Entanglement of two qubits interacting with one-mode quantum field

In the present paper we investigate the dynamics of the system of two two-level 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.