Nonlocal Transfer of Quantized Magnetic Flux Between Toroidal Superconductors with No Field in Between ✦
An experiment is proposed where a quantized magnetic field excitation in a superconducting toroid is coherently transferred to a distant toroid without the intervening region filling with magnetic field. The mechanism relies on Aharonov–Bohm-type vector potential coupling via a shared superconducting loop that stays in its ground state and enforces a global fluxoid constraint. The expected signal is a correlated, time-resolved flux exchange between the remote toroids, detected with a SQUID. The design also exhibits an apparent signaling paradox, used to explore the fundamental limits of spacetime quantum coherence. This setup serves as a testbed for ideas such as objective wavefunction collapse and for pinpointing the boundaries of macroscopic quantum coherence—essential for scaling up quantum computers.
Context
Progress in the foundations of quantum theory often stalls due to a lack of experiments that distinguish between interpretations. Superconducting circuits, developed for quantum computers, provide a platform for controlling macroscopic quantum phenomena. A key phenomenon—the Aharonov–Bohm effect, predicted by David Bohm—shows that the vector potential is physically meaningful: a charged particle feels the magnetic flux even without entering the field region. This suggests the possibility of quantum superposition and nonlocal flux transfer with no field in the gap. Testing this possibility touches on fundamental questions, including the existence of objective wave function collapse and the limits of quantum decoherence. As with the no-cloning theorem, causality violation here might be prevented by fundamental constraints.
Methods
The experiment uses two superconducting toroids, each trapping quantized magnetic flux inside via the Meissner effect. A shared superconducting loop threads through both toroids, inductively coupled to their fluxes. The key element is a Bose–Einstein condensate of Cooper pairs in this loop, which, staying in its ground state, imposes a global condition on the total fluxoid. This leads to an effective interaction between the toroidal flux modes, described as coupling through quantum information exchange without energy transfer from the loop's excitations, first proposed for such systems by John Bardeen. Readout is performed with superconducting quantum interference devices (SQUIDs), enabling quantum measurements with time resolution. Additionally, direct magnetic field probes between the toroids verify the absence of leakage.
Results
Modeling shows that in the harmonic approximation, the toroidal flux oscillators split into two normal modes, whose frequencies depend on the loop inductance and coupling orientation. In the two-level flux qubit regime, an Ising-type interaction emerges, with strength set by the flux matrix elements. The condensate-mediated exchange interaction leads to characteristic population beatings, observed as correlated flux oscillations in the SQUIDs. Calculations reveal that the full flux transfer time is inversely proportional to the number of Cooper pairs in the loop, which in the macroscopic limit conflicts with the speed of light limit: for a sufficiently large number of particles, the exchange could occur faster than a light signal. This signals a paradox that requires accounting for Faraday's law of electromagnetic induction (the curl of the electric field) and the possibility of fundamental coherence loss. Quantum sensing with SQUIDs provides the precision needed to detect individual flux quanta.
Implications
This scheme, for the first time, allows experimental separation of the contributions of the vector potential and the magnetic field to nonlocal effects. A positive result would confirm the possibility of purely field-based nonlocality without energy transfer through space, refining the macroscopic applicability limits of quantum superposition. The experiment will provide a tool to test hypotheses of Roger Penrose on gravitationally induced wave function collapse and other objective reduction models. Observing suppression of the exchange above a critical condensate density would be a direct hint of a new type of density-related quantum decoherence.
Future development
In the future, this architecture can be extended to more toroids, creating a network with nonlocal connections governed by topology. This will open the door to a new class of quantum simulators where interactions are realized not through physical fields but through topological constraints. Advances in quantum sensors based on SQUIDs will boost sensitivity to flux changes down to the single-quantum level. Theoretically, a fully covariant model of collapse, consistent with quantum field theory, needs to be developed.
Impact
The results will impact quantum information theory, superconductor physics, and the development of fault-tolerant quantum computers, establishing possible fundamental scaling limits.
Next steps
Next steps include numerical simulation of the full electrodynamic problem with time dependence and experimental implementation in low-temperature superconducting circuits with high-Q SQUIDs.
Key open problems
The experiment directly connects to unsolved problems of quantum mechanics: the measurement problem, the origin of wave function collapse, and the role of the observer. It also touches on the compatibility of macroscopic coherence with the principles of locality and causality.
🎯 Interestingly, in a superconducting ring, magnetic flux is quantized in units of Φ₀ = h/(2e) ≈ 2.07×10⁻¹⁵ Wb. This quantization is what allows us to manipulate single flux quanta, as in the proposed experiment.
Key numbers
- Magnetic flux quantum Φ₀: 2.07×10⁻¹⁵ Wb
- Critical linear condensate density: 8.2×10¹¹ m⁻¹
- Speed of light c: 3.00×10⁸ m/s
- Planck constant ℏ: 1.05×10⁻³⁴ J·s