Unusual superfluid behavior of population imbalanced atomic Fermi gases in a two-dimensional optical lattice

We study the superfluid behavior of population imbalanced ultracold atomic Fermi gases with a short range attractive interaction in a two-dimensional optical lattice (2DOL), using a pairing fluctuation theory, within the context of BCS-BEC crossover. We find that population imbalance now has highly unusual effects on the behavior of pairing and superfluidity, caused by the continuum-lattice mixing in 2DOL. We find that, in the presence of a finite population imbalance (p>0), the pair density at Tc unexpectedly approaches zero towards to deep BEC regime and thus the transition Tc is dramatically enhanced in the BEC regime and becomes proportional to the interaction strength $U$ in the BEC limit. This should be contrasted to the balanced case, for which Tc decreases as $1/U$. And the system is an intermediate-temperature polarized superfluid state at unitarity and in the BCS regime. We perform stability analysis, and present complete phase diagrams along with the behavior of superfuild density. We show that a stable polarized superfluid emerges at relatively high temperature.