Thermal entanglement in superconducting quantum-interference-device qubits coupled to cavity field

In this paper, we investigate thermal entanglement in a superconducting-quantum-interference-device qubit coupled to a cavity field. We show that the entanglement can be manipulated by varying temperature and an effective controlling parameter $B$ which depends on the external field and characteristic parameters of the system. We find that there exists a critical value of the controlling parameter $B_c$. Under a fixed temperature, increasing $B$ can increase entanglement in the regime of $B<B_c$, while the entanglement decreases with increasing $B$ in the regime of $B>B_c$.