We report on the quadrupling of the transition spectrum of an Al/AlO${}_x$/Al Cooper-pair box (CPB) charge qubit in the $4.0–7.3$ GHz frequency range. The qubit was coupled to a quasilumped-element Al superconducting resonator and measured at a temperature of 25 mK. We obtained good matches between the observed spectrum and the spectra calculated from a model Hamiltonian containing two distinct low-excitation energy two-level systems (TLS) coupled to the CPB. In our model, each TLS has a charge that tunnels between two sites in a local potential and induces a change in the CPB critical current. By fitting the model to the spectrum, we have extracted microscopic parameters of the fluctuators including the well asymmetry, tunneling rate, and a surprisingly large fractional change ($30\%–40\%$) in the critical current (12 nA). This large change is consistent with a Josephson junction with a nonuniform tunnel barrier containing a few dominant conduction channels and a TLS that modulates one of them.

• Received 3 February 2013

DOI:https://doi.org/10.1103/PhysRevB.87.174522