We use a covariant formalism that is capable of describing the electric and magnetic versions of the Aharonov-Bohm effect, as well as the Aharonov-Casher effect, through local interactions of charges and currents with the quantum electromagnetic field. By considering that only local interactions of a quantum particle with the quantum field can affect its behavior, we show that the magnetic Aharonov-Bohm effect must be present even if the solenoid generating the magnetic field is shielded by a perfect conductor, as experimentally demonstrated.
The Aharonov-Casher effect, entry in the Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, ed. F. Weinert, K. Hentschel, D. Greenberger and B. Falkenburg (Springer), to appear
We reexamine the topological and nonlocal natures of the Aharonov-Casher and scalar Aharonov-Bohm phase effects. The underlying U(1) gauge structure is exhibited explicitly. And the conditions for developing topological Aharonov-Casher and scalar Aharonov-Bohm phases are clarified. We analyse the arguments of M. Peshkin and H. J. Lipkin (Phys. Rev. Lett. 74, 2847(1995)) in detail and show that they are based on the wrong Hamiltonian which yields their conclusion incorrect.
For a believer in locality of Nature, the Aharonov-Bohm effect and the Aharonov-Casher effect are paradoxes. I discuss these and other Aharonov's paradoxes and propose a local explanation of these effects. If the solenoid in the Aharonov-Bohm effect is treated quantum mechanically, the effect can be explained via local interaction between the field of the electron and the solenoid. I argue that the core of the Aharonov-Bohm and the Aharonov-Casher effects is that of quantum entanglement: the quantum wave function describes all systems together.
Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects are treated fully relativistically in 2+1 dimensions. The influences of the relevant geometric and topological phases on an entangled spin-1/2 system are studied. It is shown that for the AC case the correlation function of the Clauser-Horne-Shimony-Holt (CHSH) inequality for certain choices of the spin measurements depends on the AC phase explicitly.
We calculate the Abraham force and the Aharonov-Casher force exerted by the electromagnetic quantum vacuum on alkaline atoms in highly excited, long-living Rydberg states. Because of their high polarizability and long-life time such atoms are good candidates to observe these forces.
We consider the problem of the bound states of a spin 1/2 chargless particle in a given Aharonov-Casher configuration. To this end we recast the description of the system in a supersymmetric form. Then the basic physical requirements for unbroken supersymmetry are established. We comment on the possibility of neutron confinement in this system.
It is argued that the Aharonov-Casher set up could be used as the basic building block for quantum computation. We demonstrate explicitly in this scenario one- and two-qubit phase shift gates that are fault tolerant to deformations of the path when encircling two sites of the computational system around each other.
We determine the (bound) ground state of a spin 1/2 chargless particle with anomalous magnetic moment in certain Aharonov-Casher configurations. We recast the description of the system in a supersymmetric form. Then the basic physical requirements for unbroken supersymmetry are established. We comment on the possibility of neutron trapping in these systems.
The Aharonov-Casher (AC) phase is calculated in relativistic wave equations of spin one. The AC phase has previously been calculated from the Dirac-Pauli equation using a gauge-like technique \cite{MK1,MK2}. In the spin-one case, we use Kemmer theory (a Dirac-like particle theory) to calculate the phase in a similar manner. However the vector formalism, the Proca theory, is more widely known and used. In the presence of an electromagnetic field, the two theories are `equivalent' and may be transformed into one another. We adapt these transformations to show that the Kemmer theory results apply…
In this manuscript, we investigate the influence of the Aharonov-Casher effect on the generalized Dirac oscillator containing the Coulomb-type potential function related to a relativistic neutral particle having a permanent magnetic dipole moment interacting with the external electromagnetic fields in (1+2)-dimensional cosmic string space-time. The eigenfunctions and energy eigenvalues of such a Dirac oscillator are derived by using the Nikifornov-Uvarov method. We indicate that implementing the scenario gives the relativistic modified exact analytical solutions. In this way, we can see that t…
We propose the Aharonov-Casher (AC) effect for four entangled spin-half particles carrying magnetic moments in the presence of impenetrable line charge. The four particle state undergoes AC phase shift in two causually disconnected region which can show up in the correlations between different spin states of distant particles. This correlation can violate Bell's inequality, thus displaying the non-locality for four particle entangled states in an objective way. Also, we have suggested how to control the AC phase shift locally at two distant locations to test Bell's inequality. We belive that a…
Bell's inequality is established based on local realism. The violation of Bell's inequality by quantum mechanics implies either locality or realism or both are untenable. Leggett's inequality is derived based on nonlocal realism. The violation of Leggett's inequality implies that quantum mechanics is neither local realistic nor nonlocal realistic. The incompatibility of nonlocal realism and quantum mechanics has been urrently confirmed by photon experiments. In our work, we propose to test Leggett's inequality using the Aharonov-Casher effect. In our scheme, four entangled particles emitted fr…
Particle motion in the fields of Aharonov-Bohm and Aharonov-Casher is considered in framework of the classical theory to reveal conditions admitting duality of the two configurations. Important role of orientation of the magnetic dipole moment is demonstrated. Duality becomes totally destroyed by addition of electric dipole and/or higher multipole moments. Correspondence between quantum and classical considerations is also discussed.
