LOFF and breached pairing with cold atoms

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We investigate here the Cooper pairing of fermionic atoms with mismatched fermi surfaces using a variational construct for the ground state. We determine the state for different values of the mismatch of chemical potential for weak as well as strong coupling regimes including the BCS BEC cross over region. We consider Cooper pairing with both zero and finite net momentum. Within the variational approximation for the ground state and comparing the thermodynamic potentials, we show that (i) the LOFF phase is stable in the weak coupling regime, (ii) the LOFF window is maximum on the BEC side near the Feshbach resonance and (iii) the existence of stable gapless states with a single fermi surface for negative average chemical potential on the BEC side of the Feshbach resonance.