Atomic swap gate, driven by position fluctuations, in dispersive cavity optomechanics

Abstract

Tracing the dynamics of a quantum system using a mesoscopic device is an important topic of interest nowadays. Here we show how a mesoscopic mechanical oscillator can be used to steer the dynamics of a coupled two-atom system and thereby to implement a two-qubit universal gate. We have theoretically studied a generic hybrid atom-optomechanical system where two identical atoms in configuration are trapped inside the cavity and the cavity mode mediates the interaction between the atoms and the mechanical oscillator. Adiabatic elimination of the lossy channels, namely, cavity decay and spontaneous emission, is adopted to obtain an effective Hamiltonian. This Hamiltonian is responsible for two-atom swap and √ SWAP gates, controlled by the position fluctuation of the oscillator. The validity of the proposal for successful implementation is assessed using presently available experimental parameters.