Electric Aharonov-Bohm Effect Research Articles

Energy-level shift of quantum systems via the scalar electric Aharonov-Bohm effect

A novel version of the electric Aharonov-Bohm effect is proposed where the quantum system which picks up the Aharonov-Bohm phase is confined to a Faraday cage with a time varying, spatially uniform scalar potential. The electric and magnetic fields in this region are effectively zero for the entire period of the experiment. The observable consequence of this version of the electric Aharonov-Bohmn effect is to shift the energy levels of the quantum system rather than shift the fringes of the 2-slit interference pattern. We show a strong mathematical connection between this version of the scalar electric AB effect and the AC Stark effect.

Is the electric potential physical?

In the yet-unmeasured electric Aharonov–Bohm effect, an electric potential influences the quantum mechanical wavefunction of charged matter—even in regions where the electric field vanishes.

Proposal for testing the electric Aharonov-Bohm effect with superconductors

The phase of the wave function of charged matter is sensitive to the value of the electric potential, even when the matter never enters any region with non-vanishing electromagnetic fields. Despite its fundamental character, this archetypal electric Aharonov-Bohm effect has evidently never been observed. We propose an experiment to detect the electric potential through its coupling to the superconducting order parameter. A potential difference between two superconductors will induce a relative phase shift that is observable via the DC Josephson effect even when no electromagnetic fields ever act on the superconductors, and even if the potential difference is later reduced to zero. This is a type of electromagnetic memory effect, and would directly demonstrate the physical significance of the electric potential.

Electric Aharonov–Bohm effect without a loop in a Cooper pair box

We predict the force-free scalar Aharonov–Bohm (AB) effect of a Cooper pair box in an electric field at a distance without forming a closed path of the interfering charges. The superposition of different charge states plays a major role in eliminating the closed loop, which is distinct from the original topological AB effect. The phase shift is determined by the charge-state-dependent local field interaction energy. In addition, our proposed setup does not require a pulse experiment for fast switching of a potential, which eliminates the major experimental obstacle for observing the ideal electric Aharonov–Bohm effect.

Electromagnetic duality and the electric memory effect

We study large gauge transformations for soft photons in quantum electrodynamics which, together with the helicity operator, form an ISO(2) algebra. We show that the two non-compact generators of the ISO(2) algebra correspond respectively to the residual gauge symmetry and its electromagnetic dual gauge symmetry that emerge at null infinity. The former is helicity universal (electric in nature) while the latter is helicity distinguishing (magnetic in nature). Thus, the conventional large gauge transformation is electric in nature, and is naturally associated with a scalar potential. We suggest that the electric Aharonov-Bohm effect is a direct measure for the electromagnetic memory arising from large gauge transformations.

Absence of the Electric Aharonov-Bohm Effect due to Induced Charges.

This paper states that the induced charge should not be neglected in the electric Aharonov-Bohm (A-B) effect. If the induced charge is taken into account, the interference pattern of the moving charge will not change with the potential difference between the two metal tubes. It means that the scalar potential itself can not affect the phase of the moving charge, and the true factor affecting the phase of the moving charge is the energy of the system including the moving charge and the induced charge.

Effective beam separation schemes for the measurement of the electric Aharonov–Bohm effect in an ion interferometer

We propose an experiment for the first proof of the type I electric Aharonov–Bohm effect in an ion interferometer for hydrogen. The performances of three different beam separation schemes are simulated and compared. The coherent ion beam is generated by a single atom tip (SAT) source and separated by either two biprisms with a quadrupole lens, two biprisms with an einzel-lens or three biprisms. The beam path separation is necessary to introduce two metal tubes that can be pulsed with different electric potentials. The high time resolution of a delay line detector allows to work with a continuous ion beam and circumvents the pulsed beam operation as originally suggested by Aharonov and Bohm. We demonstrate that the higher mass and therefore lower velocity of ions compared to electrons combined with the high expected SAT ion emission puts the direct proof of this quantum effect for the first time into reach of current technical possibilities. Thereby a high detection rate of coherent ions is crucial to avoid long integration times that allow the influence of dephasing noise from the environment. We can determine the period of the expected matter wave interference pattern and the signal on the detector by determining the superposition angle of the coherent partial beams. Our simulations were tested with an electron interferometer setup and agree with the experimental results. We determine the separation scheme with three biprisms to be most efficient and predict a total signal acquisition time of only 80s to measure a phase shift from 0 to 2π due to the electric Aharonov–Bohm effect.