We introduce an $SU(1,1)$ algebraic approach to study the $(2+1)$-Dirac oscillator in the presence of the Aharonov-Casher effect coupled to an external electromagnetic field in the Minkowski spacetime and the cosmic string spacetime. This approach is based on a quantum mechanics factorization method that allows us to obtain the $su(1,1)$ algebra generators, the energy spectrum and the eigenfunctions. We obtain the coherent states and their temporal evolution for each spinor component of this problem. Finally, for these problems, we calculate some matrix elements and the Schrödinger uncertainty…
In this Reply we argue that (i) the Hamiltonian, Eq. (17) in our paper (Phys. Rev. Lett. 108, 070405 (2012)), is definitely Lorentz invariant; (ii) the conditions of generating topological Aharonov-Casher(AC) and Scalar Aharonov-Bohm (SAB) effects are essential and physically meaningful; (iii) the Hamiltonians both in Phys. Rev. Lett. 74, 2847 (1995) and arXiv:1311.4011 are not suitable to describe the polarized spinor particles.
It is shown that the paper `Energy spectrum of a Dirac particle with position-dependent mass under the influence of the Aharonov-Casher effect', by Oliveira, Borges and Sousa [Braz. J. Phys. 49, 801 (2019)], is based on a series of ingredients clearly incorrect.
The ideal scalar Aharonov-Bohm (SAB) and Aharonov-Casher (AC) effect involve a magnetic dipole pointing in a certain fixed direction: along a purely time dependent magnetic field in the SAB case and perpendicular to a planar static electric field in the AC case. We extend these effects to arbitrary direction of the magnetic dipole. The precise conditions for having nondispersive precession and interference effects in these generalized set ups are delineated both classically and quantally. Under these conditions the dipole is affected by a nonvanishing torque that causes pure precession around …
In this paper, we study the influence of the Aharonov-Casher effect [Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984).] on the Dirac oscillator in three different scenarios of general relativity: the Minkowski spacetime, the cosmic string spacetime and the cosmic dislocation spacetime. In this way, we solve the Dirac equation and obtain the energy levels for bound states and the Dirac spinors for positive-energy solutions. We show that the relativistic energy levels depend on the Aharonov-Casher geometric phase. We also discuss the influence of curvature and torsion on the relativist…
The Aharonov Casher effect predicts the existence in two dimensions of ceil(Phi/2pi) -1 bounded zero modes associated with a magnetic flux Phi. Aharonov and Casher discussed the case of gyromagnetic factor equals 2, we will discuss the general case of any gyromagnetic factor. As a simple model, we study the case where the magnetic field lies in a thin annulus. First we examine the wavefunctions of the zero-energy bounded states, predicted by the Aharonov Casher Effect for electrons with gyromagnetic ratio equal 2. We then calculate the wave function and energies for a gyromagnetic ratio g not …
In this Comment we point out (i) that the Hamiltonian, Eq. (17) in the Letter(Phys. Rev. Lett. 108, 070405 (2012)), is not a relativistic Hamiltonian, (ii) then that the conditions in the Letter are irrelevant for a topological AC and SAB effects, and (iii) conclusively that the non-relativistic Hamiltonian employed by Peshkin and Lipkin (Phys. Rev. Lett. 74, 2847 (1995)) has the same $U(1)_{mm}$ gauge structure for a fixed spin and then is not wrong, but their incorrect interpretation of the spin autocorrelations led to the incorrect conclusion.
