  We report on the quadrupling of the transition spectrum of an Al/AlOx/Al
Cooper-pair box (CPB) charge qubit in the 4.0-7.3 GHz frequency range. The
qubit was coupled to a quasi-lumped 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 non-uniform
tunnel barrier containing a few dominant conduction channels and a TLS that
modulates one of them.
