In a recent experiment by Eichmann et al. [Phys. Rev. Lett. 70, 2359 (
1993)], polarization-sensitive measurements of the fluorescence from t
wo four-level ions driven by a linearly polarized laser were made. Dep
ending on the polarization chosen, different degrees of interference w
ere observed. We carry out a theoretical and numerical study of this s
ystem, 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 held. The interference and its loss may be desc
ribed in terms of the difference between coherent and incoherent drivi
ng of the various atomic transitions in the steady state. In the numer
ical simulations, which are carried out using the Monte Carlo wave-fun
ction method, we remove the assumption that the atoms radiate independ
ently and consider the photodetection process in detail. This allows u
s to see the total interference pattern build up from individual photo
detections and also to see the effects of superfluorescence, which bec
ome important when the atomic separation is comparable to an optical w
avelength. The results of the calculations are compared with the exper
iment We also carry out simulations in the non-steady-state regime and
discuss the relationship between the visibility of the interference p
attern and which-path considerations.