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.
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.
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 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 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).
Bohmian mechanics, also referred to as the de Broglie-Bohm pilot-wave theory, represents a deterministic and nonlocal interpretation of quantum mechanics. Central to this framework is a description of quantum motion in terms of particle trajectories, whose reconciliation with relativity remains a fundamental challenge. Although relativistic guidance laws have been proposed, their predicted dynamics has remained experimentally untested. Here we use weak measurements in a single-photon interferometer to jointly reconstruct the photon energy and momentum weak values and the associated relativistic velocity field. The reconstructed average trajectories agree with theoretical predictions. Near destructive interference, the flow exhibits local reconstructed velocities exceeding the speed of light and negative values of the effective squared-mass parameter. Our results establish an experimental basis for investigating the physical meaning of quantum trajectories and their role in describing motion in relativistic spacetime.
Revised manuscript submitted to New Journal of Physics (NJP-120031), September 2026. We propose a weak-measurement protocol for reconstructing the conditional momentum field of atomic matter waves using transverse sheets of far-detuned light ("photon curtains"). The dispersive and elastic atom–light interaction weakly encodes the atomic transverse position in the deflection of the transmitted photons. Conditioning the position-resolved deflection record on the atom's final screen position and applying an exact free-flight reconstruction identity recovers the conditional momentum field J/ρ. This field is the Madelung hydrodynamic velocity and, by Wiseman's theorem, coincides with the de Broglie–Bohm guidance velocity; the protocol measures it as an ensemble property of the quantum state and makes no ontological claim that individual atoms follow the reconstructed trajectories. The manuscript identifies the atomic operator the photon meter reads and fixes the per-photon coupling by momentum conservation; derives the reconstruction formula and its free-propagation identities, with the residual term written and bounded; obtains the measurement-induced decoherence by an explicit partial trace over the light; introduces a dual-colour, force-balanced multipass photon-curtain configuration that preserves coherence while making the deterministic optical-dipole back-action calibratable, with an in situ single-slit calibration strategy; and gives quantitative budgets for spontaneous emission, optical imbalance, Coriolis deflection, magnetic forces, background-gas collisions, screen detection and multipass optics. A complete forward model of the estimator identifies the moment contraction required for velocity reconstruction, rather than weak-value detectability, as the statistical bottleneck: five-sigma detection of the conditional momentum field at the first curtain plane requires approximately 2.2 × 10^8 atoms, one to ten weeks at the projected slit-coherent yield, and detects the far-field ballistic component of the field; quantitative mapping of the fringe-channelling structure near the interference nodes requires one to two orders of magnitude more atoms and is identified as a future target. Four engineering elements beyond the published record are stated explicitly, together with their best demonstrated values. Version 2 corrects two errors of version 1 — a per-photon coupling normalization that conflated the per-photon phase with a per-time-slice phase, and the omission of gravity from the free-fall kinematics — with more conservative feasibility conclusions and a new two-arm force-balanced multipass operating configuration; the prior atomic programme towards this measurement is now cited, and the feasibility statements were revised after an independent literature audit. Version 1 should not be relied on for its numbers. The verification code, numerical results, figure-generation scripts and reproducibility harness are archived separately (linked under Related works) and re-derive every quoted number from the model.
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.