A non-qubit quantum adder as one-dimensional cellular automaton

A complete quantum addition machine is presented and compared with methods employing unitary transformations first. A quantum half-adder circuit shown earlier can be implemented into each cell of a 1D cellular automaton. An electric Aharonov–Bohm effect version of the quantum circuit is used to illustrate this implementation. Whatever a quantum Turing machine can achieve is realized in the cellular automata architecture we propose here. The coherence requirement is limited to one cell area. The magnetic flux needed is 0.1Φ0, corresponding to 0.414mT for a ring area of 1 square micron or an electric potential of 0.414mV at 1ps with an energy dissipation of 0.041eV per iteration.

Dynamical features of interference phenomena in the presence of entanglement

A strongly interacting, and entangling, heavy nonrecoiling external particle effects a significant change of the environment. Described locally, the corresponding entanglement event is a generalized electric Aharonov-Bohm effect, which differs from the original one in a crucial way. We propose a gedanken interference experiment. The predicted shift of the interference pattern is due to a self-induced or ``private'' potential difference experienced while the particle is in vacuum. We show that all nontrivial Born-Oppenheimer potentials are ``private'' potentials. We apply the Born-Oppenheimer approximation to interference states. Using our approach, we calculate the relative phase of the external heavy particle as well as its uncertainty throughout an interference experiment or entanglement event. We thus complement the Born-Oppenheimer approximation for interference states.

TOPOLOGICAL EFFECTS IN QUANTUM MECHANICS AND HIGH VELOCITY ESTIMATES

We consider the problem of obtaining high-velocity estimates for finite energy solutions (wave packets) to Schrödinger equations for N-body systems. We discuss a time-dependent method that allows us to obtain precise estimates with error bounds that decay as a power of the velocity. We apply this method to the electric Aharonov–Bohm effect. We give the first rigorous proof that quantum mechanics predicts the existence of this effect. Our result follows from an estimate in norm, uniform in time, that proves that the Aharonov–Bohm Ansatz is a good approximation to the exact solution to the Schrödinger equation for high velocity.

The electric Aharonov-Bohm effect

The seminal paper of Aharonov and Bohm [Phys. Rev. 115, 485 (1959)]10.1103/PhysRev.115.485 is at the origin of a very extensive literature in some of the more fundamental issues in physics. They claimed that electromagnetic fields can act at a distance on charged particles even if they are identically zero in the region of space where the particles propagate, that the fundamental electromagnetic quantities in quantum physics are not only the electromagnetic fields but also the circulations of the electromagnetic potentials; what gives them a real physical significance. They proposed two experiments to verify their theoretical conclusions. The magnetic Aharonov-Bohm effect, where an electron is influenced by a magnetic field that is zero in the region of space accessible to the electron, and the electric Aharonov-Bohm effect where an electron is affected by a time-dependent electric potential that is constant in the region where the electron is propagating, i.e., such that the electric field vanishes along its trajectory. The Aharonov-Bohm effects imply such a strong departure from the physical intuition coming from classical physics that it is no wonder that they remain a highly controversial issue after more than fifty years, in spite of the fact that they are discussed in most of the text books in quantum mechanics. The magnetic case has been studied extensively. The experimental issues were settled by the remarkable experiments of Tonomura et al. [Phys. Rev. Lett. 48, 1443 (1982); Phys. Rev. Lett. 56, 792 (1986)] with toroidal magnets, that gave a strong evidence of the existence of the effect, and by the recent experiment of Caprez et al. [Phys. Rev. Lett. 99, 210401 (2007)]10.1103/PhysRevLett.99.210401 that shows that the results of the Tonomura et al. experiments cannot be explained by the action of a force. The theoretical issues were settled by Ballesteros and Weder [Commun. Math. Phys. 285, 345 (2009)10.1007/s00220-008-0579-1; J. Math. Phys. 50, 122108 (2009)10.1063/1.3266176; Commun. Math. Phys. 303, 175 (2011)]10.1007/s00220-010-1166-9 who rigorously proved that quantum mechanics predicts the experimental results of Tonomura et al. and of Caprez et al. The electric Aharonov-Bohm effect has been much less studied. Actually, its existence, that has not been confirmed experimentally, is a very controversial issue. In their 1959 paper Aharonov and Bohm proposed an ansatz for the solution to the Schrödinger equation in regions where there is a time-dependent electric potential that is constant in space. It consists in multiplying the free evolution by a phase given by the integral in time of the potential. The validity of this ansatz predicts interference fringes between parts of a coherent electron beam that are subjected to different potentials. In this paper we prove that the exact solution to the Schrödinger equation is given by the Aharonov-Bohm ansatz up to an error bound in norm that is uniform in time and that decays as a constant divided by the velocity. Our results give, for the first time, a rigorous proof that quantum mechanics predicts the existence of the electric Aharonov-Bohm effect, under conditions that we provide. We hope that our results will stimulate the experimental research on the electric Aharonov-Bohm effect.