We establish systematic consolidation of the Aharonov-Bohm and Aharonov-Casher effects including their scalar counterparts. Their formal correspondences in acquiring topological phases are revealed on the basis of the gauge symmetry in non-simply connected spaces and the adiabatic condition for the state of magnetic dipoles. In addition, investigation of basic two-body interactions between an electric charge and a magnetic dipole clarifies their appropriate relative motions and discloses physical interrelations between the effects. Based on the two-body interaction, we also construct an exact …
In this paper we give a covariant expression for Aharonov-Casher phase. This expression is a combination of the canonical electric field, Aharonov-Casher phase plus a magnetic field phase shift. We use this covariant expression for the Aharonov-Casher phase to investigate the case of a neutral particle with a non-zero magnetic moment moving in the {\it time dependent} electric and magnetic fields of a plane electromagnetic wave background. We focus on the case where the magnetic moment of the particle is oriented so that both the electric and magnetic field lead to non-zero phases, and we look…
In this work, we study the Aharonov-Casher effect in the $(2+1)$-dimensional Dirac oscillator coupled to an external electromagnetic field. We set up our system in two different scenarios: in the Minkowski spacetime and the cosmic string spacetime. In both cases, we solve exactly the Dirac oscillator and we determine the energy spectrum and the eigenfunctions for the bound states. We verify that in the Minkowski spacetime, the Dirac oscillator spectrum depends linearly on the strength of the magnetic field $B$, and on the Aharonov-Casher phase. In addition, we explicitly obtain the corrections…
The Aharonov-Casher problem in the presence of a Lorentz-violating background nonminimally coupled to a spinor and a gauge field is examined. Using an approach based on the self-adjoint extension method, an expression for the bound state energies is obtained in terms of the physics of the problem by determining the self-adjoint extension parameter.
In this work bound states for the Aharonov-Casher problem are considered. According to Hagen's work on the exact equivalence between spin-1/2 Aharonov-Bohm and Aharonov-Casher effects, is known that the $\boldsymbol{\nabla}\cdot\mathbf{E}$ term cannot be neglected in the Hamiltonian if the spin of particle is considered. This term leads to the existence of a singular potential at the origin. By modeling the problem by boundary conditions at the origin which arises by the self-adjoint extension of the Hamiltonian, we derive for the first time an expression for the bound state energy of the Ahar…
A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov-Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase.
Dipoles interference is studied when atomic systems are coupled to classical electromagnetic fields. The interaction between the dipoles and the classical fields induces a time-varying Aharonov-Casher phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be observable and almost as large as the corresponding one for coherent electrons. We analyze different trajectories in order to show the dependence of the decoherence factor with the velocity of the part…
A periodic network of connected rhombii, mimicking a spintronic device, is shown to exhibit an intriguing spin selective extreme localization, when submerged in a uniform out of plane electric field. The topological Aharonov Casher phase acquired by a travelling spin is seen to induce a complete caging, triggered at a special strength of the spin orbit coupling, for half odd integer spins s \ge n\hbar/2, with n odd, sparing the integer spins. The observation finds exciting experimental parallels in recent literature on caged, extreme localized modes in analogous photonic lattices. Our results …
We suggest a system in which the amplitude of macroscopic flux tunneling can be modulated via the Aharonov-Casher effect. The system is an rf-SQUID with the Josephson junction replaced by a Bloch transistor -- two junctions separated by a small superconducting island on which the charge can be induced by an external gate voltage. When the Josephson coupling energies of the junctions are equal and the induced charge is q=e, destructive interference between tunneling paths brings the flux tunneling rate to zero. The device may also be useful as a qubit for quantum computation.
