Quantum Waltz: Nonlocal Transfer of Magnetic Flux ✛ ✦

Original: "Nonlocal transfer of quantized toroidal magnetic flux"
· Adel Ali, Alexey Belyanin
arXiv:2607.05581 · 2026-07-06 · CC BY 4.0 · 3 min
An experiment shows how quantized magnetic flux changes synchronously in two separated toroids, linked only by vector potential, with no magnetic field in between.

In the quantum world, there is its own dance. Two superconducting toroids, each comfortably holding its quantized magnetic flux, whirl in a synchronous waltz. Between them is a vacuum, not a single field line, yet they mirror each other’s moves without fail. This strange choreography embodies a long-standing dream: to test whether quantum information can be transferred without energy transfer, relying solely on the all-pervading vector potential.

The key to the waltz is a common superconducting loop that threads both rings. Inside it, like a shared vascular system, Cooper pairs condense, forming a Bose–Einstein condensate. Even in the works of John Bardeen, the idea of quantum exchange without real excitations flickered. It is the condensate, remaining unexcited, that imposes a global condition on the total fluxoid. Thus, a bond is born between isolated modes — an echo of the Aharonov–Bohm effect, predicted by David Bohm. This is not induction, but an exchange of quantum numbers — as if two orchestras in different halls play to a single score, without hearing each other.

Magnetic flux in a superconductor is quantized in units of Φ₀ = h/(2e) ≈ 2.07×10⁻¹⁵ Wb. This is the 'atomic' dance step — the fluxoid does not change by less.

Simulations show: the toroidal oscillators split into symmetric and antisymmetric normal modes. In the qubit regime, an Ising-type coupling emerges, and populations begin to oscillate — flux fades in one ring and appears in the other. The dancers take turns picking up the melody. But the most intriguing part: the exchange time is inversely proportional to the number of Cooper pairs. For a macroscopic condensate, it could become arbitrarily short, threatening to outpace light and conflict with Faraday’s law of induction. Clearly, constraints come into play — likely, fundamental quantum decoherence.

If the loop held 10²⁰ Cooper pairs, the flux exchange could beat a light signal. This paradox hints: the condensate density itself generates a new dissipation — nature seems to protect causality.

The experiment offers a rare chance to separate the contributions of vector potential and magnetic field. Success will allow probing the boundary between quantum and classical reality — here, effects of wavefunction collapse, predicted by Roger Penrose, may appear. If the exchange is suppressed at a critical condensate density, that would be direct evidence of a new decoherence channel. And perhaps, hidden here is the resolution to why our macroscopic world is so stubbornly real — and why large quantum systems lose coherence. Such discoveries are critical for quantum computers: understanding the nature of decoherence will suggest how to build robust qubit architectures.

In the future, chains of such toroids, linked by topological constraints, will form a new class of quantum simulators. Interactions in them will be dictated not by fields, but by global conditions — like a dance where partners communicate through glances. Detection using superconducting interferometers (SQUIDs) will provide temporal resolution to track every quantum step. Then — networks with nonlocal connections and distributed information, where a signal needs no wires.

Interestingly, the magnetic flux quantum Φ₀ = h/(2e) can be considered as the smallest 'atom' of magnetism in a superconductor. It serves as the 'step' of the dance in the described experiment.

\Phi_{\text{link}} = \Phi_b + s_2 \hat{\phi}_2 + s_3 \hat{\phi}_3
The total flux circulating in the common loop is the sum of the bias flux and signed contributions from each toroid.
\Omega^2_{\pm} = \frac{1}{C_T} \left( \frac{1}{L_T} + \frac{1}{L} \pm \frac{s_2 s_3}{L} \right)
The collective oscillation frequencies depend on the inductance of the common loop L and the relative orientation (winding direction) of the toroids.
Scientists
William WoottersJohn Stewart BellDavid DeutschGeorge GamowLeo EsakiRichard Feynman
Concepts
flux quantization quantum teleportation quantum field theory in curved spacetime magnetic flux Aharonov–Bohm effect transmon qubit magnetic vortex temporal entanglement nonlocality transmon superfluid vortex momentum transfer josephson current domain wall ferron hall effect quantum switch Faraday's law of electromagnetic induction magnetic flux quantum curved space commutator