Quasiparticle tunneling and 1/f charge noise in ultrastrongly coupled superconducting qubit and resonator

We report on an experimentally observed doubly split spectrum and its split-width fluctuation due to charge fluctuation in an ultrastrongly coupled superconducting qubit and resonator. From an analysis of the circuit model Hamiltonian, we found that the doubly split spectrum and split-width fluctuation are caused by discrete charge hops due to quasiparticle tunneling and a continuous background charge fluctuation in islands of a flux qubit. During 70 h of spectrum measurement, the split width fluctuated but the middle frequency of the split was constant. This observation indicates that the quasiparticles in our device mainly tunnel in one particular junction, as expected from the energy difference between quasiparticle states, during this 70 h. The background offset charge obtained from the split width has the $1/f$ noise characteristic.