In this paper, we study the effect of population imbalance and its interplay with pairing strength and lattice effect in atomic Fermi gases in a one-dimensional optical lattice. We compute various phase diagrams as the system undergoes BCS-BEC crossover, using the same pairing fluctuation theory as in Part I of this work [Phys. Rev. A 101, 053617 (2020)]. We find widespread pseudogap phenomena beyond the BCS regime and intermediate temperature superfluid states for relatively low population imbalances. The Fermi surface topology plays an important role in the behavior of
Tc. For large
d and/or small
t, which yield an open Fermi surface, superfluidity can be readily destroyed by a small amount of population imbalance
p. The superfluid phase, especially in the BEC regime, can exist only for a highly restricted volume of the parameter space. An open Fermi surface often leads to destruction of the superfluid ground state in the BEC regime. Due to the continuum-lattice mixing, population imbalance gives rise to a new mechanism for pair hopping, as assisted by excessive majority fermions, which may lead to significant enhancement of
Tc on the BEC side of the Feshbach resonance, and also render
Tc approaching a constant asymptote in the BEC limit, when it exists. Furthermore, we find that not all minority fermions will be paired up in BEC limit, unlike the 3D continuum case. These predictions can be tested in future experiments.
We investigate effects of optical lattice potential in one- and two-dimensional two-component trapped Fermi gases with population imbalances. Using the exact diagonalization and the density matrix renormalization group methods complementarily, we calculate the atom-density profile from the ground state many-body wave function as a function of attractive interaction strength for various population imbalances. The numerical results reveal that although a phase separation between the superfluid core and the shell cloud of excess atoms occurs as observed in experiments without the optical lattice, the population imbalance generally remains in the core region in contrast to the nonlattice cases. The essence of the numerical results in a strong attractive regime can be explained by an effective model composed of Cooper pairs and excess major fermions.