Low frequency Rabi spectroscopy of dissipative two level systems. The dressed state approach

We have analyzed a dissipative two level quantum system (TLS) which is continuously and simultaneously irradiated by a high and low frequency excitation. The interaction of the TLS with a high frequency excitation is considered in the frame of the dressed state approach. A linear response of the coupled TLS and corresponding photon field system to a signal whose frequency is of the order of the Rabi frequency is found. The response exhibits undamped low frequency oscillations, whose amplitude has a clear resonance at the Rabi frequency with the width being dependent on the damping rates of the TLS. The method can be useful for low-frequency Rabi spectroscopy in various physical systems described by a two-level Hamiltonian, such as nuclei spins in NMR, double well quantum dots, superconducting flux and charge qubits, etc. The application of the method to a superconducting flux qubit and to the detection of NMR is considered in detail.