Gap solitons of superfluid Fermi gas in one-dimensional optical lattices

We analyze the localized states of superfluid Fermi gases in one-dimensional optical lattices. Using the hydrodynamics model, we study the band gap structure of the matter-wave spectrum in the linear and nonlinear regimes. We find that the system exhibits a series of gap solitons in the first and second band gaps. Moreover, there are not only fundamental solitons but also subfundamental solitons in the second band gap, which have two peaks with opposite signs in a single well of the periodic potential. Meanwhile, in addition to the fundamental soliton and its bound states, there exist higher-order localized modes and their corresponding bound states (such as states I and J). More importantly, the number of atoms in the higher-order solitons is also an integer multiple of the fundamental solitons. Finally, we prove that the gap soliton families are stable by linear stability analysis and real-time evolution.