Josephson Oscillation and Self-Trapping in a Fermi Superfluid Gas across the BCS-BEC Crossover

Josephson oscillation is the phenomenon of supercurrent tunneling through a potential barrier separating two superfluids, resulting in the oscillation of the population difference. In the experiment of Bose-condensed gas, with increasing the initial population difference between the two condensate wavefunctions, a transition from the Josephson oscillation to "self-trapping", in which the population difference oscillates around the nonzero value, has been observed. We study normal Josephson oscillations and self-trapping in a Fermi superfluid gas across the BCS-BEC crossover by numerically solving the time-dependent Bogoliubov-de Gennes equations. We confirm that self-trapping occurs in the whole region across the BCS-BEC crossover. We also discuss detailed behaviors of plasma frequencies and critical values of initial population difference for the transition between normal Josephson oscillations and self-trapping across the BCS-BEC crossover.