Manipulating and Imaging the Shape of an Electronic Wave Function by Magnetotunneling Spectroscopy

Abstract

We measure the current due to electrons tunneling through the ground state of hydrogenic Si donors placed in a GaAs quantum well in the presence of a magnetic field tilted at an angle to the plane of the well. The component of B parallel to the direction of current compresses the donor wave function. By measuring the current as a function of the perpendicular component of B, we probe how the magnetocompression affects the spatial form of the wave function and observe directly the transition from Coulombic to magnetic confinement at high fields.

Radii of Rydberg states of isolated silicon donors

“…The images are difficult to interpret with high accuracy because the signal caused by the donor is a small modulation on top of the density due to the surface atoms, and a very careful Fourier transform filtering and other processing is required [28]. The tunneling spectroscopy of donors in contact with a barrier is also possible [31,32]. In either case, imaging and tunneling spectroscopy are limited to near-interface states that are naturally strongly perturbed.…”

Asymmetry of charge relaxation times in quantum dots: The influence of degeneracy

“…When investigating the non-equilibrium transport between a reservoir and the dot system, the charging and discharging dynamics are given by the tunneling matrix element, which gives access to, e.g., wave function mapping [5][6][7] and manipulation [8][9][10].…”

Controlling the Shannon Entropy of Quantum Systems

“…This task can be numerically accomplished by computer simulation or discretization. Moreover, in practice, some methods have been developed for the real-time measurement of quantum PDF under some special cases [32, 35]. If the quantum PDF can be measured online in the future, we can directly measure ψ ( x , t ) and calculate U ( t ) with (30).…”

“…While quantum Shannon entropy can reveal a great deal of information from the perspective of geometrical changes to the density [21], it shows interesting features about the bond forming and breaking process that are not apparent from the conventional reaction energy profile. Recent research has studied how to image and manipulate the shape of electronic wavefunction [32] and how to directly measure the quantum wavefunction for photons [33]. If the probability density function can be well measured and controlled in the future, we can directly control the detailed spatial distribution for both pure and mixed states.…”