Weak-Value Tomography of Electron Flow in an Aharonov–Bohm Interferometer

This manuscript proposes a solid-state electron-interferometry protocol to reconstruct quantum flow lines in an Aharonov–Bohm ring using weak values. A triggered single-electron wave packet propagates coherently through the two arms of the interferometer. A gate-defined Rashba segment implements a tunable weak coupling between the electron’s spin (as a pointer) and the local gauge-invariant kinetic momentum. Conditioning on the detected output port (postselection) allows extraction of the real part of the weak kinetic-momentum value, from which a local velocity field associated with thepostselected subensemble is reconstructed. Integrating this velocity field yields flux-dependent flow lines while preserving interference visibility in the weak-coupling regime. The work provides an operational, gauge-consistent route to map electron probability-current flow, with a clear ontological reading in de Broglie–Bohm dynamics.