Interference of Resonance Fluorescence from two four-level atoms

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.