Engineering phonon-photon interactions with a driven trapped ion in a cavity
Rony Peterson Alves Rodrigues, M. H. Y. Moussa, Celso J. Villas-Bôas · Physical Review A · 2006
We show how to generate quadratic and biquadratic phonon-photon interactions through a driven three-level ion inside a cavity. With such a system it is possible to squeeze the cavity-field state, the ion motional state, or even the entangled phonon-photon state. We present a detailed analysis of the cavity-field squeezing process, distinguishing three different regimes of this amplification mechanism: the subcritical, critical, and supercritical regimes, which depend, apart from the coupling parameters, on the excitation of the vibrational state. As an application of the engineered Hamiltonians, we show how to implement a Fock-state filter for the vibrational mode. Different aspects of the technique of adiabatic elimination emerge in this analysis.