Measuring a coherent superposition of multiple states

A simple method for measuring the parameters of a completely or partially coherent superposition of multiple atomic states is proposed. The method, which can be applied in principle to a superposition of arbitrary energy states, is described in the case of a superposition of magnetic sublevels of a degenerate ground level. It is based upon coupling the sublevels involved in the superposition to the sublevels of a degenerate excited level by using a single elliptically polarized laser pulse. Such an interaction maps the parameters of the initial superposition onto the populations of the excited sublevels. By measuring the subsequent fluorescence from the excited sublevels for several suitably chosen laser polarizations one can deduce unambiguously the parameters of the initial superposition.