Normal mode splitting in quantum degenerate Fermi gas in nano-cavity

Abstract

We report the normal mode splitting in the fermionic displacement spectrum as a single mode light field interacts with a mechanical mode of ultra-cold quantum degenerate Fermi gas trapped inside a Fabry–Perot cavity in the strong coupling regime. We explain the normal mode splitting in the outgoing field of the cavity field and in the field quadratures as well. As a function of system parameters, such as coupling strength between fermionic mode and field mode, number of fermionic atoms, cavity decay rate and fluctuations associated with the fermionic mode we explain the phenomenon of normal mode splitting. The low-lying fermions ensemble displays a collective density oscillation associated with particle-hole excitations, which interacts with cavity light field and lead to the observation of NMS in the fermion quadratures and light modes. The numerical results based on the present day laboratory experiments agree with the obtained analytical results.