Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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

Barack Ndenga

Published Feb 23, 2026• 0 citations
Publisher

Abstract

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).

DOI
10.5281/zenodo.18737369

Related papers

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

Barack Ndenga

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.

•Feb 21, 2026•0 citations

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

Barack Ndenga

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.

•Feb 21, 2026•0 citations

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

Barack Ndenga

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.

•Feb 12, 2026•0 citations

Gauge-invariant Aharonov–Bohm streamlines

Michael Berry

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.

Journal of Physics A Mathematical and Theoretical•Sep 8, 2017•9 citations

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

Ndenga Lumbu Barack

•Jan 1, 2026•0 citations

Half Gauge-Dependent, Half Gauge-Invariant: The Aharonov-Bohm Effect Reconsidered

Shan Gao

The standard semiclassical treatment of the Aharonov-Bohm (AB) effect, which predicts no observable phase shift for open electron paths in field-free regions due to gauge dependence, is shown to be incomplete. By fully quantizing both the probe electron and the electromagnetic source within quantum electrodynamics (QED), we derive an effective action that decomposes the AB phase into two equal contributions: a gauge-dependent probe phase from the source's potential acting on the electron, and a gauge-invariant source phase arising from the electron's quantum backreaction on the source via virtual-photon exchange. For open paths, where the probe phase vanishes under gauge choice, the source phase persists as a measurable part of the closed-loop value, isolated through a polarization--magnetization decomposition that separates its invariant bulk from a gauge-dependent boundary term. This uncovers a leading-order QED correction to nonrelativistic quantum mechanics, resolves longstanding debates on the AB phase's origin and locality, and refines gauge principles by revealing hidden gauge invariants in formally gauge-dependent quantities. While challenging to test directly, a conceptual scheme involving phase transfer to auxiliary qubits illustrates its potential observability, emphasizing its novelty beyond conventional closed-loop paradigms.

•Jan 1, 2026•0 citations
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 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 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.
The standard semiclassical treatment of the Aharonov-Bohm (AB) effect, which predicts no observable phase shift for open electron paths in field-free regions due to gauge dependence, is shown to be incomplete. By fully quantizing both the probe electron and the electromagnetic source within quantum electrodynamics (QED), we derive an effective action that decomposes the AB phase into two equal contributions: a gauge-dependent probe phase from the source's potential acting on the electron, and a gauge-invariant source phase arising from the electron's quantum backreaction on the source via virtual-photon exchange. For open paths, where the probe phase vanishes under gauge choice, the source phase persists as a measurable part of the closed-loop value, isolated through a polarization--magnetization decomposition that separates its invariant bulk from a gauge-dependent boundary term. This uncovers a leading-order QED correction to nonrelativistic quantum mechanics, resolves longstanding debates on the AB phase's origin and locality, and refines gauge principles by revealing hidden gauge invariants in formally gauge-dependent quantities. While challenging to test directly, a conceptual scheme involving phase transfer to auxiliary qubits illustrates its potential observability, emphasizing its novelty beyond conventional closed-loop paradigms.