Scalar Aharonov-Bohm experiment with neutrons

Abstract

The scalar version of the Aharonov-Bohm effect predicts a phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space. Unlike the more familiar effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. Rather than using electrons acted on by electrostatic potentials, we have performed an analogous interferometry experiment with thermal neutrons subject to pulsed magnetic fields. The expected phase shifts have been observed to a high degree of accuracy.PACS numbers: 03.65.Bz, 42.50.-p In classical electrodynamics, potentials are merely a convenient mathematical tool for calculating electromagnetic fields of force. In quantum mechanics, however, potentials have a primary physical significance and are an essential ingredient which cannot be readily eliminated from the Schrodinger equation. In a paper entitled "Significance of Electromagnetic Potentials in Quantum Theory" published in 1959, Aharonov and Bohm [1] proposed two types of actual electron interference experiments aimed at exhibiting these conclusions. The phenomena predicted came to be known as the AharonovBohm (AB) effect, and have given rise to a literature of almost 400 journal articles over the last thirty-odd years.The essence of the AB experiments [2] is that electrons suffer phase shifts in passing through regions of space of zero fields but nonzero potentials. The effects are of two types, the usual magnetic (or vector) AB effect, and the less often cited electric (or scalar) AB effect which is conceptually quite simple. It concerns the phase shift caused by the scalar potential V= -eU in the Schrodinger equation:(H 0 +V)yr=ihdifr/dt.(1) Figure 1 (a) shows a divided electron wave packet traveling down two conducting cylinders which act as Faraday cages, i.e., have a field-free interior irrespective of their electrostatic potentials U\ and Ui* To exhibit the scalar AB effect, the potential of cylinder 2 alone is pulsed during a time when the wave packet is contained inside it. In spite of the absence of a force at all times, a relative phase shift A# is expected, A<t> = (\/h)feU 2 (t)dt.(2)The correctness of this AB prediction is of such importance to the consistency of quantum mechanics [3] that the actual experiment deserves a serious attempt. However, such an experiment has not yet been performed because of technical difficulties with existing types of electron interferometers. The closely related experiment of Mateucci and Pozzi [4] involves forces acting on the electron and is not, therefore, a clear-cut test of the effect. Realizations with protons or ions are hindered by the lack of suitable interferometers for such particles.In the present experiment with neutrons, the phase shift is due to a scalar potential, V s -JI * B, which is the analog of V*= -eU, the scalar potential in the scalar AB effect for electrons. (This parallels a previous situation in which th...

Observation of Scalar Aharonov-Bohm Effect with Longitudinally Polarized Neutrons

“…The forces acting on the electrons render the experiment by Mateucci and Pozzi [2] inconclusive. A SAB neutron interferometry experiment, the analog of the electron experimental idea, was first suggested by Zeilinger [3] and later by Anandan [4], and subsequently carried out by Allman et al using unpolarized incident neutron [5]. In this experiment, the magnetic moments m of unpolarized thermal neutrons were subjected to a spatially uniform, but time-dependent magnetic induction B͑t͒ B͑t͒x.…”

“…Furthermore, the detection probability through the 12 mm diameter cylindrical 3 He detectors is also included to model the observed TOF pattern. The details of the pulse coil and the time-of-flight computations can be found in the papers by Allman et al [5]. Multichannel scalars with channel advance every 2 ms are connected to the detectors to record the TOF pattern.…”

“…However, the experimental realization of the scalar Aharonov-Bohm (SAB) effect has proven to be challenging due to the technical difficulties in electron interferometry. [5]. In this experiment, the magnetic moments m of unpolarized thermal neutrons were subjected to a spatially uniform, but time-dependent magnetic induction B͑t͒ B͑t͒x.…”

The photo-neutronrefractive effect

“…The reason is that the amazing perspectives opened up by the results of the corresponding experiments justify the performance of this difficult task: Measurements with polarised neutrons would allow us to detect Aharonov-Casher (spinorbit) [124] as well as Foldy contributions [30,31] to the diffraction, and might even offer a novel experimental approach towards the fundamental question of the EDM of the neutron. Some of the effects have already been carefully studied [78,79,80,83,125] using interferometric techniques. Moreover, during the last few years different experimental approaches were offered to lower the limit of a tentative EDM [126,127,128,129,130,131,132] including open debates, and this still remains a challenging topic.…”

“…The neutron itself and its behaviour in various potentials, e.g. in a magnetic field [70], a gravitational field [71,72,73,74,75,76,77] or such of pure topological nature [78,79,80,81,82,83], was studied as a model quantum mechanical system by means of the interferometer. Some very recent and amazing results on quantum states of the neutron in the gravitational field demonstrate the demand of further research on those topics [84].…”