  In a recent experiment by Eichmann et al., polarization-sensitive
measurements of the fluorescence from two four-level ions driven by a linearly
polarized laser were made. Depending on the polarization chosen, different
degrees of interference were observed. We carry out a theoretical and numerical
study of this system, showing that the results can largely be understood by
treating the atoms as independent radiators which are synchronized by the phase
of the incident laser field. The interference and its loss may be described in
terms of the difference between coherent and incoherent driving of the various
atomic transitions in the steady-state. In the numerical simulations, which are
carried out using the Monte Carlo wave function method, we remove the
assumption that the atoms radiate independently and consider the photodetection
process in detail. This allows us to see the total interference pattern build
up from individual photodetections and also to see the effects of
superfluorescence, which become important when the atomic separation is
comparable to an optical wavelength. The results of the calculations are
compared with the experiment. We also carry out simulations in the non
steady-state regime and discuss the relationship between the visibility of the
interference pattern and which-path considerations.
