Optical mapping of amplitude and phase of excitonic wave functions in a quantum dot system

We propose a technique based on a near-field scanning optical microscope, able to measure the spatial variations of both amplitude and phase of the wave functions of the individual eigenstates of a quantum dot system. The proposed scheme is based on a near-field optical microscope working in collection mode combined with a Mach-Zehnder interferometer. We analyze the response function of this device and present microscopic numerical calculations simulating the measurements. These results show that spatially resolved spectroscopy can go beyond measurements of local density of states and open the way to an optical microscopy that, exploiting the coherence properties of light, is able to provide direct and complete quantum-mechanical information on the spatial variations of solid-state mesoscopic quantum eigenfunctions.