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.

我们研究耗散或增益对双阱势中超流体费米气体的约瑟夫森动力学的影响。为此，我们从现象学上将一个虚项引入阶参数方程，并在双模近似下推导出非保守的全双模 (fTM) 模型。fTM 模型包含与不同位置的波函数混合产物相关的交叉（高阶）相互作用，双模 (TM) 模型忽略了这些相互作用。这是因为原子总数的时间依赖方程与人口不平衡和相对相位耦合的交叉相互作用。因此，派生的非保守 fTM 模型会导致新的约瑟夫森行为，而这些行为在 TM 模型中无法捕获。特别地，我们发现约瑟夫森振荡在零相位和π相模式可以通过耗散或增益控制，这可能在原子电子器件中用作开关或门。