Optomechanical response of a strongly interacting Fermi gas

We study a Fermi gas with strong, tunable interactions dispersively coupled to high-finesse cavity. Upon probing the system along cavity axis, we observe strong optomechanical Kerr nonlinearity originating from density response of intracavity field and measure it as function interaction strength. find that zero-frequency increases by factor two Bardeen-Cooper-Schrieffer Bose-Einstein condensate regime. The results are in quantitative agreement theory based on operator-product expansion, expressing terms universal functions interactions, contact, internal energy gas. This provides an example driven-dissipative, strongly correlated nonlinear response, opening up perspectives for sensing weak perturbations or inducing long-range gases.