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

Physical Review A

Quantum phase of an electric dipole moving in a magnetic dipole field

Tae-Yeon Lee

Published Nov 6, 2000• 4 citations
Publisher

Abstract

It is shown that a neutral particle with an electric dipole moment acquires a quantum phase of Aharonov-Bohm type which is induced by a magnetic dipole field, in addition to the He-McKellar-Wilkens phase which requires a magnetic monopole field. Therefore this phase is measurable in principle. This phase is related to the Casella phase in the sense of the electromagnetic duality.

DOI
10.1103/physreva.62.064101

Related papers

Quantum dynamics of magnetic and electric dipoles and the geometric phase

Claudio Furtado, Carlos Alberto de Lima Ribeiro

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.

arXiv:quant-ph/0306090•Physical Review A•Jun 9, 2004•46 citations

Quantum phases for electric charges and electric (magnetic) dipoles: physical meaning and implication

Alexander L. Kholmetskii, O. Missevitch, Tolga Yarman

We analyse the physical meaning of quantum phase effects for point-like charges and electric (magnetic) dipoles in an electromagnetic (EM) field. At present, there are known eight effects of such a kind: four of them (the magnetic and electric Aharonov – Bohm phases for electrons, the Aharonov – Casher phase for a moving magnetic dipole and the He – McKellar – Wilkens phase for a moving electric dipole) had been disclosed in 20th century, while four new quantum phases had recently been found by our team (A. L. Kholmetskii, O. V. Missevitch, T. Yarman). In our analysis of physical meaning of these phases, we adopt that a quantum phase for a dipole represents a superposition of quantum phases for each charge, composing the dipole. In this way, we demonstrate the failure of the Schrödinger equation for a charged particle in an EM field to describe new quantum phase effects, when the standard definition of the momentum operator is used. We further show that a consistent description of quantum phase effects for moving particles is achieved under appropriate re-definition of this operator, where the canonical momentum of particle in EM field is replaced by the interactional EM field momentum. Some implications of this result are discussed.

Journal of the Belarusian State University Physics•Feb 9, 2021•4 citations

Quantum phases of electric and magnetic dipoles as special cases of the Aharonov-Bohm phase

Tae-Yeon Lee

It is shown that the vector potential of the Aharonov-Bohm effect is effectively the same as vector potentials of the quantum phases of electric and magnetic dipoles such as the Aharonov-Casher effect, when the Aharonov-Bohm solenoid is a straight cylinder with symmetric cross sections. With a circular cross section, the Aharonov-Bohm vector potential is effectively the same as the Aharonov-Casher vector potential, while with a rectangular cross section, it is effectively the same as the vector potential of the Casella phase. Therefore, we may say that the quantum phases of the dipoles belong to a subclass of the Aharonov-Bohm phase, and they must share the topological origin of the Aharonov-Bohm phase, even though their topological freedom is limited to the particle trajectories. However, the dipole phases have the extra relativistic effect that a magnetic (electric) dipole moving in an electric (magnetic) field feels an additional magnetic (electric) field, in its rest frame. This effect limits further the topological freedom of the dipole phases.

Physical Review A•Aug 15, 2001•5 citations

Quantum Phase of Induced Dipoles Moving in a Magnetic Field

Haiqing Wei, Rushan Han, Xiuqing Wei

We derive the quantum phase accompanying a neutral particle (with no permanent electric dipole moment) moving in an area where a nonuniform electric field and a uniform magnetic field are simultaneously applied. Such a quantum phase can be ascribed to the sum of the Aharonov-Bohm phases of the charges constituting the neutral particle. An experimental configuration much more practical than a previous suggestion is proposed to test for the phase. The possible nonzero superfluid velocity in the ground state of the ${}^{4}\mathrm{He}$ condensate is theoretically demonstrated.

