We report an experimentally observed anomalous doubly split spectrum and its split-width 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 tunnelings and a continuous background charge fluctuation in islands of a flux qubit. During 70 hours in the spectrum measurement, split-width fluctuates but the middle frequency of the split is constant. This result indicates that quasiparticles in our device seem mainly tunnel one particular junction, which can be expected from the difference of each quasiparticle state, in this 70 hours. The background offset charge obtained from split-width has the 1/f noise characteristic.

Keywords: superconducting qubit, ultrastrong coupling, charge noise