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arXiv:2410.17010

The Optical HMW Geometric Phase and the Abraham Minkowski Controversy

J. Hainge, Miladinovic, N., Duncan H J O’Dell

Published Oct 22, 2024• 1 citation
arXivHTMLPDF

Abstract

The question of the correct formulation for the momentum of light in a dielectric medium is typically referred to as the ``Abraham-Minkowski controversy". Experiments conducted to elucidate the issue have primarily focused on measuring forces and momentum transfers. In this work, we propose an interferometric approach using matter waves to measure the light-induced version of the He-McKellar-Wilkens (optical HMW) phase for a neutral atomic dipole in dynamical electromagnetic fields. Beginning from the action principle, we show that this geometric phase is directly related via the Euler-Lagrange equations of motion to the Abraham force lying at the heart of the controversy.

DOI
10.48550/arxiv.2410.17010

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The question of the correct formulation for the momentum of light in a dielectric medium is typically referred to as the ``Abraham-Minkowski controversy". Experiments conducted to elucidate the issue have primarily focused on measuring forces and momentum transfers. In this work, we propose an interferometric approach using matter waves to measure the light-induced version of the He-McKellar-Wilkens (optical HMW) phase for a neutral atomic dipole in dynamical electromagnetic fields. Beginning from the action principle, we show that this geometric phase is directly related via the Euler-Lagrange equations of motion to the Abraham force lying at the heart of the controversy.
We consider forces on an atom due to a plane-wave light pulse. The standard view of the optical dipole force indicates that red-detuned light should attract the atom towards high intensity. While the atom is inside the pulse, this would increase the average momentum per photon from p_{0} to p_{0}n, where n is the average refractive index due to the presence of the atom. We show, however, that this is the wrong conclusion and that the dispersive forces repel the atom from the light in this particular case, giving the photons a momentum p_{0}/n. This leads us to identify Abraham's optical momentum with the kinetic momentum transfer. The form due to Minkowski is similarly associated with the canonical momentum. We consider the possibility of demonstrating this in the laboratory, and we note an unexpected connection with the Aharonov-Casher effect.
We present the Abraham-Minkowski dilemma of matter wave, which origins from the difference between the kinetic and canonical momentum of the matter wave and is complementary to the centaury-old AbrahamMinkowski dilemma of light. We solve the dilemma in light-atom interacting systems and find that for systems with perfect light and atomic coherence, the systems prefer to show Minkowski momentum and canonical momentum for the atoms and light, respectively; while for the incoherent systems, the momenta of light and atoms would choose the Abraham and kinetic forms. The provement of our solution can be realized with current techniques, using three-dimensional optical lattices and electromagnetically-induced absorption (EIA) to distinguish the kinetic and canonical recoil momentum of ultra-cold atoms.
We study the quantum dynamics of a neutral particle that posseses a permanent magnetic and electric dipole moments in the presence of an electromagnetic field. The analysis of this dynamics demonstrates the appearance of a quantum phase that combines the Aharonov-Casher effect and the He-Mckellar-Wilkens effect. We demonstrate that this phase is a special case of the geometric quantum phase. A series of field configurations where this phase would be found is presented. A generalized Casella-type effect is found in one of these configurations. A physical scenario for the quantum phase in an interferometric experiment is proposed.
An ad hoc quantization scheme for the electromagnetic field in a weakly dispersive, transparent dielectric leads to the definition of canonical and kinetic forms for the momentum of the electromagnetic field in a dispersive medium. The canonical momentum is uniquely defined as the operator that generates spatial translations in a uniform medium, but the quantization scheme suggests two possible choices for the kinetic momentum operator, corresponding to the Abraham or the Minkowski momentum in classical electrodynamics. Another implication of this procedure is that a wave packet containing a single dressed photon travels at the group velocity through the medium. The physical significance of the canonical momentum has already been established by considerations of energy and momentum conservation in the atomic recoil due to spontaneous emission, the Cerenkov effect, the Doppler effect, and phase matching in nonlinear optical processes. In addition, the data of the Jones and Leslie radiation pressure experiment is consistent with the assignment of one $\ensuremath{\hbar}\mathbf{k}$ unit of canonical momentum to each dressed photon. By contrast, experiments in which the dielectric is rigidly accelerated by unbalanced electromagnetic forces require the use of the Abraham momentum.
A quantum-mechanical description of a photon in refractive mediums is proposed. Here we assume that the medium is isotropic and linear, and the material constants (the dielectric constant and permeability) are both the functions of the position coordinates only and dispersionless. It is found that the momentum operator is generally ill defined as well as the position operator. The momentum operator, however, becomes approximately well defined when the extents of the appreciable changes of the material constants are very large compared to the photon wavelengths. Then, it is shown that the various expressions of the physical quantities in the classical electromagnetic theory, such as the energy and momentum, can be obtained from the expectation values of the corresponding operators. The Abraham-Minkowski controversy in the classical electromagnetic theory is glanced from the viewpoint of our quantum-mechanical approach.
In this Letter, we report a measurement of the He-McKellar-Wilkens (HMW) topological phase by atom interferometry. The experiment is done with our lithium atom interferometer, and in order to suppress the stray effects present in our first experiment, we use optical pumping of the (7)Li atoms in their F=2, m(F)=+2 (or -2) ground state sublevel. In these conditions, the measured phase shift is the sum of the HMW phase and of the Aharonov-Casher phase, which are separated due to their different m(F) dependence. The HMW phase has been measured for different lithium beam velocities and the results are in very good agreement with a phase independent of the atom velocity, as expected for a topological phase.