A Theory of BCS-BEC Crossover

In ultracold atomic fermions, the sign and the magnitude of pairing interactions can be controlled by using the magnetically-tuned Feshbach resonances to achieve a continuous transition between Cooper pairs of dilute fermi gas to BEC of diatomic molecules, which is known as the ``BCS-BEC crossover.'' At present, although several models have been proposed, there is still no exact analytical solution of the many-body problem of BCS-BEC crossover region. The standard BCS mean-field theory of superconductivity was used to describe the whole crossover resulting a useful approximation. In our studies, we introduced solvable models for an exact analytical solutions of BCS-BEC crossover region at T = 0 using the generalized SU(2) X SU(1,1) coherent states.