We propose an experiment that would produce and measure a large Aharonov-Casher (A-C) phase in a solid-state system under macroscopic motion. A diamond crystal is mounted on a spinning disk in the presence of a uniform electric field. Internal magnetic states of a single NV defect, replacing interferometer trajectories, are coherently controlled by microwave pulses. The A-C phase shift is manifested as a relative phase, of up to 17 radians, between components of a superposition of magnetic substates, which is two orders of magnitude larger than that measured in any other atom-scale quantum sys…
The Aharonov-Casher (AC) effect for quantum motion of a neutral magnetized particle in the electric field is believed to be a topological effect closely related to the known Aharonov-Bohm (AB) effect. We study how it depends on the spin of the particle involved. Duality of the AB and AC effects is demonstrated to exist only for two extreme spin (and magnetic moment) projections. Classical consideration confirms the conclusion. Motion of a classical magnetized particle with generally oriented magnetic moment in the AC field appears to be subjected to both forces and torques. Only for two specia…
The effects of a Lorentz symmetry violating background vector on the Aharonov-Casher scattering in the nonrelativistic limit is considered. By using the self-adjoint extension method we found that there is an additional scattering for any value of the self-adjoint extension parameter and non-zero energy bound states for negative values of this parameter. Expressions for the energy bound states, phase-shift and the scattering matrix are explicitly determined in terms of the self-adjoint extension parameter. The expression obtained for the scattering amplitude reveals that the helicity is not co…
It is shown that the molecular Aharonov-Bohm effect is neither nonlocal nor topological in the sense of the standard magnetic Aharonov-Bohm effect. It is further argued that there is a close relationship between the molecular Aharonov-Bohm effect and the Aharonov-Casher effect for an electrically neutral spin$-{1/2}$ particle encircling a line of charge.
The nonlocal and topological nature of the molecular Aharonov-Bohm (MAB) effect is examined for real electronic Hamiltonians. A notion of preferred gauge for MAB is suggested. The MAB effect in the linear + quadratic $E\otimes ε$ Jahn-Teller system is shown to be essentially analogues to an anisotropic Aharonov-Casher effect for an electrically neutral spin$-{1/2}$ particle encircling a certain configuration of lines of charge.
A recent Letter [1] has proposed a device, consisting of an rf SQUID with the junction replaced by a double one, i.e. a Bloch transistor. For symmetric Josephson couplings, and for specific flux bias and gate voltage applied to the transistor's island, the tunneling of encircled flux between its two local potential minima is claimed to be suppressed completely due to destructive interference. This comment purports to show that this claim in general is not valid. Namely, the very Hamiltonian (1) in [1], from which the effect is derived, describes the circuit only under an additional condition. …
The original topological Aharonov-Casher (AC) effect is due to the interaction of the anomalous magnetic dipole moment (MDM) with certain configurations of electric field. Naively one would not expect an AC effect for a scalar particle for which no anomalous MDM can be defined in the usual sense. In this letter we study the AC effect in supersymmetric systems. In this framework there is the possibility of deducing the AC effect of a scalar particle from the corresponding effect for a spinor particle. In 3+1 dimensions such a connection is not possible because the anomalous MDM is zero if super…
We consider a neutral particle with permanent magnetic dipole moment in an elastic medium with the presence of a uniform distribution of screw dislocations interacting with a radial electric field. We show that the uniform distribution of dislocations plays the role of an effective uniform magnetic field, and obtain a spectrum of energy which depends on the Aharonov-Casher geometric phase [Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984)]. Moreover, from the dependence of energy levels on the Aharonov-Casher geometric phase, we calculate the persistent spin currents in this elastic L…
Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-bohm effect which involving a coherent superposition of particles with opposite charges moving along single open interferometric path. By means of the experimental considerations a limit $\sqrtθ\simeq\left( 0,13T\text{eV}\right) ^{-1}$ is achieved, improving by 10 orders of magnitude the derived by Chaichian et. al. for the Aharonov-Bohm effect. It…
Bound states of massive fermions in the Aharonov-Bohm like fields have analytically been studied. The Hamiltonians with the Aharonov--Bohm like potentials are essentially singular and therefore require specification of a one-parameter self-adjoint extension. We construct self-adjoint Dirac Hamiltonians with the Aharonov-Bohm (AB) potential in 2+1 dimensions that are specified by boundary conditions at the origin. It is of interest that for some range of extension parameter the AB potential can bind relativistic charged massive fermions. The bound-state energy is determined by the AB magnetic f…
We investigate two models for performing topological quantum gates with the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and two-qubit Abelian phases can be enacted with the AB effect using charge qubits, whereas the AC effect can be used to perform all single-qubit gates (Abelian and non-Abelian) for spin qubits. Possible experimental setups suitable for a solid state implementation are briefly discussed.
