A trapped ion in an optomechanical system: entanglement dynamics

Abstract

In this paper a system includes of a trapped two-level ion interacting with an optomechanical cavity is studied. The motivation of this investigation is to study about all existed entanglements between the involved subsystems, i.e., “ion” and “phonon” of the trapped ion in addition to “photon” and “phonon” of the optomechanical system. To achieve this purpose, at first we obtain the effective quadripartite interaction Hamiltonian and choose a particular initial state vector of the under-considered system by which we arrive at the time-dependent state vector of the system. In this way, we are able to investigate the dynamics of various types of entanglements between the mentioned subsystems via evaluating the linear entropy and the negativity as the appropriate criteria of entanglement measurement. One of the surprising conclusions which has been achieved in this study is that, even though the ion (or the phonon of trapped ion) cannot be separately entangled with the “photon” or “phonon” of the optomecanical cavity, moreover, it is considerably entangled with the whole optomechanical (“phonon+photon”) system. Also, via studying the distribution functions of the optomechanical cavity and the phonon of trapped ion system, the conditions under which the most entangled “photon−phonon” (“ion−phonon”) state of optomechanical system (trapped ion) can be generated are presented. At last, we introduce the optomechanical system as the master interface for sharing the information which is carried by the trapped ion between all the subsystems.