Entanglement of two qubits interacting with one-mode quantum field

Abstract

In the present paper we investigate the dynamics of the system of two twolevel natural or artificial atoms, in which only one atom couples to a thermal one-mode field in finite-Q cavity, since one of them can move around the cavity. For the description of the dynamics of the system we find the eigenvalues and eigenfunctions of a Hamiltonian of the system. With their help we derive the exact expression for a density matrix of the system in case of a pure initial state of atoms and a thermal state of a field. The reduced atomic density matrix is found. The one-qubit transposing of an atomic density matrix is carried out. With its help the Peres-Horodecki criterium is calculated. Numerical calculations of entanglement parameter is done for different initial pure states of atoms and mean photon numbers in a thermal mode. It is found that the thermal field can induce a high degree of qubits entanglement in considered model. Thus we have derived that one can use the strength of dipole-dipole interaction and cavity temperature for entanglement control in the considered system. It is shown also that the maximum degree of entanglement is reached for one-atom excited state.

Keywords

• entanglement
• qubit
• thermal noise
• dipole-dipole interaction
• peres-horodecki criterium