Vortices number and the critical atoms number of a rotating Bose-Einstein condensates in two-dimensional optical lattice

In this paper, the vortices number and the critical atoms number are calculated. Calculations are performed for ultracold trapped Bose gas in two-dimensional deep optical lattice. Hellmann-Feynman theorem is used here to calculate the expectation values of the angular momentum and thermal average of square radius (in situ size). The above-mentioned parameters are calculated from the thermodynamic grand potential q(alpha,s). The latter is calculated using a conventional semi-classical approximation. This thermodynamic grand potential allows us to investigate the impacts of the finite size and inter-atomic interaction effects. The obtained result for the vortices number has a peak with increase in the rate of rotation. While the critical atoms number has increase in nature with increase in the critical temperature. These parameters show a major dependence on the inter-atomic interaction, depth of optical lattice and number of particles.