  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.
