  The spectrum of the cavity-QED microlaser/micromaser is expected to show
distinctive features of the coherent light-matter interaction, which are
obscured in the conventional Schawlow-Townes linewidth theory. However, the
spectral studies has been limited to resonant atom-cavity interaction so far.
Here we consider the dispersive interaction in the off-resonance case, from
which we uncover a quantum frequency pulling effect in the
microlaser/micromaser spectrum. We present a quantum theory of the spectrum
which introduces the notion of a frequency-pulling distribution associated with
the photon number. In contrast to the conventional laser, periodic variation of
the mean frequency pulling is observed with increasing pump parameter and it is
attributed to the strong atom-cavity coupling. The pulling distribution gives
rise to a spectral broadening, which can be dominant over the non-dispersive
broadening addressed in the previous works. We also developed a corresponding
semiclassical theory and discuss how the introduction of the frequency shift
fits in with the extended quantum theory.
