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Ultra cold fermionic atoms placed in a synthetic magnetic field arrangethemselves in Landau levels. We theoretically study the optomechanicalinteraction between the light field and collective excitations of suchfermionic atoms in synthetic magnetic field by placing them in side a FabryPerot cavity. We derive the effective hamiltonian for particle hole excitationsfrom a filled Landau level using a bosonization technique and obtain anexpression for the cavity transmission spectrum. Using this we show that thecavity transmission spectrum demonstrates cold atom analogue of Subnikov deHass oscillation in electronic condensed matter systems. We discuss theexperimental consequences for this oscillation for such system and the relatedoptical bistability.

Cavity optomechanics with synthetic Landau levels of ultra cold Fermi gas