  We show that the phase of a field can be determined by incoherent detection
of the population of one state of a two-level system if the Rabi frequency is
comparable to the Bohr frequency so that the rotating wave approximation is
inappropriate. This implies that a process employing the measurement of
population is not a square-law detector in this limit. We discuss how the
sensitivity of the degree of excitation to the phase of the field may pose
severe constraints on precise rotations of quantum bits involving low-frequency
transitions. We present a scheme for observing this effect in an atomic beam,
despite the spread in the interaction time.
