Comment on "Proposed Aharonov-Casher effect: Another example of an Aharonov-Bohm effect arising from a classical lag"

Laser induced enhanced coupling between photons and squeezed magnons in antiferromagnets

In this paper we consider a honeycomb antiferromagnet subject to an external laser field. Obtaining a time-independent effective Hamiltonian, we find that the external laser renormalizes the exchange interaction between the in-plane components of the spin-operators, and induces a synthetic Dzyaloshinskii-Moria interaction (DMI) between second neighbors. The former allows the control of the magnon dispersion's bandwidth and the latter breaks time-reversal symmetry inducing non-reciprocity in momentum space. The eigen-excitations of the system correspond to squeezed magnons whose squeezing parameters depend on the properties of the laser. When studying how these spin excitations couple with cavity photons, we obtain a coupling strength which can be enhanced by an order of magnitude via careful tuning of the laser's intensity, when compared to the case where the laser is absent. The transmission plots through the cavity are presented, allowing the mapping of the magnons' dispersion relation.

Asymmetry and non-dispersivity in the Aharonov-Bohm effect

Decades ago, Aharonov and Bohm showed that electrons are affected by electromagnetic potentials in the absence of forces due to fields. Zeilinger’s theorem describes this absence of classical force in quantum terms as the “dispersionless” nature of the Aharonov-Bohm effect. Shelankov predicted the presence of a quantum “force” for the same Aharonov-Bohm physical system as elucidated by Berry. Here, we report an experiment designed to test Shelankov’s prediction and we provide a theoretical analysis that is intended to elucidate the relation between Shelankov’s prediction and Zeilinger’s theorem. The experiment consists of the Aharonov-Bohm physical system; free electrons pass a magnetized nanorod and far-field electron diffraction is observed. The diffraction pattern is asymmetric confirming one of Shelankov’s predictions and giving indirect experimental evidence for the presence of a quantum “force”. Our theoretical analysis shows that Zeilinger’s theorem and Shelankov’s result are both special cases of one theorem.

The dispersionless nature of Aharonov-Bohm effect is still debated. Here, the authors show an asymmetry in the diffraction pattern of an electron beam induced and controlled by an inaccessible magnetic flux, which means electrons behave “as if” an Aharonov-Bohm “force” was present.

The magnetic monopole and the separation between fast and slow magnetic degrees of freedom

The Landau-Lifshitz-Gilbert (LLG) equation that describes the dynamics of a macroscopic magnetic moment finds its limit of validity at very short times. The reason for this limit is well understood in terms of separation of the characteristic time scales between slow degrees of freedom (the magnetization) and fast degrees of freedom. The fast degrees of freedom are introduced as the variation of the angular momentum responsible for the inertia. In order to study the effect of the fast degrees of freedom on the precession, we calculate the geometric phase of the magnetization (i.e. the Hannay angle) and the corresponding magnetic monopole. In the case of the pure precession (the slow manifold), a simple expression of the magnetic monopole is given as a function of the slowness parameter, i.e. as a function of the ratio of the slow over the fast characteristic times.

Classical interaction of a magnet and a point charge: the Shockley-James paradox

It is pointed out that the interaction of a magnet and a point charge has not been properly understood because the mutual interactions of the magnet's current carriers have been neglected. The magnet-point-charge interaction is important for understanding some theoretical paradoxes, such as the Shockley-James paradox, and for interpreting some experimentally observed effects, such as the Aharonov-Bohm and Aharonov-Casher phase shifts. Coleman and Van Vleck provide a discussion of the Shockley-James paradox where they note that internal relativistic mechanical momentum (hidden momentum) can be carried by the current carriers of the magnet. Although internal mechanical momentum is indeed dominant for noninteracting particles moving in a closed orbit under the influence of an external electric field, the presence of interactions among the magnet's current carriers leads to an internal electromagnetic momentum, which does not seem to be recognized in the physics literature. In the interacting multiparticle situation, the external charge induces an electrostatic polarization of the magnet, which leads to an internal electromagnetic momentum in the magnet where both the electric and magnetic fields for the momentum are contributed by the magnet particles. This internal electromagnetic momentum for the interacting multiparticle situation is equal in magnitude and opposite in direction compared to the familiar external electromagnetic momentum where the electric field is contributed by the external charged particle and the magnetic field is that due to the magnet. In the present article, the momentum balance of the Shockley-James situation for a system of a magnet and a point charge is calculated in detail for a magnet model consisting of two interacting point charges, which are constrained to move in a circular orbit on a frictionless ring with a compensating negative charge at the center.

Aharonov-Casher and scalar Aharonov-Bohm topological effects

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 analyze 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.

Classical and quantum interaction of the dipole

A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic dipoles are obtained. Several new experiments are proposed, which include observation of topological phase shifts.

Complementarity between local and nonlocal topological effects

In certain topological effects the accumulation of a quantum phase shift is accompanied by a local observable effect. We show that such effects manifest a complementarity between nonlocal and local attributes of the topology, which is reminiscent but different from the usual wave-particle complementarity. This complementarity is not a consequence of noncommutativity, rather it is due to the noncanonical nature of the observables. We suggest that a local/nonlocal complementarity is a general feature of topological effects that are "dual" to the Aharonov-Bohm effect.