We theoretically study the carrier-envelope phase dependent inversion generated in a two-level system by excitation with a few-cycle pulse. Based on the invariance of the inversion under time reversal of the exciting field, parameters are introduced to characterize the phase sensitivity of the induced inversion. Linear and nonlinear phase effects are numerically studied for rectangular and sinc-shaped pulses. Furthermore, analytical results are obtained in the limits of weak fields as well as strong dephasing, and by nearly degenerate perturbation theory for sinusoidal excitation. The results show that the phase sensitive inversion in the ideal two-level system is a promising route for constructing carrier-envelope phase detectors.
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