Aharonov-Bohm Experiment Research Articles

Spin-orbit Berry phase in conducting rings.

The spin Berry phase can be observed in conductance experiments on rings of noncentrosymmetric materials. It results in destructive interference and in the shift of the Aharonov-Bohm oscillations. The spin-orbit interaction in vacuumlike Aharonov-Bohm experiments leads to the opposite sign of the magnetoresistance in comparison with the weak localization regime in disordered conductors. A time-dependent uniaxial strain results in current in a ring.

Interaction of a moving magnetic dipole with a static electric field

The authors examine the dynamics of a magnetic dipole in a static electric field. Applications of interest are the Aharonov-Casher effect and spin-orbit coupling. The ideal Aharonov-Casher effect is shown to involve a correlation between the moving particle and the internal coordinates of a voltage source. A similar relation has been demonstrated in the Aharonov-Bohm experiment. The authors also give a simple derivation of spin-orbit coupling based purely on nonrelativistic physics.

Two-solenoid Aharonov-Bohm experiment with correlated particles

The Aharonov-Bohm (AB) effect for correlated charged particles interacting locally with the external vector potential field of two spatially separated solenoids with confined magnetic flux is examined. The joint probability for particle arrival at each of two spatially separated detectors manifests a quantum interference that depends on the flux of both solenoids. However, in marked contrast to the “standard” AB effect with one solenoid and uncorrelated particles, there is no quantum interference in the probability of particle arrival at one detector. Thus, this version of the AB effect exhibits the type of long-range correlations that are addressed by the Einstein-Podolsky-Rosen (EPR) paradox and tests of Bell's inequalities. For particles with spin, the interference term can distinguish fermions and bosons.

Phase uncertainty and loss of interference in a simple model for mesoscopic Aharonov-Bohm experiments

Incoherence introduced in two-path experiments by interactions with scatterers in thermal equilibrium is examined with an energy-momentum approach previously used for the M\ossbauer effect. Oscillations in intensity with variations in the magnetic flux are shown to be insensitive to random phase changes in the individual scattering amplitudes. Inelastic incoherent scattering may be suppressed when there are a large number of scatterers. A small loss of phase coherence negligible in cases of practical interest can occur even via elastic scattering, which does not perturb the environment. The temperature dependence of the loss of interference, analogous to the Debye-Waller factor, may be tested by experiment.

Dynamical symmetry of the magnetic vortex

The dynamics of charged point particles interacting with point vortices, as in the idealized Aharonov-Bohm experiment or in Chern-Simons physics, possesses a dynamical SO(2, 1) symmetry. Ramifications of this symmetry for the physical problem are presented. We also find an integral representation for the scattering wave function, discuss the angular momentum spectrum, and establish the absence of self-interactions in Chern-Simons electrodynamics, for which the two-body scattering state is explicitly constructed as a definite superposition of free one-body states.

Quantum effects of electromagnetic fluxes in simply connected spaces

We show that, if the prediction of quantum effects of enclosed electromagnetic fluxes is eliminated from theory by the use of discontinuous wave functions, that leads to the prediction of observable effects depending on the amount of fluxexternal to the system under consideration, a circumstance which is contrary to observation. We conclude that in a simply connected space the wave functions representing the state of the charged particles in the Aharonov-Bohm experiment are single valued and continuous.

Topological effects in neutron optics

A class of experiments in neutron optics is related to the well-known Aharonov-Bohm experiments in electron optics with which they share a common topology. Several such experiments are briefly reviewed and some others of the same type are proposed.

Internal symmetries of non-Abelian gauge field configurations.

In a topologically nontrivial gauge theory not all gauge transformations are symmetries (as defined by Forg\'acs and Manton and by Schwarz) of a given field configuration: first, there may be an obstruction to implement gauge transformations on the fields; next, even those transformations which can be implemented may fail to be symmetries. For a test particle in such a background field, those gauge transformations which are symmetries generate ordinarily conserved Noether currents, one of which is the usual electric current. These results shed a new light on the problem of ``global color'' in monopole theory and explain why the electric charge of a nucleon is not in general conserved in the non-Abelian Aharonov-Bohm experiment of Wu and Yang.

A new statement of Einstein's equivalence principle and relevant experiments

By considering the relationship between a freely falling frame and a local Lorentz frame, we propose a new expression of Einstein's equivalence principle (EEP). According to it, some feasible experiments should be done to test EEP. We point out that the effect of the magnetic-type gravitational counterpart of the Aharonov-Bohm experiment is too small to be detected now.

The inadmissibility of non-Stokesian vector potentials in quantum mechanics. Comments on a paper asserting the nonexistence of the Aharonov-Bohm effect

Since the publication of the first paper of •HARONOV and BOHM (1) in 1959, discussion has concentrated mainly on questions of interpretation with regard to the role of the electromagnetic potentials in quantum mechanics (2). Doubts as to the reali ty of the effect itself have so far only been raised in private communications and answered by A~A~ONOV and BoH~ in one of their follow-on papers (3). In a recently published article (4) of BOCCHIERI and LOING]~R, however, the nonexistence of one of the effects predicted by AI~ARO~OV and BoH~--namely that related to the vector potent ia l -has been asserted. Because the experimental situation is not so convincing that any objection to the conclusions of ArIARONOV and BOgM can be rejected out of hand, we have undertaken a critical examination of this article. BOCCHI~RI and LOINGER consider a rotating charged particle the trajectory of which is in field-free space and contains an area within which a magnetic field is present. As the whole problem consists in clarifying which vector potentials are admissible in a description of the AharonovBohm (AB) experiment, the question as to whether the eigenvalues of the particle are influenced by the magnetic field is in fact equivalent to the question of the existence of the AB effect. The gauge invariance of the second kind is also valid in the case of a magnetic field vanishing throughout space. I t then means that the general representation of momentum operators and wave functions assumes the form

Significance of the Aharonov-Bohm effect

It is shown that in an Aharonov-Bohm experiment: i) Due to superposition of the electron’s magnetic field and the solenoid’s interior magnetic field there exists an interaction energyUmwhose gradient represents a force on the electron which has not hitherto been recognized or provided for in the classical formalism, ii) This force is non-Lorentzian, it does do work, and explains the A.B. phase shiftclassically, iii) The long-standing action-reaction difficulty involved in. the application of the Biot-Savart law to unclosed circuits is eliminated by this new force in this context, iv) The same force (−gradUm) is implicitly contained in the Schrodinger equation of the A.B. effect. Thus there is no need to modify the concept of force or vector potential as proposed by Aharonov and Bohm. In the Appendix, detailed calculations are outlined showing that currents generated in the solenoid by a passing electron are negligible.