Controllable Time Evolution of Coherence of an Atom Bit inside Cavity by Manipulating the Atom Bit Outside Cavity

Abstract

Considering two atom bits in Bell state initially,one bit was injected into a vacuum cavity to produce resonance while leaving the other outside.The controllable coherence of an atom bit inside the cavity was investigated by manipulating the atom bit outside the cavity.For the cases of before and after the Hadamard,Hadamard-like,Y,and phase logic gate manipulations on the atom bit outside the cavity,the correlation of two kinds of initial Bell state was discussed by numerical calculation.The time evolution curves of off-diagonal elements in the reduced density matrix for the atom bit inside the cavity was studied.The results show that the off-diagonal elements of the density matrix for the atom bit inside the cavity are zero at any moment before operating the atom bit outside the cavity.That is,the atom bit inside the cavity is always in a mixed state or classical states,and its coherence is always suppressed.However,after Hadamard gate and Hadamard-like gate operations and ground state measurements,offdiagonal elements in the reduced density matrix of the atom bit inside the cavity show the 2π period time evolution,and the coherence can be restored except(2n+1)π/2.At nπthe maximal coherence superposition state and general coherence superposition state were prepared,and a R(π/2)rotation correlation existed between the two kinds of Bell states.In addition,performing Y gate and phase gate operations on the outside atom bit,the coherence for the inside atom bit cannot restore.The necessary condition for the restoration of the coherence of the inside atom bit was found out as following:while logic gate operations manipulate the interactions between the atom bit inside the cavity and its environment,and the two atom bits are separated from the field,a strongly coherent entanglement is necessary between the two atom bits.