We investigate the pairing problem in a two-component Fermi gas subject to periodically modulated attractive interactions. For the two-body case, we construct the Floquet bound state and find that its quasienergy decreases with the (dimensionless) driving strength, a manifestation of the renormalized $s$-wave scattering length in the high-frequency limit. For the many-body case, we find that, in sharp contrast to the static limit, the order parameter acquires nonzero time-periodic components that significantly modify the quasiparticle excitation spectrum with avoided crossings, where characteristic Floquet-induced gaps open at the boundaries of the Floquet Brillouin zone. The unique features of these unusual Floquet two-body and many-body states are further revealed by the spectral function and condensate fraction, which can be measured in experiments. Our results pave a different way for exploring nonequilibrium Fermi superfluid beyond static system through Floquet engineering.

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• Fermi gases
• Floquet systems
• Superfluids