Bose-Einstein Condensates in Optical Lattices: Study of its Experimental Signatures

Abstract

In the context of the thesis the theoretical study of experimental signatures of Bose-Einstein Condensates in an optical lattice regime is presented. The idea was to study the formalism and apply it our model where the number of particles is kept constant. First, the Hamiltonian is solved by using HFBP formalism and the condensate density fraction is calculated numerically. The integral involved has a singularity at zero, so it was almost removed by using Gaussian quadrature rule(already implemented in Mathematica). Further- more, the exchange energy part can be added to the existing Hamiltonian and momentum space density can be calculated to characterize our model. We can also look into the time of ight images for the system and other ex-perimental signatures like visibility(which also depends on the momentum space density) can also be calculated.