Extracting the density profile of an electronic wave function in a quantum dot

We use a model of a one-dimensional nanowire quantum dot to demonstrate the feasibility of a scanning probe microscope (SPM) imaging technique that can extract both the energy of an electron state and the amplitude of its wave function using a single instrument. This imaging technique can probe electrons that are buried beneath the surface of a low-dimensional semiconductor structure and provide valuable information for the design of quantum devices. A conducting SPM tip, acting as a movable gate, measures the energy of an electron state using Coulomb blockade spectroscopy. When the tip is close to the nanowire dot, it dents the wave function \ensuremath{\Psi}($x$) of the quantum state, changing the electron's energy by an amount proportional to $|{\ensuremath{\Psi}(x)|}^{2}$. By recording the change in energy as the SPM tip is moved along the length of the dot, the density profile of the electronic wave function can be found along the length of the quantum dot.