Effect Of Cavity Decay On The Coherent Control Of Atomic Tunneling

The tunneling effect and entanglement are considered as two features that distinguish the quantum and classical world. Since the quantum tunneling for intramolecular rearrangements in pyramidal molecules was testified in 1927 a lot of work has been done to study the tunneling. In a double-well potential, taking the atomic internal degrees of freedom and atom-cavity coupling into account, the tunneling has been predicted very recently. It has been shown that when taking into account the interaction between the internal and external degrees of freedom the tunneling process becomes quasiperiodic. The periodic tunneling motion is modulated by the Rabi oscillations between states with a photon in the cavity and states with an excitation in the atom.On the aspect of entanglement, a recent work of Yu and Eberly predicted that two non-interacting atoms initially entangled and coupled to two separate environments can become completely disentangled in a finite time. This is the so-called entanglement sudden death (ESD). Putting two atoms inside the same cavity, the ESD has been addressed by Tanas.In this paper we consider the same system as in Ref. Moreover we add the cavity decay and the spontaneous emission of the atom to the system. We show that the tunneling exhibits the property of quasiperiodic with damping amplitude, at the same time the so-called ESD appears. In the non-resonant case, the evolution of average position oscillates with time t after a period of initial damping.