Interplay of optical potential and condensate properties for bosons in different optical lattice geometries

Abstract

Motivated by the availability of optical lattices with tunable geometries in experiments, we compute different physical properties such as condensate fraction, fluctuation and depletion of the condensate density and quasi-particle velocity as a function of the interparticle interaction strength for bosons in different 2D optical potentials that correspond to square, triangular and honeycomb geometries. Our results demonstrate an interplay of these features with that of the coordination number and underlying lattice geometries. A triangular lattice, which has a coordination number z = 6, shows larger condensate fraction and fluctuation of the condensate density, along with a low depletion of the ground state occupancy. The other candidates, namely the square lattice (z = 4) and honeycomb lattice (z = 3) occupy second and third places, respectively, with regard to these properties. The quasi-particle velocities for these geometries follow a similar pattern as that of the condensate fraction data. The observations are explained by the behaviour of the low-energy quasi-particle density of states. Finally, to make the role of lattice geometry obvious, we include a discussion on a kagome lattice, which in spite of having the same coordination number as that of a square lattice, i.e. z = 4, yields a significantly low condensate fraction than that of the square lattice for all values of the interacting strength.