Stability diagram and parametric excitation in a strongly interacting fermionic superfluid

We investigate, both analytically and numerically, the dynamics of an elongated and strongly interacting fermionic superfluid subjected to a periodic modulation of tightly transverse confinement. We start from an effective one-dimensional (1D) model that is obtained by integrating over the transverse degree of freedom in the Thomas–Fermi regime due to the strong interaction. Using the approach of complex Fourier series, we solve the damped Mathieu equation derived from the 1D model, and compare the stability diagrams between the strongly and weakly interacting regimes. We further numerically simulate the effective 1D model with the parameters as in experiment to study the Faraday-wave formation, as well as excitations in a low-frequency modulation. Our analytical and numerical findings can provide a theoretical support for the experiments on the observation of the Faraday waves in a strongly correlated regime.