Abstract
We explore theoretically the optomechanical interaction between a light field
and a mechanical mode of ultracold fermionic atoms inside a Fabry-Pérot
cavity. The low-lying phonon mode of the fermionic ensemble is a collective
density oscillation associated with particle-hole excitations, and is
mathematically analogous to the momentum side mode excitations of a bosonic
condensate. The mechanical motion of the fermionic particle-hole system behaves
hence as a ``moving mirror''. We derive an effective Hamiltonian for system and
show that it is of the form of generic optomechanical systems. We also discuss
the experimental consequences the optomechanical coupling in optical
bistability and in the noise spectrum of the system.
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