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AIP conference proceedings

Interplay of Superfluidity and Lattice Geometry in Bose Systems

Apurba Barman, Saurabh Basu, Alka B. Garg, R. Mittal, R. Mukhopadhyay

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We compute the superfluid fraction for a gas of bosonic atoms at zero temperature for different lattice geometries in two dimensions. It is observed that the superfluid fraction is higher in a triangular lattice than that in a square lattice, thereby emphasizing the importance of lattice geometry (and coordination number) in the study of condensed gas of boson. Further, we find that the condensed fraction vanishes for a system of one‐dimensional array of chains.

DOI
10.1063/1.3606159

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We compute the superfluid fraction for a gas of bosonic atoms at zero temperature for different lattice geometries in two dimensions. It is observed that the superfluid fraction is higher in a triangular lattice than that in a square lattice, thereby emphasizing the importance of lattice geometry (and coordination number) in the study of condensed gas of boson. Further, we find that the condensed fraction vanishes for a system of one‐dimensional array of chains.
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We evaluate the Bose-Einstein condensate density and the superfluid fraction of bosons in a periodic external potential using path-integral Monte Carlo methods. The periodic lattice consists of a cubic cell containing a potential well that is replicated along one dimension using periodic boundary conditions. The aim is to describe bosons in a one-dimensional optical lattice or helium confined in a periodic porous medium. The one-body density matrix is evaluated and diagonalized numerically to obtain the single boson natural orbitals and the occupation of these orbitals. The condensate fraction is obtained as the fraction of bosons in the orbital that has the highest occupation. The superfluid density is obtained from the winding number. From the condensate orbital and superfluid fraction, we investigate (1) the impact of the periodic external potential on the spatial distribution of the condensate, and (2) the correlation of localizing the condensate into separated parts and the loss of superflow along the lattice. For high-density systems, as the well depth increases, the condensate becomes depleted in the wells and confined to the plateaus between successive wells, as in pores between necks in a porous medium. For low-density systems, as the well depth increases the BEC is localized at the center of the wells (tight binding) and depleted between the wells. In both cases, the localization of the condensate suppresses superflow leading to a superfluid-insulator crossover. The impact of the external potential on the temperature dependence of the superfluidity is also investigated. The external potential suppresses the superfluid fraction at all temperatures, with a superfluid fraction significantly less than one at low temperature. The addition of an external potential does not, however, significantly reduce the transition temperature.
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We experimentally investigate the superfluid properties of a two-dimensional, weakly interacting Bose-Einstein condensate in the zero-temperature regime, when it is subjected to a triangular optical lattice potential. We implement an original method, which involves solving the hydrodynamic continuity equation to extract the superfluid fraction tensor from the measured in situ density distribution of the fluid at rest. In parallel, we apply an independent dynamical approach that combines compressibility and sound velocity measurements to determine the superfluid fraction. Both methods yield consistent results in good agreement with simulations of the Gross-Pitaevskii equation as well as with the Leggett bounds determined from the measured density profiles.
Bose–Einstein condensation in a finite one-dimensional atomic Bose gas trapped in an optical lattice is studied within Bogoliubov’s approximation and then beyond this approximation, within the static fluctuation approximation. A Bose–Hubbard model is used to construct the Hamiltonian of the system. The effect of the potential strength on the condensate fraction is explored at different temperatures; so is the effect of temperature on this fraction at different potential strengths. The role of the number of lattice points (the size effect) at constant number density (the filling factor) is examined; so is the effect of the number density on the condensate fraction. The results obtained are compared to other published results wherever possible.