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Physical Review Letters

Electromagnetic Acceleration of Neutrons and Its Observability

Apoorva G. Wagh, Veer Chand Rakhecha

Published Feb 24, 1997• 8 citations
Publisher

Abstract

Using the energy and canonical momentum conservation, we delineate the acceleration of neutrons in uniform electric and magnetic fields, first enunciated by Anandan. We determine bounds of the velocity change, made cumulative by reversing the electric field periodically in space. We show that the acceleration is observable in an interference experiment, disproving claims to the contrary made by Casella and Werner.

DOI
10.1103/physrevlett.78.1399

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Using the energy and canonical momentum conservation, we delineate the acceleration of neutrons in uniform electric and magnetic fields, first enunciated by Anandan. We determine bounds of the velocity change, made cumulative by reversing the electric field periodically in space. We show that the acceleration is observable in an interference experiment, disproving claims to the contrary made by Casella and Werner.
The question as to whether neutron acceleration can occur in uniform electromagnetic fields is examined. Although such an effect has been predicted using the canonical equations of motion, some doubt has been raised recently as to whether it is in principle observable for a spin-1/2 particle. To resolve this issue a gedanken experiment is proposed and analyzed using wave-packet construction for the neutron beam. By allowing an arbitrary orientation for the neutron spin as well as for the electric and magnetic fields, a nonvanishing acceleration of the center of the neutron wave packet is found that confirms the predictions of the canonical formalism.
We note that the neutron spin must be treated as an intrinsically quantum variable when determining electromagnetically induced phase shifts in neutron interferometry by computing the otherwise-classical action over the classical orbit. We show that a putative acceleration of the neutron (\ensuremath{\gamma}/mc)E\ifmmode\times\else\texttimes\fi{}(\ensuremath{\mu}\ifmmode\times\else\texttimes\fi{}B) recently suggested by Anandan, is essentially unobservable in such measurements over segments of the orbit where the electric and magnetic fields are constant (or vary slowly), within standard electroweak theory.
The motion of an electron in a uniform electric field, as in free fall, is characterized by the existence of pairs of trajectories that rejoin on the same final point. The corresponding interference pattern was first observed in 1996, and explained by the elementary model of uniform acceleration starting from a motionless electron source. In the experiment, however, the electron source is a fast-moving negative ion, which makes direct application of the model questionable. Relativistic arguments can be used to ascertain that no phase changes are actually produced by the motion of the source. The quantum phase of the electron can also be checked all along its two interfering trajectories. This method, which produces the same reassuring result as relativity, gives us the opportunity to revisit the relativistic transformation of the Schrödinger phase. It also makes it possible to calculate the effect of an acceleration of both the free electron and the electron emitter. Only in this case is a change of the interference pattern expected, but it is quantitatively negligible in the actual experiment.
The dynamics of neutral spinning particles in electromagnetic fields is investigated. The phase interference of unpolarized neutron beams is reasonably interpreted as the observed spin precession in external fields instead of potential effects in the quantum physics; namely, the Aharonov-Bohm and Aharonov-Casher effects. It is also pointed out that the recent experiment claimed to be the verification of Aharonov-Casher phase with neutron interferometry, however, can be considered as a test of new anyon model.
Canonical and kinetic momentum have representations in quantum mechanics that imply differences in the measurability of these related quantities in external fields. The measurability of kinetic momentum in external electric and magnetic fields and in free space is examined for several different measurement procedures. It is shown that kinetic momentum is a measurable physical observable, at least in uniform external fields. The quantum limitations of measurement are found to be greater for measurement of kinetic momentum in magnetic fields than in either free space or electric fields, in a way that is consistent with the standard operator representation of kinetic momentum.
The implications of complementarity on two-path neutron interferences and on separated-oscillatory-field resonances are discussed. The studies are extensions of those by Furry and Ramsey [Phys. Rev. 118, 623 (1960)] on two-path electron interferences which showed that an apparatus used to determine the electron path introduces uncertainties in the scalar and vector potentials which in turn disturb the phase of the electron wave function so much through the Aharonov-Bohm effects [Phys. Rev. 115, 485 (1959)] that the interference fringes disappear. A similar result is derived here for the neutron, but with the phase uncertainties coming from the magnetic moment's motion through an electric field as discussed by Anandan [Phys. Rev. Lett. 48, 1660 (1982)], and Aharonov and Casher [Phys. Rev. Lett. 53, 319 (1984)]. A corresponding result is also obtained for separated-oscillatory-fields resonances, which can be interpreted as an interference between two different paths in spin space. An interesting difference between the separated-path and separated-oscillatory-field experiments is that the latter may be interpreted classically.