STUDY OF BARDEEN COOPER STATE (BCS) TO BOSE EINSTEIN CONDENSATION (BEC) CROSSOVER

Abstract

This study presents a simple idea and a conceptual understanding of the crossover from the Bardeen Cooper (BCS) state of weakly-correlated pairs of fermions to the Bose{Einstein condensation (BEC) of diatomic molecules in the atomic Fermi gas. In the context of ultra cold Fermi gases, a BCS-BEC crossover means that by tuning the interaction strength, one goes from a BCS state to a BEC state without encountering a phase transition. BEC state is a Bose-Einstein condensate of two-atom molecules (boundfermions), while the BCS state is made up of pair of atoms. The difference between the pairs and the molecules is that the molecules are localized in the real space, whereas the BCS pairs are made of two particles with opposite momenta in the momentum space.