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