Quantum interference is studied for a charged particle on a multiply connected configuration space. The holes of the space are assumed to accommodate independent magnetic fluxes. As follows from an instanton calculation, tunneling of the particle is suppressed completely in such a geometry for appropriately chosen field strengths. This set of values defines an algebraic variety in parameter space, not a manifold. The quenching persists even if the geometric symmetry of the system is broken. Aharonov-Bohm–type experiments and mesoscopic tunneling devices are natural candidates to observe many-path interference.
Quantum interference is studied for a charged particle on a multiply connected configuration space. The holes of the space are assumed to accommodate independent magnetic fluxes. As follows from an instanton calculation, tunneling of the particle is suppressed completely in such a geometry for appropriately chosen field strengths. This set of values defines an algebraic variety in parameter space, not a manifold. The quenching persists even if the geometric symmetry of the system is broken. Aharonov-Bohm–type experiments and mesoscopic tunneling devices are natural candidates to observe many-path interference.
The motion of a particle along a one-dimensional closed curve in a plane is considered. The only restriction on the shape of the loop is that it must be invariant under a twofold rotation about an axis perpendicular to the plane of motion. Along the curve a symmetric double-well potential is present leading to a twofold degeneracy of the classical ground state. In quantum mechanics, this degeneracy is lifted: the energies of the ground state and the first excited state are separated from each other by a slight difference \ensuremath{\Delta}E, the tunnel splitting. Although a magnetic field perpendicular to the plane of the loop does not influence the classical motion of the charged particle, the quantum-mechanical separation of levels turns out to be a function of its strength B. The dependence of \ensuremath{\Delta}E on the field B is oscillatory: for specific discrete values Bn the splitting drops to zero, indicating a twofold degeneracy of the ground state. This result is obtained within the path-integral formulation of quantum mechanics; in particular, the semiclassical instanton method is used. The origin of the quenched splitting is intuitively obvious: it is due to the fact that the configuration space of the system is not simply connected, thus allowing for destructive interference of quantum-mechanical amplitudes. From an abstract point of view this phenomenon can be traced back to the existence of a topological term in the Lagrangian and a nonsimply connected configuration space. In principle, it should be possible to observe the splitting in appropriately fabricated mesoscopic rings consisting of normally conducting metal.
Examples of charged-particle interferometry are descibed whereby isolated magnetic fields—i.e., fields through which the particles do not pass—influence the clustering, as well as spatial distribution, of the particles. The configurations, which combine features characteristic of (i) Aharonov–Bohm and Hanbury Brown–Twiss experiments, and (ii) Aharonov–Bohm and Einstein–Podolsky–Rosen experiments, manifest simultaneously the effects of three distinct kinds of interference: (i) interference, dependent upon optical path length difference, resulting from wavelike propagation of particles; (ii) interference, dependent upon confined magnetic flux, resulting from particle charge and spatial topology; and (iii) interference, dependent upon quantum statistics, resulting from particle indistinguishability under exchange.
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, Φ, due to a (classical) magnetic field, 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, 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}, corresponding to the charge.
The motion of a nonrelativistic charged particle in a plane, multiply-connected region is studied within the framework of Feynman's path-integral approach to quantum mechanics. In particular, the authors study the simple case when the multiply-connected region is obtained by excluding a disc from the plane. If a nonzero magnetic flux is confined inside the disc, this is shown to include a change in the one-dimensional unitary representation of the fundamental group of the space which enters a proper definition of the path-integral. In this way, a simple explanation of the Aharonov-Bohm effect is shown to arise.
In 1959, Yakir Aharonov and David Bohm pointed out an experiment that should be impossible according to the standard intuitions of classical electromagnetism. A charged particle is sent through a double‑slit apparatus with a long thin solenoid placed between the two paths. The solenoid contains a magnetic field; the regions traversed by the particle do not. In classical mechanics, the particle should be entirely unaffected — no force, no torque, no Lorentz coupling. The interference pattern should be unchanged whether the solenoid is on or off. It isn't. When the solenoid is energized, the interference pattern shifts by Δφ = (q/ℏ) Φ, where Φ = ∫B·dA is the magnetic flux threading the solenoid. The particle’s wavefunction registers a region of magnetic field through which the particle never travels. Chambers performed the experiment in 1960; Tonomura confirmed it definitively with superconducting measurements in 1986. The effect is now standard textbook material and one of the deepest empirical phenomena in quantum mechanics. The puzzle is structural. In classical electromagnetism, the magnetic vector potential A was treated as a mathematical convenience — a quantity from which B = ∇×A could be computed but with no independent physical reality. The AB effect breaks this picture: the interference shift depends on ∮A·dx around the closed path, a gauge‑invariant integral that is non‑zero in regions where B = 0. The vector potential carries physical information that the magnetic field alone does not. Standard QM accommodates this by accepting that A is the physically meaningful quantity in the quantum context. This works mathematically but leaves a deeper question open: why should A have physical reality at all? This walkthrough shows how the Event Density framework provides an answer through Theorem 17. T17 establishes that gauge fields are the continuum‑level appearance of the substrate’s rule‑type connection — the substrate object that carries rule‑type label information from one substrate region to another. The gauge potential is not a mathematical convenience; it is the substrate’s parallel‑transport infrastructure for the rule‑type relabeling group. The AB phase is the integral of this substrate connection around a non‑contractible loop in a multiply‑connected substrate channel — a substrate‑level monodromy with observable consequences whenever the substrate’s topology supports closed loops the wavefunction can wind around. Stokes’ theorem connects the monodromy to the enclosed flux: Δφ = qΦ/ℏ. The structural payoff: the AB phase is not a mysterious nonlocal effect of the gauge potential. It is the substrate‑level monodromy of the rule‑type connection around a closed loop in a multiply‑connected substrate region. The gauge potential’s physical reality is not a postulate; it is what T17 establishes the substrate to provide.
Abstract Preservation of quantum coherence can be achieved by harnessing a system’s topology—encoding information in global geometric properties of quantum states insensitive to local perturbations. The robustness arises as certain geometric properties depend only on the trajectory of a quantum operation and the curvature in the controlled-parameter space, rather than on details of the system’s dynamics, thereby offering a topology-based framework for fault-tolerant quantum computation. To probe a system’s topology, geometric phase interference (Berry phase) has been studied in various optical systems and condensed matter physics, including molecular magnets (MMs). However, its direct detection in 4f-based MMs—prospective qudit (multi-level qubits) platforms—has remained elusive due to large tunnel gaps and environmental coupling. Here, we report a magneto-spectroscopic approach: the μSQUID-EPR technique, to directly resolve tunnel splittings in the 160 Gd-based MM [ 160 GdPc₂]⁻ (Pc = phthalocyanine). By irradiating single crystals with microwaves under transverse magnetic fields, we map the spin manifold and report the first direct observation of pronounced oscillations in the tunnel splitting—a signature of quantum phase interference. These oscillations reveal topological quenching of tunnelling and highlight the role of fourth-order transverse anisotropy in shaping the spin orientation space. Our findings uncover a nontrivial topological structure in 4f-MMs, opening possibilities towards holonomic quantum computation.