Theoretical analysis of continuously driven dissipative solid-state qubits

We study a realistic model for driven qubits using the numerical solution of the Bloch-Redfield equation as well as analytical approximations using a high-frequency scheme. Unlike in idealized rotating-wave models suitable for NMR or quantum optics, we study a driving term which neither is orthogonal to the static term nor leaves the adiabatic energy value constant. We investigate the underlying dynamics and analyze the spectroscopy peaks obtained in recent experiments. We show, that unlike in the rotating-wave case, this system exhibits nonlinear driving effects. We study the width of spectroscopy peaks and show, how a full analysis of the parameters of the system can be performed by comparing the first and second resonance. We outline the limitations of the NMR linewidth formula at low temperature and show, that spectroscopic peaks experience a strong shift which goes much beyond the Bloch-Siegert shift of the eigenfrequency.