lattice wave vector, increases the local condensate fraction at each lattice site but reduces the superfluid fraction of the whole system.01/2011; - [Show abstract] [Hide abstract]

**ABSTRACT:**For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrisation principle (SP) and for massive particles also conform to super-selection rules (SSR) that prohibit coherences between differing total particle numbers. Here we consider bi-partitite states for systems of massive bosons, where both the system and subsystems are modes (or sets of modes), particles being associated with differing mode occupancies. To define non-entangled or separable states the subsystem density operators are also required to satisfy the SP and conform to SSR, in contrast to some other approaches. Whilst in the presence of these additional constraints some of the known entanglement criteria are still valid, we present a detailed treatment to establish the validity of known criteria and derive new ones.New Journal of Physics 07/2013; 16(1). · 4.06 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**For a series of incoherent and ultracold atoms with an orbital angular momentum (or vortices) released from an optical lattice, we consider the density-density correlation of this freely expanding ultracold gases. Because of the unique phase structure originating from the quantized angular momentum, it is shown that the phase structure plays an important role in the distribution of the density-density correlation through the appearance of crescent-shaped peaks accompanying the ordinary round-shaped peaks. In particular, it is found that the orientation of the crescent-shaped peaks corresponds with the rotation direction of the atoms prepared in the optical lattices.Physical Review A 06/2008; 77(6). · 3.04 Impact Factor

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