UNIFIED THEORY OF QUANTUM RESONANCE

Using the multiple time scale perturbation analysis on the Schrodinger equation, we derive the resonance equations for a quantum system with a discrete spectrum. To first order these are the RWA equations for a resonant system that describe Rabi flopping. To second order we get the combined effect of Bloch-Siegert and a.c. Stark shifts. When the equations are applied to a three-state model with two resonant states, the need for mathematical consistency gives rise to a set of ordinary differential equations for the resonant amplitudes that manifest detuning due to the cited shifts and a phase difference, i.e. level shifts, for the states both resonant and nonresonant originating just from the a.c. Stark shift. The hypothesis of treating different phenomena like Rabi flopping and resonance shifts as just different time scale effects gives a unified framework to work with quantum resonance.