Manipulating Cooper pairs with a controllable momentum in periodically driven degenerate Fermi gases

We here present an experimentally feasible proposal for manipulating Cooper pairs in degenerate Fermi gases trapped by an optical lattice. Upon introducing an $\mathit{\text{in}}\mathit{\text{situ}}$ periodically driven field, the system may be described by an effective time-independent Hamiltonian, in which the Cooper pairs, generated by the bound molecule state in Feshbach resonance, host a nonzero center-of-mass momentum. The system thus processes a crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid phase to a Fulde-Ferrell (FF) one. Furthermore, the magnitude and direction of the Cooper pairs in the synthetic FF superfluids are both directly controllable via the periodically driven field. Our proposal offers a reliable and feasible scenario for manipulating the Cooper pairs in cold atoms, serving as a tunable as well as powerful platform for quantum-emulating and exploring the FF superfluid phase.