  We study theoretically quantum statistical and spectral properties of the
resonance fluorescence of a single atom or system with angular momentum $J=1/2
- J'=1/2$ driven by a monochromatic linearly polarized laser field, due to
quantum interference among its two antiparallel, $\pi$ transitions. A magnetic
field parallel to the laser polarization is applied to break the degeneracy
(Zeeman effect). In the nondegenerate case, the $\pi$ transitions evolve at
different generalized Rabi frequencies, producing quantum beats in the
intensity and the dipole-dipole, intensity-intensity, and quadrature-intensity
correlations. For a strong laser and large Zeeman splitting the beats have mean
and modulation frequencies given by the average and difference, respectively,
of the Rabi frequencies, unlike thebeats studied in many spectroscopic systems,
characterized by a modulated exponential-like decay. Further, the Rabi
frequencies are those of the pairs of sidebands of the Mollow-like spectrum of
the system. In the two-time correlations, the cross contributions, i.e., those
with products of probability amplitudes of the two $\pi$ transitions, have a
lesser role than those from the interference of the probability densities. In
contrast, there are no cross terms in the total intensity. We also consider
nonclassical and non-Gaussian properties of the phase-dependent fluorescence
for the cases of weak to moderate excitation and in the regime of beats. The
fluorescence in the beats regime is nonclassical, mainly from third-order
dipole fluctuations, which reveal them to be also strongly non-Gaussian, and
their quadrature spectra show complex features around the Rabi frequencies. For
small laser and Zeeman detunings, a weak to moderate laser field pumps the
system partially to one of the ground states, showing slow decay in the two
time correlations and a narrow peak in the quadrature spectra.
