The Quantum Parametric Oscillator

Abstract

Abstract In this chapter, we include a Duffing nonlinearity and a parametric pump in our quantum oscillator, and study their effects in the limit of a small number of particles occupying the system. We find that the nonlinearity can turn the oscillator into an effective two-level system, and that parametric pumping gives rise to cat states. An external force can be used to induce Rabi oscillations between even and odd cat states, similarly to Rabi oscillations in a two-level system. We conclude with a brief outlook onto systems of coupled quantum parametric oscillators