The dynamics of a spin--1/2 neutral particle possessing electric and magnetic dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms of a semiclassical constrained Hamiltonian system. The relation between the quantum phase acquired by a particle interacting with an electromagnetic field and the (semi)classical force acting on the system is examined and generalized to establish a formulation of the quantum phases in noncommutative coordinates. The general formalism is applied to physical s…
We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three phenomena. We also elucidate Lorentz transformations that allow these effects to be understood in an intuitive fashion in the rest frame of the moving quantum particle. Finally, we propose two experimental schemes for measuring the He-McKellar-Wilkens phase.
The planar non-relativistic quantum dynamics of a neutral massive fermion with an anomalous magnetic moment (AMM) in the presence of the electric field of infinitely long and thin thread with a charge density distributed uniformly along it (an Aharonov--Casher field) is examined. The relevant Hamiltonian is singular and requires additional specification of a one-parameter self-adjoint extension, which can be given in terms of physically acceptable (self-adjoint) boundary conditions. We find all possible self-adjoint Hamiltonians with an Aharonov--Casher field (ACF) by constructing the correspo…
An atomic analogue of Landau quantization based on the Aharonov-Casher (AC) interaction is developed. The effect provides a first step towards an atomic quantum Hall system using electric fields, which may be realized in a Bose-Einstein condensate.
Through tunneling, or barrier penetration, small wavefunction tails can enter a finitely shielded cylinder with a magnetic field inside. When the shielding increases to infinity the Lorentz force goes to zero together with these tails. However, it is shown, by considering the radial derivative of the wavefunction on the cylinder surface, that a flux dependent force remains. This force explains in a natural way the Aharonov-Bohm effect in the idealized case of infinite shielding.
Although there is no force on the electron in Aharonov-Bohm solenoid effect, the electron exerts a force on the solenoid related to the inequality of action and reaction forces of two subsystems in three-system configuration. The AB phase which is related to the force exerted by the electron on the solenoid . The momentum changes of the mechanical oscillator are equal in magnitude and opposite in sign to the changes in the momentum of the em fields. It is proposed to investigate momentum changes of "micro" bodies producing magnetic fields in AB systems which will clarify the nature of these ef…
An experiment to observe the Aharonov-Bohm effect is discussed. A solenoid which consists of a large number of point magnetic dipoles is considered as the source of a vector potential, which acts on a charged particle, and such potential has an electromagnetic field of zero strength in the region of a nonzero vector potential. A detailed microscopic analysis of the change in the quantum state phase of the entire system, namely, a particle and a set of dipoles, reveals the origin of the apparent nonlocality of the action of the vector potential, and shows the locality of the phase change mechan…
This work analyzes the effects of shielding on the Aharonov-Bohm scattering of electrons endowed with spin. The interaction of polarized electrons with bare and shielded magnetic strings is studied with the aid of the Dirac equation. It is found that the difference between the amplitudes for the scattering by bare and shielded strings of incident wave packets of width $δ$ and impact parameter $d$ is proportional to $\exp(-d^2/2δ^2)$.
Recent neutron interferometry experiments have been interpreted as demonstrating a new topological phenomenon similar in principle to the usual Aharonov-Bohm (AB) effect, but with the neutron's magnetic moment replacing the electron's charge. We show that the new phenomenon, called Scalar AB (SAB) effect, follows from an ordinary local interaction, contrary to the usual AB effect, and we argue that the SAB effect is not a topological effect by any useful definition. We find that SAB actually measures an apparently novel spin autocorrelation whose operator equations of motion contain the local …
