Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Abraham-Minkowski Dilemma of Matter Wave

Wenzhuo Zhang, Peng Zhang, Ruquan Wang, Wu‐Ming Liu

Published Dec 13, 2010• 0 citations
OpenAlex

Abstract

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.

Related papers

Momentum Exchange between Light and a Single Atom: Abraham or Minkowski?

Edward A. Hinds, Stephen Mark Barnett

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.

arXiv:0811.2771•Physical Review Letters•Feb 3, 2009•81 citations

The Optical HMW Geometric Phase and the Abraham Minkowski Controversy

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

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.

arXiv:2410.17010•Oct 22, 2024•1 citation

Interferometry with correlated matter-waves

Oksana Streltsova, Alexej I. Streltsov

Matter-wave interferometry of ultra-cold atoms with attractive interactions is studied at the full many-body level. First, we study how a coherent light-pulse applied to an initially-condensed solitonic system splits it into two matter-waves. The split system looses its coherence and develops correlations with time, and inevitably becomes fragmented due to inter-particle attractions. Next, we show that by re-colliding the sub-clouds constituting the split density together, along with a simultaneous application of the same laser-pulse, one creates three matter-waves propagating with different momenta. We demonstrate that the number of atoms in the sub-cloud with zero-momentum is directly proportional to the degree of fragmentation in the system. This interferometric-based protocol to discriminate, probe, and measure the fragmentation is general and can be applied to ultra-cold systems with attractive, repulsive, short- and long-range interactions.

arXiv:1412.4049•Dec 12, 2014•4 citations

Who Has Seen a Free Photon?

Izumi Ojima, Hayato Saigo

While the notion of the position of photons is indispensable in quantum optical situations, it has been known in mathematical physics that any position operator cannot be defined for a massless free particle with a non-zero finite spin. This dilemma is resolved by introducing the "effective mass" of a photon due to the interaction with matter. The validity of this interpretation is confirmed in reference to the picture of "polariton", a basic notion in optical and solid physics. In this connection, we discuss the long-standing controversy between Minkowski's and Abraham's definitions of the momenta of a photon in media from the general viewpoint adopted in the Appendix.

arXiv:1101.5782•Open Systems & Information Dynamics•Mar 1, 2012•4 citations

Canonical and kinetic forms of the electromagnetic momentum in anad hocquantization scheme for a dispersive dielectric

J. C. Garrison, R. Y. Chiao

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.

arXiv:quant-ph/0406222•Physical Review A•Nov 30, 2004•67 citations

Recoil and Photon Momentum in a Dielectric

Peter W. Milonni, Robert W. Boyd

We consider the recoil momentum of a spontaneously emitting atom in a dispersive dielectric, first from a microscopic approach, in which the dielectric is treated as a collection of atoms and the field is quantized in vacuum , and, then, from the macroscopic approach of quantizing the field in the dielectric. The atom's recoil momentum differs from both the Abraham and Minkowski forms of the field momentum, and this difference is explained in terms of a dispersive contribution to the momentum acquired by the medium.

Laser Physics•Jan 1, 2005•25 citations
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 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.
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.
Matter-wave interferometry of ultra-cold atoms with attractive interactions is studied at the full many-body level. First, we study how a coherent light-pulse applied to an initially-condensed solitonic system splits it into two matter-waves. The split system looses its coherence and develops correlations with time, and inevitably becomes fragmented due to inter-particle attractions. Next, we show that by re-colliding the sub-clouds constituting the split density together, along with a simultaneous application of the same laser-pulse, one creates three matter-waves propagating with different momenta. We demonstrate that the number of atoms in the sub-cloud with zero-momentum is directly proportional to the degree of fragmentation in the system. This interferometric-based protocol to discriminate, probe, and measure the fragmentation is general and can be applied to ultra-cold systems with attractive, repulsive, short- and long-range interactions.
While the notion of the position of photons is indispensable in quantum optical situations, it has been known in mathematical physics that any position operator cannot be defined for a massless free particle with a non-zero finite spin. This dilemma is resolved by introducing the "effective mass" of a photon due to the interaction with matter. The validity of this interpretation is confirmed in reference to the picture of "polariton", a basic notion in optical and solid physics. In this connection, we discuss the long-standing controversy between Minkowski's and Abraham's definitions of the momenta of a photon in media from the general viewpoint adopted in the Appendix.
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.
We consider the recoil momentum of a spontaneously emitting atom in a dispersive dielectric, first from a microscopic approach, in which the dielectric is treated as a collection of atoms and the field is quantized in vacuum , and, then, from the macroscopic approach of quantizing the field in the dielectric. The atom's recoil momentum differs from both the Abraham and Minkowski forms of the field momentum, and this difference is explained in terms of a dispersive contribution to the momentum acquired by the medium.