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Europhysics Letters (EPL)

Aharonov-Bohm scattering of neutral atoms

Ulf Leonhardt, Martin Wilkens

Published May 15, 1998• 20 citations
Publisher

Abstract

We study the scattering of quantum particles in the presence of an Aharonov-Bohm vortex and in an arbitrary cylindrically symmetric potential. In particular we address the scattering of atoms carrying dipole moments induced by an electrically charged wire and a homogeneous magnetic field. We argue that, despite the strong attraction of the wire, an Aharonov-Bohm effect will be visible.

DOI
10.1209/epl/i1998-00256-8

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We study the scattering of quantum particles in the presence of an Aharonov-Bohm vortex and in an arbitrary cylindrically symmetric potential. In particular we address the scattering of atoms carrying dipole moments induced by an electrically charged wire and a homogeneous magnetic field. We argue that, despite the strong attraction of the wire, an Aharonov-Bohm effect will be visible.
The Aharonov-Bohm (AB) scattering of charged particles by the magnetic field of an infinitely long and infinitely thin solenoid (magnetic string) in an absorbing medium is studied. We discuss the partial-wave approach to this problem and show that the standard partial-wave method can be adjusted to this case. The effect of absorption leads to oscillations of the AB cross section. Based on this we investigate the scattering of neutral atoms with induced electric dipole moments by a charge wire of finite radius, which is placed in a uniform magnetic field. The physical realistic and practically important case that all atoms that collide with the wire are totally absorbed at its surface is studied in detail. The dominating terms of the scattering amplitude are evaluated analytically for different physical constellations. The remaining terms are written in a form suitable for a numerical computation. We show that if the magnetic field is absent, the absorbing charged wire causes oscillations of the cross section. In the presence of the magnetic field the cross section increases and the dominating Aharonov-Bohm peak appears in the forward direction, suppressing the oscillations.
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.
The scattering of relativistic spin-1/2 neutral particles with a magnetic dipole moment by a long straight charged line and a magnetic flux line at the same position is studied. The scattering cross sections for unpolarized and polarized particles are obtained by solving the Dirac-Pauli equation. The results are in general the same as those for pure Aharonov-Casher scattering (by the charged line alone) as expected. However, in special cases when the incident energy, the line charge density, and the magnetic flux satisfy some relations, the cross section for polarized particles is dramatically changed. Relations between the polarization of incident particles and that of scattered ones are presented, both in the full relativistic case and the nonrelativistic limit. The characteristic difference between the general and special cases lies in the backward direction: in the general cases the incident particles are simply bounced while in the special cases their polarization is turned over simultaneously. For pure Aharonov-Casher scattering there exist cases where the helicities of all scattered particles are reversed. This seems to be remarkable but appears unnoticed previously. Two mathematical approaches are employed to deal with the singularity of the electric and magnetic field and it turns out that the physical results are essentially the same.
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.