The Self-trapping And Landau-Zener Tunneling Of Fermi Superfluid Gases

Many quantum phenomena of ultra-cold superfluid atomic gases have arousedwide attention. In the present paper, we study the self-trapping and tunnelingphenomenon of Fermi superfluid gases in depth.Firstly, we give the basic dynamic equation of the Fermi superfluid gasesthrough BCS-BEC crossover. By using the double well potential model and ex-panding the wave function in the two state vector of a double well potential, weobtain the dynamic equations of Fermi superfluid gases in the double-well poten-tial. We obtain the Hamiltonian system of Fermi superfluid gases by rewriting thewave functions and combining with the canonical transformation of Hamiltoniansystem.Then, we study the Josephson oscillation and self-trapping phenomenon ofFermi superfluid gases in the double-well potential. In a symmetric double-wellpotential, we find that there will appear Josephson oscillation (JO), oscillating-phase-type self-trapping (OPTST) and running-phase-type self-trapping (RPTST).Three of them are corresponding to the different evolution of phase trajectoryin phase plane respectively. Combining with the analysis of fixed points of theHamiltonian system, we obtain the numerical and analytical results of the crit-ical conditions for the three phenomena. In the asymmetric double-well poten-tial, five states, that is, Josephson oscillation, oscillating-phase-type self-trapping,running-phase-type self-trapping, similar-oscillation-phase-type self-trapping (SOPTST)and similar-running-phase-type self-trapping (SRPTST) are found. The criticalconditions for the five phenomena also are given numerically and analytically.Finally, we study the Landau-Zener tunneling of Fermi superfluid gases byappling a linear drive between the two wells of the double-well potential. Ac-cording to the basic theory of linear Landau-Zener tunneling, we find that thequantum adiabatic theory no longer satisfies the condition that the interaction isstrong enough at the adiabatic limit of scanning rate, but the quantum adiabatic theory satisfied the case that the interaction is weak at the adiabatic limit. Com-paring with the standard Landau-Zener tunneling modle, we obtain the exponen-tial law between the tunneling rate and scanning rate in the weak interactions.