Physical Review Letters•Sep 11, 1995•154 citations

Dynamics of dipoles and quantum phases in noncommutative coordinates

Ö. F. Dayi

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 systems yielding the Aharonov-Bohm, Aharonov-Casher, He-McKellar-Wilkens and Anandan phases in noncommutative coordinates. Bounds for the noncommutativity parameter θ are derived comparing the deformed phases with the experimental data on the Aharonov-Bohm and Aharonov-Casher phases.

arXiv:0810.5468•Europhysics Letters (EPL)•Feb 1, 2009•9 citations

Topological phases reviewed: The Aharonov Bohm, Aharonov Casher, and He McKellar Wilkens phases

Bruce H. J. McKellar, X-G. He, A. G. Klein

There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of "an electric dipole encircles magnetic charges" was realised experimentally, and discuss possible future experimental realisations.

AIP conference proceedings•Jan 1, 2014•4 citations
It is shown that a neutral particle with an electric dipole moment acquires a quantum phase of Aharonov-Bohm type which is induced by a magnetic dipole field, in addition to the He-McKellar-Wilkens phase which requires a magnetic monopole field. Therefore this phase is measurable in principle. This phase is related to the Casella phase in the sense of the electromagnetic duality.
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.
We analyse the physical meaning of quantum phase effects for point-like charges and electric (magnetic) dipoles in an electromagnetic (EM) field. At present, there are known eight effects of such a kind: four of them (the magnetic and electric Aharonov – Bohm phases for electrons, the Aharonov – Casher phase for a moving magnetic dipole and the He – McKellar – Wilkens phase for a moving electric dipole) had been disclosed in 20th century, while four new quantum phases had recently been found by our team (A. L. Kholmetskii, O. V. Missevitch, T. Yarman). In our analysis of physical meaning of these phases, we adopt that a quantum phase for a dipole represents a superposition of quantum phases for each charge, composing the dipole. In this way, we demonstrate the failure of the Schrödinger equation for a charged particle in an EM field to describe new quantum phase effects, when the standard definition of the momentum operator is used. We further show that a consistent description of quantum phase effects for moving particles is achieved under appropriate re-definition of this operator, where the canonical momentum of particle in EM field is replaced by the interactional EM field momentum. Some implications of this result are discussed.
It is shown that the vector potential of the Aharonov-Bohm effect is effectively the same as vector potentials of the quantum phases of electric and magnetic dipoles such as the Aharonov-Casher effect, when the Aharonov-Bohm solenoid is a straight cylinder with symmetric cross sections. With a circular cross section, the Aharonov-Bohm vector potential is effectively the same as the Aharonov-Casher vector potential, while with a rectangular cross section, it is effectively the same as the vector potential of the Casella phase. Therefore, we may say that the quantum phases of the dipoles belong to a subclass of the Aharonov-Bohm phase, and they must share the topological origin of the Aharonov-Bohm phase, even though their topological freedom is limited to the particle trajectories. However, the dipole phases have the extra relativistic effect that a magnetic (electric) dipole moving in an electric (magnetic) field feels an additional magnetic (electric) field, in its rest frame. This effect limits further the topological freedom of the dipole phases.
We derive the quantum phase accompanying a neutral particle (with no permanent electric dipole moment) moving in an area where a nonuniform electric field and a uniform magnetic field are simultaneously applied. Such a quantum phase can be ascribed to the sum of the Aharonov-Bohm phases of the charges constituting the neutral particle. An experimental configuration much more practical than a previous suggestion is proposed to test for the phase. The possible nonzero superfluid velocity in the ground state of the 4He{}^{4}\mathrm{He}4He condensate is theoretically demonstrated.
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 systems yielding the Aharonov-Bohm, Aharonov-Casher, He-McKellar-Wilkens and Anandan phases in noncommutative coordinates. Bounds for the noncommutativity parameter θ are derived comparing the deformed phases with the experimental data on the Aharonov-Bohm and Aharonov-Casher phases.
There are three topological phases related to electromagnetic interactions in quantum mechanics: 1. The Aharonov Bohm phase acquired when a charged particle encircles a magnetic field but travels through a field free region. 2. The Aharonov Casher phase acquired when a magnetic dipole encircles electric charges but travels through a charge free region. 3. The He McKellar Wilkens phase acquired when an electric dipole encircles magnetic charges but travels through a charge free region. We review the conditions under which these phases are indeed topological and their experimental realisation. Because the He McKellar Wilkens phase has been recently observed we pay particular attention to how the basic concept of "an electric dipole encircles magnetic charges" was realised experimentally, and discuss possible future experimental realisations.