Imaging of classical trajectories and quantum mechanical states in open quantum dots

Full text: In this work, we show classical and quantum mechanical simulations as well as scanning gate microscopy (SGM) to probe the ballistic motion of electrons within an open GaAs/AlGaAs quantum dot (QD). SGM, in combination with transport measurements, can provide an interesting tool to image the motion of electrons in quantum systems. Recently, it has been theoretically argued for an open QD that, due to the induced perturbation of the SGM tip the imaging of the original open QD states is ambiguous. However in this theoretical approach a system with a hard wall potential was used. Our model calculations are performed by using a soft-wall as opposed to a hard-wall potential. This potential is obtained from fully self-consistent calculations. From the classical and quantum mechanical simulations we are able to extract the electron trajectories and probability density, respectively. Conductance maps are recorded by using SGM. Here, a biased tip in a cryogenic SGM is scanned over the open quantum dot while a magnetic eld is applied. We show that, for specific magnetic fields, the measured conductance images resemble the classical transmitted and backscattered trajectories and their quantum mechanical analogue. The demonstrated direct imaging technique is essential for the fundamental understanding of wave function scarring and quantum decoherence theory. (author)