Beyond the Dirac Phase Factor: Dynamical Quantum Phase-Nonlocalities in the Schrödinger Picture

Generalized solutions of the standard gauge transformation equations are presented and discussed in physical terms. They go beyond the usual Dirac phase factors and they exhibit nonlocal quantal behavior, with the well-known Relativistic Causality of classical fields affecting directly the phases of wavefunctions in the Schroedinger Picture. These nonlocal phase behaviors, apparently overlooked in path-integral approaches, give a natural account of the dynamical nonlocality character of the various (even static) Aharonov-Bohm phenomena, while at the same time they seem to respect Causality. Indeed, for particles passing through nonvanishing magnetic or electric fields they lead to cancellations of Aharonov-Bohm phases at the observation point, generalizing earlier semiclassical experimental observations (of Werner & Brill) to delocalized (spread-out) quantum states. This leads to a correction of previously unnoticed sign-errors in the literature, and to a natural explanation of the deeper reason why certain time-dependent semiclassical arguments are consistent with static results in purely quantal Aharonov-Bohm configurations. These nonlocalities also provide a remedy for misleading results propagating in the literature (concerning an uncritical use of Dirac phase factors, that persists since the time of Feynman's work on path integrals). They are shown to conspire in such a way as to exactly cancel the instantaneous Aharonov-Bohm phase and recover Relativistic Causality in earlier "paradoxes" (such as the van Kampen thought-experiment), and to also complete Peshkin's discussion of the electric Aharonov-Bohm effect in a causal manner. The present formulation offers a direct way to address time-dependent single- vs double-slit experiments and the associated causal issues -- issues that have recently attracted attention, with respect to the inability of current theories to address them.

Nontrivial systems and the necessity of the scalar quantum mechanics axioms

We discuss the necessity of the axioms of scalar quantum mechanics introduced by Paschke and clearly demonstrate their geometric and/or physical meaning. We show that reasonable nonrelativistic quantum mechanics is exactly specified by the axioms. A system describing the electric Aharonov–Bohm effect is presented. It illustrates the topological obstructions for the existence of a Hamiltonian.

Quantum effects of electric fields and potentials on electron motion: an introduction to theoretical and practical aspects

In the so-called electric Aharonov–Bohm effect, a quantum interference pattern shift is produced when electrons move in an electric field free region but, at the same time, in the presence of a time-dependent electric potential. Analogous fringe shifts are observed in interference experiments where electrons, travelling through an electrostatic field, suffer a classical lag effect produced by electric forces. Since these experiments are reported mainly in specialized journals, it could be rather difficult and time consuming for a student to attain a comprehensive overview of the subject. Therefore, particular attention has been addressed to reviewing the theory, to describing a couple of experiments and to the interpretation of the results. We believe that students can be suitably introduced to exploring the ‘paradoxical’ aspects of the interaction of electrons with electric potentials and fields.

