Probability amplitude dynamics for a two-level system

Abstract

The time-dependent probability amplitudes are determined for a two-level system without invoking the rotating wave approximation. A new analytic solution is obtained in the limit of small ratio of Rabi frequency to driver frequency. An analytic solution is also obtained in the limit of large ratio of Rabi frequency to driver frequency for a restricted range of parameters. The form of this solution guides the selection of parameters that cause substantial changes in the character of the solution. The dependence on parameter values is studied numerically for the transition probability and the coherent spectrum.