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arXiv:2607.05581

Nonlocal transfer of quantized toroidal magnetic flux

Adel Ali, Alexey Belyanin

quant-phcond-mat.supr-conSubmitted Jul 6, 2026• Announced Jul 8, 2026• 0 citations
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Abstract

We propose a nonlocal flux-transfer experiment in which a quantized magnetic-field excitation confined within one toroidal superconducting structure is coherently transferred to a spatially separated toroid without magnetic-field occupation of the intervening region. The transfer arises from quantized Aharonov-Bohm-type vector potential coupling mediated by a superconducting loop threading the toroids, which, however, remains in the ground state, acting only through a global fluxoid constraint. A direct experimental signature would be the observation of correlated, time-resolved flux exchange between remote toroids in a SQUID readout. We analyze an apparent signaling paradox related to this interaction as a probe of the broader question of whether spatiotemporal quantum coherence is fundamentally bounded. The proposed setup can provide an experimental testbed for addressing foundational questions such as the existence of an objective collapse of a wavefunction or the fundamental limits of macroscopic quantum coherence which is relevant to large scale quantum computers.

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23 pages, 1 figure

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We propose a nonlocal flux-transfer experiment in which a quantized magnetic-field excitation confined within one toroidal superconducting structure is coherently transferred to a spatially separated toroid without magnetic-field occupation of the intervening region. The transfer arises from quantized Aharonov-Bohm-type vector potential coupling mediated by a superconducting loop threading the toroids, which, however, remains in the ground state, acting only through a global fluxoid constraint. A direct experimental signature would be the observation of correlated, time-resolved flux exchange between remote toroids in a SQUID readout. We analyze an apparent signaling paradox related to this interaction as a probe of the broader question of whether spatiotemporal quantum coherence is fundamentally bounded. The proposed setup can provide an experimental testbed for addressing foundational questions such as the existence of an objective collapse of a wavefunction or the fundamental limits of macroscopic quantum coherence which is relevant to large scale quantum computers.
The Aharonov–Bohm effect has been conclusively established through electron interferenceexperiments using toroidal magnetic geometries fully shielded by superconductors,demonstrating measurable phase shifts in electrons traveling exclusively through regionswhere magnetic field B = 0. However, these experiments have primarily investigated staticor quasi‑static flux conditions. This paper proposes a time‑resolved extension of thesuperconducting‑toroid Aharonov–Bohm experiment designed to measure the temporalresponse of electron interference phase following controlled flux modulation within a fullyshielded superconducting toroid. The proposed experiment exploits moderninterferometric instrumentation and superconducting flux control to test whether the phaseresponse exhibits purely circuit‑limited behavior or additional propagation or relaxationdynamics. Because existing interferometry and superconductivity laboratories alreadypossess the required infrastructure, the incremental cost of implementing the experiment isestimated at $10,000–$50,000 USD. The proposed experiment therefore represents auniquely accessible and decisive extension of a foundational quantum interferencemeasurement.
We propose a method to achieve coherent, field-free coupling between the toroidal flux qubit (tfluxon), which is isolated from the environment, and a charged particle on a quantum ring. The resulting nonlocal coupling is mediated only by the vector potential and can be used to control the tfluxon by acting on the quantum ring's degrees of freedom. Furthermore, the emergent coupling can facilitate coherent interaction between states of distant tfluxons mediated by an electron on a quantum ring. We demonstrate that the topological and nonlocal aspects of this system are of fundamental interest and can have important applications in quantum information, benefiting from the decoupling from the environment and the topological protection.
The electron holography technique was employed to make a crucial test of the existence of the Aharonov-Bohm (AB) effect. The relative phase shift was measured between two electron waves passing through spaces inside and outside a tiny toroidal ferromagnet, covered completely with a superconductor layer and a Cu layer. Below the transition temperature the relative phase shift was measured to be 0 or \ensuremath{\pi} due to the magnetic-flux quantization in units of h/2e. The results directly demonstrated the existence of the AB effect even when the magnetic field was confined by the surrounding superconductor due to the Meissner effect and an electron beam was prevented from penetrating the magnet.
The Aharonov-Bohm effect is a fundamental topological phenomenon with a wide range of applications. It consists of a charge encircling a region with a magnetic flux in a superposition of wave packets having their relative phase affected by the flux. In this work we analyze this effect using an entropic measure known as realism, originally introduced as a quantifier of a system's degree of reality and mathematically related to notions of global and local quantum coherence. More precisely, we look for observables that lead to gauge-invariant realism associated with the charge before it completes its loop. We find that the realism of these operators has a sudden change when the line connecting the center of both wave packets crosses the solenoid. Moreover, we consider the case of a quantized magnetic-field source, pointing out similarities and differences between the two cases. Finally, we discuss some consequences of these results.
Evidence for the Aharonov-Bohm effect was obtained with magnetic fields shielded from the electron wave. A toroidal ferromagnet was covered with a superconductor layer to confine the field, and further with a copper layer for complete shielding from the electron wave. The expected relative phase shift was detected with electron holography between two electron beams, one passing through the hole of the toroid, and the other passing outside. The experiment gave direct evidence for flux quantization also.
The Aharonov-Bohm effect is a physical phenomenon in which the quantum state of a charged particle acquires a phase shift that is directly proportional to the magnetic flux, ΦΦΦ, due to a (classical) magnetic field, B{\mathbf B}B, which is confined in a spatial region from which the magnetic field cannot escape. Even though the charged particle is not allowed to interact with the magnetic field, it accumulates a phase shift that affects the interference pattern produced. Not surprisingly, this apparent nonlocality is puzzling and counter intuitive. In this work, we provide an explanation that explains the physics underlying this apparent nonlocality. We find that the role of the confined magnetic field is to impart a puncture in the configuration space, R2\mathbb{R}^2R2, of the charge. Therefore, the quantum state corresponding to the charged quantum particle acquires the phase shift due to its response to the modified topology of the configuration space, R2−{0}\mathbb{R}^2-\{0\}R2−{0}, corresponding to the charge.