Coherent coupling between the motional fluctuation of a mirror and a trapped ion inside an optical cavity: Memory, state transfer, and entanglement

Abstract

We show how the motional fluctuations of two systems of very different sizes---a trapped ion and a mirror---can be coupled coherently, via their common interaction with an optical cavity. Specifically, we show that the fluctuations can be transferred from one system to the other by using pulsed excitation of the cavity mode, and vibrational fluctuations can exhibit entanglement in steady state. We numerically display a sudden death of this entanglement at certain pulse parameters and ambient equilibrium temperature. More interestingly, the state of the driving pulse can also be coherently mapped, in a selective way, into the vibrational mode of the trapped ion or the mirror, which acts as a quantum memory for the optical pulse. We further present a detailed analysis to show that it is also possible to map the state of the pulse into a binomial entangled state of its vibrational fluctuations. We finally investigate how to sympathetically cool the mirror by cooling the ionic vibration, thanks to an effective coupling between the two modes.