Tensorial phases in multiple beam atomic interference

The atomic tensor polarizability in a pulsed optical field can generate a phase-shift scaling quadratically with the interfering path number in a multiple beam Ramsey experiment. The phase can be interpreted as an internal atomic-state version of the electric (or scalar) Aharonov-Bohm effect. In the absence of classical forces, this nonlinear phase shift causes collapse and revival of the Airy-function-like interference pattern. The technique also holds promise for experiments testing for a permanent electric dipole moment of an atom.

Chiral disorder and QCD at finite chemical potential

We investigate the effects of a finite chemical potential μ in QCD viewed as a disordered medium. In the quenched approximation, A 4= iμ induces a complex electric Aharonov-Bohm effect that causes the diagonal contribution to the quark return probability to vanish at μ= m π /2 (half the pion mass). In two-color QCD, the weak-localization contribution to the quark return probability remains unaffected causing a mutation in the spectral statistics. In full QCD, the complex electric flux is screened and the light quarks are shown to diffuse asymmetrically with a substantial decrease in the conductivity along the `spatial' directions. Mean-field arguments suggest that a d=1 percolation transition may take place in the range 1.5 ρ 0< ρ<3 ρ 0, where ρ 0 is nuclear matter density.

Polarization and magnetization fields in the Aharonov-Bohm effect

The electric Aharonov-Bohm effect is usually explained by means of the scalar potential, which is present in a multiply connected region of space time where no electric field acts on the charged particle. An alternative interpretation is given in terms of the particle's polarization field penetrating the region occupied by the electric field but inaccessible to the particle itself. Similarly, the magnetic Aharonov-Bohm effect is usually explained by means of the vector potential, which is present in a multiply connected region of space where no magnetic-induction field acts on the charged particle. An alternative interpretation of this effect is given in terms of the particle's magnetization field penetrating the region occupied by the magnetic-induction field but inaccessible to the particle itself. Our interpretations of the electric and magnetic Aharonov-Bohm effects are both developed by using the multipolar form of the Lagrangian instead of the minimal-coupling form in the Feynman path integral.

Magnetic and electric Aharonov—Bohm effects in nanostructures

The paper reviews and extends the magnetic Aharonov—Bohm effect (persistent current, resistance oscillation) in normalmetal rings including spin-independent and spin-dependent hopping, Zeeman splitting, magnetic textures and wheels, ring rotation and weak coupling, as well as the electric Aharonov—Bohm effect (“persistent charge”) in small metallic contacts. We then discuss dynamical screening effects in a surface charge in a metal. Energy dissipation due to motion of the surface charge has a singularity at the velocity of motion equal to the phonon propagation velocity. Surface image of an external charge inside the metal is strongly distorted at the velocity of motion larger than the Fermi velocity.

Complementary electric Aharonov-Bohm effect.

A complementary electric Aharonov-Bohm (AB) effect is proposed and investigated where one branch of a chopped and split electron beam traverses a region with an electric field and upon interference with the other branch no phase shift would be observed. The analysis of the proposed experiment is carried out (1) in a semiclassical (SC) eikonal approximation and (2) in a complete quantum-mechanical (QM) calculation with a plane-wave approximation similar to AB's original paper. The QM phase shift is the sum of the SC phase shift plus an AB-like phase shift for a constant potential. While the SC analysis predicts that there must be a phase shift, the full QM indicates that a null phase shift is possible.

A bound state model of the electric Aharonov-Bohm effect

It is shown how the electric form of the Aharonov-Bohm effect can be demonstrated using a very simple one dimensional bound state model system. The measurable effects of an inaccessible field in such a model are examined and the results of some explicit calculations are given. Their bearing on the question of the localization of electromagnetic causation in quantum mechanics is discussed.