Entanglement between two qubits with two-photon transitions interacting with a slightly detuned thermal field

In this paper, we investigate entanglement between two qubits when they simultaneously not-resonantly interact with a single-mode thermal field through the degenerate two-photon transitions. We obtain the exact solution of the quantum Liouville equation for density matrix of the considered systems in the "dressed" states representation. On its basis the calculate the qubit-qubit reduced density matrix and negativity. We show that a slight detuning between the qubit transition frequency and the twice field frequency might cause high entanglement between the qubits.