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Probing the FFLO phase by double occupancy modulation spectroscopy

We propose here that for a spin-imbalanced two-component attractive Fermi gas loaded in a 1D optical lattice in presence of an harmonic confining potential, the observation of the change in the double occupancy after a lattice depth modulation can provide clear evidence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Simulating the time evolution of the system, we can characterize the double occupancy spectrum for different initial conditions, relating its features to the FFLO wavevector $q$. In particular, the narrowing of the width of the spectrum can be related, through Bethe-ansatz equations in the strongly interacting limit, to the FFLO wavevector $q$.