Aharonov–Bohm Effect Explained: How Interference Stops Tunnelling

The Aharonov–Bohm effect is a change in quantum interference caused by magnetic flux enclosed between two paths, even when the magnetic field is zero along those paths. The observable change is in their relative phase. A classical account based only on a magnetic force acting on the travelling particle misses it.

A recent Oxford experiment brings that idea into a different setting: a quantum simulation in which matter and the field controlling its motion are both quantum systems. The result shows how destructive interference can suppress tunnelling. Understanding it starts with the distinction between changing a particle’s trajectory and changing how alternative paths combine.

What is the Aharonov–Bohm effect?

Imagine an electron wave split into two coherent paths that pass on opposite sides of a confined magnetic flux. The paths meet again at a detector. Changing the enclosed flux shifts the interference pattern, although the electrons do not enter the region containing the magnetic field.

In the ideal static magnetic arrangement, there is no Lorentz-force deflection along either arm. Nevertheless, the quantum amplitudes arriving by the two routes acquire a flux-dependent relative phase. Aharonov and Bohm’s 1959 paper identified this distinction between the classical force picture and quantum interference.

The experiment does not require a human observer to change the outcome. It requires coherent alternatives that can interfere, as in the double-slit experiment. Here, the controlled variable is enclosed flux rather than a measurement revealing which path was taken.

The phase-shift equation, with a worked example

For a static magnetic flux, the additional phase difference is

Here q is the particle’s charge, ℏ is the reduced Planck constant, A is the magnetic vector potential and Φ is the flux enclosed by the loop formed from the two paths. The sign depends on charge and orientation. It determines the direction of the fringe shift.

For an electron, define the interference flux period as Φ_e = h/e. Increasing the enclosed flux by this amount changes the phase by a full turn, so the pattern repeats. Half that flux gives a phase change of magnitude π: a bright fringe becomes dark where the two amplitudes have equal magnitude. This electron period must not be confused with the h/(2e) flux quantum associated with superconducting pairs.

At one output of an ideal balanced two-path interferometer, with the other phase contributions fixed, the normalised probability is P = [1 + cos(Δφ)]/2. Substituting zero phase gives 1; substituting π gives 0. These are calculated limiting cases, not measurements from the Oxford apparatus.

Calculated example: an ideal balanced output

On a narrow screen, swipe the table sideways. The first column stays fixed.

Why zero magnetic field does not mean zero phase

The vector potential satisfies B = ∇ × A. A zero magnetic field along the accessible paths does not force the integral of A around the whole loop to vanish when the loop surrounds an excluded region containing flux.

Nor does this make a chosen value of A at one point a directly measurable quantity. Potentials can change under a gauge transformation while the observable interference remains the same. What matters here is the phase accumulated around the closed loop, modulo a full turn. Wu and Yang’s formulation in terms of phase factors makes this distinction explicit.

The effect therefore supports a precise experimental statement: the field encountered along each path alone does not specify the interference result. Broader claims that it proves one particular account of what potentials “really are” go beyond that measurement. This article concerns the static magnetic effect; changing a flux during flight also requires accounting for induced electric fields.

How experiments ruled out a stray-field explanation

A serious experimental objection is straightforward: perhaps a small leaking magnetic field deflects the electrons and imitates the predicted shift. Shielding and geometry are therefore central to the evidence.

In Tonomura and colleagues’ 1986 experiment, a tiny toroidal ferromagnet was surrounded by a superconducting layer that confined the field and a copper layer that prevented the electron wave entering the magnet. Electron holography compared waves passing through the toroid’s hole with waves passing outside it. The measured phase difference provided evidence with the field shielded from the electron wave.

This is why a picture of an electron being pushed around a magnet is misleading. The decisive comparison concerns the relative phase of coherent paths around confined flux. The observed interference shift, rather than an imagined microscopic orbit, is the quantity the experiment tests.

What Oxford’s 2026 quantum simulation changed

Saner and colleagues’ peer-reviewed study was published online in Nature Physics on 25 September 2026. Its loop used two qubits and two oscillators. The internal states of trapped ions encoded gauge fields; selected vibrational modes encoded bosonic matter. The simulated loop was defined by couplings between these degrees of freedom, not by ions physically travelling around a magnet.

The model has a discrete ℤ₂ gauge structure. In the language of the Oxford team’s explanation, entangled field qubits encoded flux through the loop. Changing the flux state changed whether the two tunnelling routes reinforced or cancelled each other. The experiment observed the resulting suppression of matter transfer.

The distinction from the textbook arrangement is that the gauge field belongs to the simulator’s quantum dynamics. It is not simply a fixed classical background imposed on an electron. This makes the experiment a controlled example of coupled matter and gauge fields, a central problem in quantum simulations of particle physics.

How interference can stop tunnelling

Consider two routes connecting an initial state to the same final state. If their transition amplitudes are t₁ and t₂, the combined amplitude has the schematic form

For equal amplitudes and zero relative phase, the routes add. For equal amplitudes and a π phase difference, they cancel: t_eff = 0. In this idealised two-route model, coherent transfer is blocked even though each route separately permits it. The cancellation concerns indistinguishable alternatives, not two particles colliding.

The qualifications matter. Unequal couplings prevent exact cancellation; loss of coherence can remove the interference term. Additional accessible routes can also change the result. “Interference stops tunnelling” describes a controlled arrangement, not a general rule that magnetic fields switch off quantum tunnelling.

This also differs from detecting which path was taken. Path information can reduce interference through decoherence; a controlled phase instead changes where coherent alternatives reinforce and cancel. A dark output need not mean the quantum state has been destroyed.

What the result establishes, and what remains open

The magnetic Aharonov–Bohm effect is established experimentally. The new study extends the setting to a small simulator with dynamical gauge fields. It does not report the first observation of the effect, a simulation of the full Standard Model, or a computation beyond the reach of classical machines.

Our assessment is that the useful advance is control: the experiment connects an encoded field state to a measurable change in matter motion. Whether this architecture can retain that control across much larger lattices is a separate question. Scaling requires managing more modes, more couplings and accumulated errors, while checking that the intended gauge constraints remain valid.

The paper discloses Oxford Ionics links: R. Srinivas was partially employed by the company and C. J. Ballance was a director. Oxford’s accompanying announcement is institutional commentary from the research team. Neither those affiliations nor the announcement substitute for the experimental evidence and its limited scale.