Self-trapping And Macroscopic Periodic Tunneling Of Superfluid Fermi Gases In The BCS-BEC Crossover

The recent realization of the superfluidity of ultra-cold fermions in optical latticesprovides a new frontier of researches for ultracold atom physics. Experimentally,condensed fermionic atomic pairs in the regimes of BEC, BCS, and their crossoverhave been observed successfully and their various superfluid properties has beeninvestigated in detail recently. And self-trapping, periodic quantum tunneling ofsuperfluid Fermi gases are presented.In the first part, we present an investigation of the dynamical self-trapping ofperiodic quantum tunneling in the BCS-BEC crossover. From the usualGross-Pitaevskii (GP) equation for bosons, we obtain the analytical tunnelingdynamical result of superfluid Fermi gas trapped in multi-well system by multi-modeapproximation. In zero-phase mode, firstly, the self-trapped state takes place more andmore easy with increasing η (0)for double-well, three-well, five-well and seven-wellsystems. Secondly, the self-trapped state takes place easier in the molecular BEC statethan in the weak-coupling BCS and the unitarity states for double-well, three-wellcases. It is remarkable that for five-well and seven-well systems the status isabsolutely contrary. It means that, for five-well and seven-well cases self-trapped stateoccurs easier in the weak-coupling BCS and the unitarity states than in the molecularBEC state. For φ (0)=π, the self-trapped state takes place more and more difficultwith increasing η (0)for double-well, three-well systems. And the self-trapped statetakes place easier in the molecular BEC state than in the weak-coupling BCS and theunitarity states for double-well, three-well cases.In the second part, we have studied the tunneling of a Fermi superfluid confined ina double-well potential in the BEC-BCS crossover regime and find zero-mode andπ-mode frequencies of coherent atomic oscillations. From the usual Gross-Pitaevskii(GP) equation for bosons, we obtain the analytical tunneling dynamical result ofsuperfluid Fermi gas trapped in double-well system by two-mode approximation.Finally, we summarize the main result of this paper and give an outlook of thefuture in the field.