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Journal of Physics A Mathematical and Theoretical

The Aharonov–Bohm effect in neutral liquids

Edouard B Sonin

Published Aug 12, 2010• 9 citations

Abstract

The Aharonov–Bohm effect was discovered as a quantum-mechanical effect for charged particles, but it has its counterpart in classical wave mechanics. The Aharonov–Bohm interference arises at the scattering of a sound wave by a vortex in classical and quantum hydrodynamics. This interference leads to a transverse force between quasiparticles and vortices in superfluids and superconductors. The Aharonov–Bohm effect was also generalized to neutral particles with magnetic or electric dipole momenta. The Aharonov–Bohm effect for charge particles and its modification for magnetic momenta (the Aharonov–Casher effect) have already been experimentally observed, and the efforts to detect the Aharonov–Bohm effect for electrically polarized neutral particles are on the way. A possible system for this detection is a Bose-condensate of excitons in a double quantum well. Observation of the Aharonov–Bohm effect in this system would provide direct evidence of Bose–Einstein condensation.

DOI: 10.1088/1751-8113/43/35/354003

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The Aharonov–Bohm effect was discovered as a quantum-mechanical effect for charged particles, but it has its counterpart in classical wave mechanics. The Aharonov–Bohm interference arises at the scattering of a sound wave by a vortex in classical and quantum hydrodynamics. This interference leads to a transverse force between quasiparticles and vortices in superfluids and superconductors. The Aharonov–Bohm effect was also generalized to neutral particles with magnetic or electric dipole momenta. The Aharonov–Bohm effect for charge particles and its modification for magnetic momenta (the Aharonov–Casher effect) have already been experimentally observed, and the efforts to detect the Aharonov–Bohm effect for electrically polarized neutral particles are on the way. A possible system for this detection is a Bose-condensate of excitons in a double quantum well. Observation of the Aharonov–Bohm effect in this system would provide direct evidence of Bose–Einstein condensation.

In 1984 Aharonov and Casher proposed that a beam of neutral particles with magnetic dipole moments passing around opposite sides of a line charge will undergo a relative quantum phase shift. This is currently under experimental investigation. Aharonov and Casher claimed that the magnetic dipole particles should undergo the phase shift despite experiencing no classical force. They suggested that this new effect has a ``duality'' with the solenoid Aharonov-Bohm effect where charged particles passing around a magnetic solenoid experience a phase shift despite, it is claimed, experiencing no classical force. Here it is pointed out that a magnetic dipole particle passing a line charge does indeed experience a classical electromagnetic force in the usual electric-current model for a magnetic dipole. This force will produce a relative lag between dipoles passing on opposite sides of the line charge, and the classical lag then leads to a quantum phase shift in exact agreement with that calculated by Aharonov and Casher. Thus actually the proposed Aharonov-Casher effect has a transparent explanation as a classical lag effect. It is emphasized that the solenoid Aharonov-Bohm effect is currently the only phase-shift effect which cannot be explained in an obvious fashion as arising from a classical lag and it is again proposed that also this shift may actually involve a classical electromagnetic lag effect. A natural experimental consequence suggested by the lag point of view is the breakdown of the interference pattern when the lag becomes comparable to the wave-packet coherence length.

Quantum-mechanical scattering of nonrelativistic charged particles by a magnetic vortex of nonzero transverse size is considered. The high-frequency limit of a scattered particle corresponds to the quasiclassical limit, and we show that the scattering Aharonov-Bohm effect persists in the quasiclassical limit owing to the Fraunhofer diffraction in the forward direction. Therefore, the flux of a magnetic vortex serves as a gate for the propagation of quasiclassical particles moving orthogonally to the vortex. The issue of the experimental detection of the Fraunhofer diffraction peak and the scattering Aharonov-Bohm effect is discussed.

We propose a hydrodynamic analog of the Aharonov-Bohm experiment in which second-sound waves are scattered on a quantized vortex in superfluid helium. The time lag that develops between the two sides of a second-sound plane wave impinging on a vortex from the side would be compared. Estimates for these experiments show that for reasonable experimental conditions the wavefront splitting can be readily measured at reduced temperatures of 10 −6 . The advantages of doing this experiment near the superfluid transition is discussed. This experiment would compliment the three other Aharonov-Bohm–type experiments which involve all four possible combinations of classical/quantum waves and classical/quantum vortices. This technique would provide a non-invasive means of investigating the dynamics of quantum vortex nucleation and their stability as well as addressing the problem of multiply quantized.

Quantum-mechanical scattering of coherent high-energy charged particles by a magnetic vortex is considered. The vortex core is assumed to be impermeable to scattered particles, and effects of its transverse size are taken into account. The limit of high energies of scattered particles corresponds to the quasiclassical limit, and we show that in the scattering the Aharonov-Bohm effect persists in this limit owing to the Fraunhofer diffraction in the forward direction. The issue of the experimental detection of the Fraunhofer diffraction peak and the Aharonov-Bohm effect in the quasiclassical limit is discussed.