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We study fermionic superfluidity in strongly anisotropic optical latticeswith attractive interactions utilizing the cluster DMFT method, and focusing inparticular on the role of non-local quantum fluctuations. We show thatnon-local quantum fluctuations impact the BCS superfluid transitiondramatically. Moreover, we show that exotic superfluid states with delicateorder parameter structure, such as the Fulde-Ferrell-Larkin-Ovchinnikov phasedriven by spin population imbalance, can emerge even in the presence of suchstrong fluctuations.

Non-local quantum fluctuations and fermionic superfluidity in the imbalanced attractive Hubbard model