  Superconducting qubits often show signatures of coherent coupling to
microscopic two-level fluctuators (TLFs), which manifest themselves as avoided
level crossings in spectroscopic data. In this work we study a phase qubit, in
which we induce Rabi oscillations by resonant microwave driving. When the qubit
is tuned close to the resonance with an individual TLF and the Rabi driving is
strong enough (Rabi frequency of order of the qubit-TLF coupling), interesting
4-level dynamics are observed. The experimental data shows a clear asymmetry
between biasing the qubit above or below the fluctuator's level-splitting.
Theoretical analysis indicates that this asymmetry is due to an effective
coupling of the TLF to the external microwave field induced by the higher qubit
levels.
