  Ultra cold fermionic atoms placed in a synthetic magnetic field arrange
themselves in Landau levels. We theoretically study the optomechanical
interaction between the light field and collective excitations of such
fermionic atoms in synthetic magnetic field by placing them in side a Fabry
Perot cavity. We derive the effective hamiltonian for particle hole excitations
from a filled Landau level using a bosonization technique and obtain an
expression for the cavity transmission spectrum. Using this we show that the
cavity transmission spectrum demonstrates cold atom analogue of Subnikov de
Hass oscillation in electronic condensed matter systems. We discuss the
experimental consequences for this oscillation for such system and the related
optical bistability.
