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Anomalous pseudogap in population imbalanced Fermi superfluids

In a Fermi superfluid increasing population imbalance leads initially to reduction of the transition temperature, then the appearance of modulated Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, and finally the suppression of pairing itself. For interaction strength such that the `balanced' system has a normal state pseudogap, increasing imbalance reveals anomalous spectral behavior. At a fixed weak imbalance (small polarization) the stable homogeneous superfluid occurs only above a certain temperature. The density of states has a minimum at the Fermi level, then a weak peak {\it within the gap}, and then the large, gap edge, coherence features. On heating, this non monotonic energy dependence changes to a more conventional fluctuation driven pseudogap, with a monotonic energy dependence. At large imbalance the ground state is FFLO and `pseudogapped' due to the modulated order. It changes to a gapless normal state on heating, and then shows a pseudogap again at a higher temperature. These weak imbalance and strong imbalance features both involve effects well beyond mean field theory. We establish them by using a Monte Carlo technique on large lattices, motivate the results in terms of the pairing field distribution, and compare them to spectroscopic results in the imbalanced unitary Fermi gas.