Dispersive readout of adiabatic phases

We propose a method for the measurement of adiabatic phases of periodically driven quantum systems coupled to an open cavity that enables dispersive readout. It turns out that the cavity transmission exhibits peaks at frequencies determined by a resonance condition that involves the dynamical and the geometric phase. Since these phases scale differently with the driving frequency, one can determine them by fitting the peak positions to the theoretically expected behavior. For the derivation of the resonance condition and for a numerical study, we develop a Floquet theory for the dispersive readout of ac-driven quantum systems. The feasibility is demonstrated for two test cases that generalize Landau-Zener-St\"uckelberg-Majorana interference to two-parameter driving.