Rabi oscillations in an infinite-order correction to the adiabatic approximation for a two-level system

Abstract

We derive an infinite-order correction to the adiabatic approximation for the polarization induced in a two-level system by nearly resonant laser irradiation in the low-Rabi-frequency limit for two general classes of field envelopes. We find that Rabi oscillations at the resonant sideband frequency are a general occurrence and study the influence of the pulse shape on the form of the asymptotically decreasing amplitude of the Rabi oscillations as a function of the detuning and time constant. We go beyond the low-Rabi-frequency limit by comparing the analytic solution with numerical solutions of Schrödinger’s time-dependent equation. For symmetric laser-pulse envelopes, the numerical solutions predict eigenvalues of the pulse area at which the amplitude of the Rabi oscillations is zero. The phase of the temporal oscillations changes by π at these eigenvalues. For the special case of a hyperbolic-secant envelope, these eigenvalues correspond to the 2nπ-area pulses of self-induced transparency. For large-area pulses, the central region of the polarization as a function of time contains additional oscillations, the number of oscillations being determined by the number of pulse-area eigenvalues. For a propagating pulse, these oscillations are impressed on the field and amplified, thereby initiating pulse breakup (nonresonant self-induced transparency).