BCS-BEC crossover and quantum phase transition forLi6andK40atoms across the Feshbach resonance

Abstract

We systematically study the BCS-BEC crossover and the quantum phase transition in ultracold $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ atoms across a wide Feshbach resonance. The background scattering lengths for $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ have opposite signs, which lead to very different behaviors for these two types of atoms. For $^{40}\mathrm{K}$, both the two-body and the many-body calculations show that the system always has two branches of solutions: one corresponds to a deeply bound molecule state; and the other, the one accessed by the current experiments, corresponds to a weakly bound state with population always dominantly in the open channel. For $^{6}\mathrm{Li}$, there is only a unique solution with the standard crossover from the weakly bound Cooper pairs to the deeply bound molecules as one sweeps the magnetic field through the crossover region. Because of this difference, for the experimentally accessible state of $^{40}\mathrm{K}$, there is a quantum phase transition at zero temperature from the superfluid to the normal Fermi gas at the positive detuning of the magnetic field where the $s$-wave scattering length passes its zero point. For $^{6}\mathrm{Li}$, however, the system changes continuously across the zero point of the scattering length. For both types of atoms, we also give a detailed comparison between the results from the two-channel and the single-channel model over the whole region of the magnetic field detuning.