Decoherence, Autler-Townes effect, and dark states in two-tone driving of a three-level superconducting system

We present a detailed theoretical analysis of a multilevel quantum system coupled to two radiation fields and subject to decoherence. We concentrate on an effect known from quantum optics as Autler-Townes splitting, which has been recently demonstrated experimentally in a superconducting phase qubit. In the three-level approximation, we derive analytical solutions and describe how they can be used to extract the decoherence rates and to account for the measurement data. Better agreement with the experiment can be obtained by extending this model to five levels. Finally, we investigate the stationary states created in the experiment and show that their structure is close to that of dark states.