Josephson dynamics of superfluid Fermi gases in a double-well potential with dissipation or gain

Abstract We study the effects of dissipation or gain on Josephson dynamics of superfluid Fermi gases in a double-well potential. To this end, we phenomenologically introduce an imaginary term into the order-parameter equation, and derive a nonconservative and full two-mode (fTM) model under the two-mode approximation. The fTM model contains cross (high-order) interactions relevant to mixed products of wavefunctions at different sites, which are ignored by the two-mode (TM) model. It is because the cross interactions that the time-dependent equation for the total number of atoms is coupled to population imbalance and relative phase. Therefore, the derived nonconservative fTM model can lead to new Josephson behaviors that cannot be captured within the TM model. Specially, we find that the transitions of Josephson oscillations between the zero-phase and π-phase modes can be controlled by dissipation or gain, which may have applications in atomtronics devices serving as a switch or gate.