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American Journal of Physics

More than one mystery: Quantum interference with correlated charged particles and magnetic fields

Mark P. Silverman

Published Jun 1, 1993• 12 citations
Publisher

Abstract

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.

DOI
10.1119/1.17203

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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.
Interference experiments characterized by the degree of first-order coherence (Young’s fringes, Fresnel, and Fraunhofer diffraction, etc.) have been performed with massive particles, in particular electrons and neutrons, as well as with light. Optical intensity interference or correlation experiments characterized by the degree of second-order coherence have not yet been performed with particles. The theory for such experiments shows striking differences in the behavior of electrons compared with that of light deriving from the differences in quantum statistics and charge. Photons are neutral bosons. They can be prepared in states that exhibit bunching, no bunching, or antibunching; they are unaffected by the presence of electromagnetic potentials. Electrons are charged fermions. Theory indicates that they exhibit antibunching regardless of the coherence of the source, and that their degree of second-order coherence can be influenced by electromagnetic fields through which they do not pass. A remarkable example is the Hanbury Brown-Twiss experiment with electrons that have interacted locally with the vector potential of an inaccessible magnetic field. The electron intensity correlation at two detectors is shown to be sensitive to the confined magnetic flux; experimental conditions differ considerably from those of the well-known Aharonov-Bohm effect.
Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. This interference is a direct result of quantum exchange statistics, however, it is observed only in the joint probability to find the particles in two separated detectors. Here we report the first observation of such interference fringes between two independent and non-interacting electrons in an interferometer proposed by Yurke et al. and Samuelsson et al. Our experiment resembles the "Hanbury Brown and Twiss" (HBT) experiment, which was performed with classical waves. In the experiment, two independent and mutually incoherent electron beams were each partitioned into two trajectories. The combined four trajectories enclosed an Aharonov-Bohm (AB) flux (but not the two trajectories of a single electron). While individual currents were found to be independent of the AB flux, as expected, the cross-correlation between current fluctuations in two opposite points across the device exhibited strong AB oscillations. This is a direct signature of orbital entanglement between two electrons even though they never interact with each other.
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.
Introduction Aharonov and Bohm (1959) drew attention to the quantum mechanical prediction that an interference pattern due to a beam of charged particles could be produced or altered by the presence of a constant magnetic field in a region from which the particles were excluded. This effect was first experimentally detected by Chambers (1960), and since then has been repeatedly and more convincingly demonstrated in a series of experiments including the elegant experiments of Tonomura et al. (1986). At first sight, the Aharonov-Bohm effect seems to manifest nonlocality. It seems clear that the (electro)magnetic field acts on the particles since it affects the interference pattern they produce; and this must be action at a distance since the particles pass through a region from which that field is absent. Now it is commonly believed that this appearance of nonlocality can be removed by taking it to be the electromagnetic potential A μ rather than the field F μν that acts locally on the particles: indeed, Bohm and Aharonov themselves took the effect to demonstrate the independent reality of the (electro)magnetic potential. But the nonlocality is real, not apparent, and cannot be removed simply by invoking the electromagnetic potential. While there may indeed be more to electromagnetism than can be represented just by the values of F μν at all space-time points, acknowledging this fact still does not permit a completely local account of the Aharonov-Bohm effect.