Ultranarrow spectral line of the radiation in double qubit-cavity ultrastrong coupling system

The ultrastrongly coupling (USC) system has very important research significance in quantum simulation and computing. In this paper, the ultranarrow spectrum of a circuit QED with two qubits coupled to single-mode cavity is studied. regime USC, JC model breaks down counter-rotating terms Rabi Hamiltonian leads level anti-crossing energy spectrum. Choosing single-photon driving field at point avoided-level crossing, we can get an equivalent four-level dressed state model, which dissipation intermediate states only related decay. Due electron shelving these metastable states, narrow peak appears emission Furthermore, find that physical origin for spectral narrowing vacuum-induced interference between transition pathways. And effect couples slowly decaying incoherent components density matrix into equations sidebands. This result provides possibility study USC system.