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We investigate the effects of quantum fluctuations on the low-energycollective modes of two-dimensional (2D) $s$-wave Fermi superfluids from theBCS to the Bose limit. We compare our results to recent Bragg scatteringexperiments in 2D box potentials, with very good agreement. We show thatquantum fluctuations in the phase and modulus of the pairing order parameterare absolutely necessary to give physically acceptable chemical potential anddispersion relation of the low-energy collective mode throughout the BCS toBose evolution. Furthermore, we demonstrate that the dispersion of thecollective modes change from concave to convex as interactions are tuned fromthe BCS to the Bose regime, and never crosses the two-particle continuum,because arbitrarily small attractive interactions produce bound states in 2D.

Effects of quantum fluctuations on the low-energy collective modes of two-dimensional superfluid Fermi gases from the BCS to the Bose Limit