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Pulsed Weak-Value Tomography of Gauge-Invariant Electron Flow in an Aharonov–Bohm Interferometer, with a Route to Quantum Backflow

Barack Ndenga

Published Feb 21, 2026• 0 citations
Publisher

Abstract

This work proposes a gauge-consistent protocol to reconstruct local electron flow in a coherent Aharonov–Bohm interferometer using weak values. A single-electron wave packet propagates through the ring while a time-gated (pulsed) weak interaction couples a local kinetic-momentum density operator to a spin pointer, avoiding momentum-insensitivity that can occur with static spin–orbit segments due to time-of-flight cancellation. Conditioning on the detected output drain (postselection) yields the weak value of the local flow operator and enables reconstruction of a drain-conditioned velocity field and its flow lines while preservinginterference in the weak-coupling limit. The method includes an internal weak-regime certification (signal linear in coupling, visibility loss quadratic) and provides a practical route toward observing electron quantum backflow, i.e., negative local probability current despite preparation with support only on positive kinetic momenta.

DOI
10.5281/zenodo.18718229

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Pulsed Weak-Value Tomography of Gauge-Invariant Electron Flow in an Aharonov–Bohm Interferometer, with a Route to Quantum Backflow

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This work proposes a gauge-consistent protocol to reconstruct local electron flow in a coherent Aharonov–Bohm interferometer using weak values. A single-electron wave packet propagates through the ring while a time-gated (pulsed) weak interaction couples a local kinetic-momentum density operator to a spin pointer, avoiding momentum-insensitivity that can occur with static spin–orbit segments due to time-of-flight cancellation. Conditioning on the detected output drain (postselection) yields the weak value of the local flow operator and enables reconstruction of a drain-conditioned velocity field and its flow lines while preservinginterference in the weak-coupling limit. The method includes an internal weak-regime certification (signal linear in coupling, visibility loss quadratic) and provides a practical route toward observing electron quantum backflow, i.e., negative local probability current despite preparation with support only on positive kinetic momenta.
This work proposes a gauge-consistent protocol to reconstruct local electron flow in a coherent Aharonov–Bohm interferometer using weak values. A single-electron wave packet propagates through the ring while a time-gated (pulsed) weak interaction couples a local kinetic-momentum density operator to a spin pointer, avoiding momentum-insensitivity that can occur with static spin–orbit segments due to time-of-flight cancellation. Conditioning on the detected output drain (postselection) yields the weak value of the local flow operator and enables reconstruction of a drain-conditioned velocity field and its flow lines while preserving interference in the weak-coupling limit. Themethod includes an internal weak-regime certification (signal linear in coupling, visibility loss quadratic) and provides a practical route toward observing electron quantum backflow, i.e., negative local probability current despite preparation with support only on positive kinetic momenta.
This record contains the final version of my manuscript on pulsed weak-value tomography of gauge-invariant electron flow in an Aharonov–Bohm interferometer. The work proposes an operational protocol to reconstruct a drain-conditioned local velocity/flow field from postselected weak values of a local kinetic-momentum density (hence a gauge-consistent probability-current flow observable). A key element is a time-gated (pulsed) von Neumann coupling to a spin pointer, introduced to avoid potential momentum insensitivity that can arise in static interaction regions due to time-of-flight cancellation. The manuscript also provides internal weak-regime certification criteria (linear signal scaling in coupling strength and quadraticvisibility loss), AB-flux falsifiability checks (periodicity and drain dependence), and a minimum viable experiment outlining the minimal requirements for an experimental demonstration. Finally, it presents a roadmap toward a high-impact extension: testing electron quantum backflow (negative local current under a verified positive-momentum preparation constraint).
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.
Abstract The phase gradient of the wave describing the Aharonov–Bohm effect (AB) is proportional to the local canonical momentum. This vector field contains vortices (phase singularities), whose strengths cannot be detected in quantum mechanics because they increase (discontinuously) with the magnetic flux, violating gauge invariance. The analogous quantity which is gauge-invariant is the kinetic momentum field, proportional to the local electron velocity. Investigation of the streamlines (integral curves) of this velocity field reveals that as the flux increases from 0 to 1/2 (in quantum units), a vortex V is generated at the flux line, accompanied by a stagnation point (saddle) S that emerges from V and then collapses back into V. The VS pair is always small: the maximum distance between V and S is approximately 0.0209 de Broglie wavelengths. The VS phenomenon survives generalization to a superposition of AB waves. If the flux is confined within an impenetrable tube of radius R , S persists if R < 0.004 de Broglie wavelengths, and is swallowed by the tube for larger R . An experiment is envisaged.
Quantum backflow (QB), a counterintuitive interference phenomenon where particles with positive momentum can propagate backward, is important in applications involving light-matter interactions. To date, experimental demonstrations of backflow have been restricted to classical optical systems using techniques such as slit scanning or Shack-Hartmann wavefront sensing, which suffer from low spatial resolution due to the inherent limitations in slit width and lenslet array density. Here, we report an observation of azimuthal backflow (AB) both theoretically and experimentally by employing the weak measurement technique, which enables the precise extraction of photon momentum at each pixel. Our results show that a heralded single photon, prepared in specific superposition states with solely negative orbital angular momentum (OAM), can exhibit positive OAM. The effects of mode ratio, propagation distance, and OAM index on the azimuthal backflow are systematically investigated. This work provides new techniques for observing and manipulating backflow in quantum systems.
Quantum backflow refers to the appearance of negative probability current in a state whose momentum distribution is essentially positive. We propose a scheme to prepare such states in a noninteracting Bose-Einstein condensate using large-momentum-transfer (LMT) atom interferometry. Our approach extends the single-pulse proposal of Palmero et al. by allowing one interferometer arm to undergo a tunable sequence of momentum-transfer pulses before recombination with a freely propagating arm. For realistic parameters for Sr-88, the protocol generates interference states with tunable probability current and negligible negative-momentum contamination. We evaluate both the probability current and the critical-density criterion introduced by Palmero et al., and identify parameter regimes in which the backflow signature is enhanced relative to the single-pulse scheme. These results present LMT interferometry as a flexible route for preparing candidate quantum-backflow states in cold-atom experiments.