Order parameter and Josephson effect of nonuniform molecular Bose-Einstein condensates

For two-component Fermi gases at zero temperature, through a general derivation based on the BCS wave function, our research shows that the nonuniform molecular Bose-Einstein condensate has off-diagonal long-range order and can be described well by an order parameter when the size of molecules is much smaller than the size of the whole system. We also give the equation of state and nonlinear evolution equation for the order parameter of nonuniform molecular condensates, which is similar to the Gross-Pitaevskii equation of atomic Bose condensate. The nonlinear evolution equation is applied to consider the Josephson effect for two weakly linked molecular condensates in the presence of nonuniform magnetic field. We find clear particle-number oscillation where spatially dependent binding energy of molecules plays an important role