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arXiv:0810.4219

Noiseless Quantum Transmission of Information via Aharonov - Bohm Effect

Jian-zu Zhang A B

Published Oct 23, 2008• 0 citations
arXivHTMLPDF

Abstract

The possibility of quantum transmission of information via the induced fractional angular momentum by the Aharonov - Bohm vector potential is revealed. Its special advantage is that it is noiseless: Stray magnetic fields of environments influence the energy spectrum of the ion, but cannot contribute the fractional angular momentum to cause noise.

DOI
10.48550/arxiv.0810.4219

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•Aug 25, 2005•56 citations
The possibility of quantum transmission of information via the induced fractional angular momentum by the Aharonov - Bohm vector potential is revealed. Its special advantage is that it is noiseless: Stray magnetic fields of environments influence the energy spectrum of the ion, but cannot contribute the fractional angular momentum to cause noise.
An induced fractional zero-point angular momentum of charged particles by the Bohm–Aharonov (BA) vector potential is realized via a modified combined trap. It explores a “spectator” mechanism in this type of quantum effects: In the limit of the kinetic energy approaching one of its eigenvalues the BA vector potential alone cannot induce a fractional zero-point angular momentum at quantum mechanical level in the BA magnetic field-free region; But when there is a “spectator” magnetic field the BA vector potential induces a fractional zero-point angular momentum. The “spectator” does not contribute to such a fractional angular momentum, but plays essential role in guaranteeing non-trivial dynamics at quantum mechanical level in the required limit. This “spectator” mechanism is significant in investigating the BA effects and related topics in both aspects of theory and experiment.
The induced fractional zero-point canonical angular momentum on charged particles by the Aharonov - Bohm (AB) vector potential is realized via modified combined traps. It explores new features for this type of quantum effects: In a limit of vanishing mechanical kinetic energy the AB vector potential alone cannot induce a fractional zero-point canonical angular momentum on charged particles at the quantum mechanical level in the AB magnetic field-free region; But for the case of the AB vector potential with another one of a "spectator" magnetic field the AB vector potential induces a fractional zero-point canonical angular momentum in the same limit. The "spectator" one does not contribute to such a fractional zero-point quantity, but plays essential role in guaranteeing non-trivial dynamics survived in this limit at the quantum mechanical level. These results are significance in investigations of the AB effects and related fields for both theories and experiments.
The AB (Aharonov-Bohm) effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle's wave function, even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect, an electron beam is split into two paths, with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams, the vector potential A associated with the magnetic flux  through the solenoid induces a phase shift in the electron's wave function.This phase shift, quantified by qc     , manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED (quantum electrodynamics), where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems, beyond its classical role.This article outlines the AB effect, including its theoretical framework, experimental observations, and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.
It is often said that the Aharonov-Bohm (AB) effect (1959) is an effect that is due to the vector potential. This is considered remarkable since a quantity that is not uniquely determined has a measurable effect. The authors show that, in the symmetric Coulomb gauge, (e/c)A(r) is simply the momentum of the electromagnetic field. The effect may equally well be considered an effect of the electromagnetic momentum. Thus, it is possible to discuss the AB effect strictly in terms of observables. The idea that the effect is due to the vector potential is correct, but sheds little light on the physics of the effect.
The magnetic Aharonov-Bohm effect shows that charged particles may be affected by the vector potential in regions without any electric or magnetic fields [1]. The Aharonov-Bohm effect was experimentally confirmed [2-3] and has been found in many situations [4-6]. A common explanation is based on quantum mechanics, which states that the wavefunctions associated with the charges will accumulate a phase shift due to the vector potential. However, consensus about its nature and interpretation has not been achieved [7-14]. We here propose a simple but reasonable interpretation based on the theory for electromagnetic radiation and couplings [15]. The energy associated with a pulse radiator is divided into a Coulomb-velocity energy and a radiative energy, together with a macroscopic Schott energy accounting for the energy exchange between them. All these energies are expressed with terms including the potentials, so are the mutual coupling energies. There exists a force acting on the moving charges even though the fields completely vanish. This force makes the charges pass through the magnetic solenoid in different velocity with different path length, causing a phase shift the same as that obtained with quantum mechanics. The theory is originally aimed for providing an interpretation for electromagnetic radiation and mutual coupling. It is derived directly from the Maxwell theory with no modification but only substitution and reorganization.
The Aharonov-Bohm (AB) effect in non-commutative quantum mechanics (NCQM) is studied. First, by introducing a shift for the magnetic vector potential we give the Schrddoto\\ddot{o}ddotodinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then by solving the Schrddoto\\ddot{o}ddotodinger equations, we obtain the Aharonov-Bohm (AB) phase on NC space and NC phase space, respectively.