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

Journal of Mathematical Physics

Non-Abelian Berry’s phase in a slowly rotating electric field

Ho-Meoyng Choi, Chueng‐Ryong Ji, Hyun Kyu Lee

Published Mar 1, 1997• 3 citations
Publisher

Abstract

We observe that the non-Abelian Berry’s potential can appear in the atomic system under the slowly rotating electric field (Stark effect). We calculate Berry’s phase using the perturbation theory in the weak external electric field. To elaborate the nature of non-Abelian character, we demonstrate the change of states during the adiabatic transportation for a particular set of paths.

DOI
10.1063/1.531811

Related papers

Dynamic origin of non-Abelian Berry’s-phase effects in a simple atomic system

Martin Ligare

The full effect of adiabatically varying Hamiltonians on systems prepared in eigenstates of the stationary Hamiltonian often includes geometric Berry's phases. For degenerate systems these effects may result in transitions between distinct degenerate eigenstates that can be described in terms of a non-Abelian gauge potential. I demonstrate the explicit dynamic origin of such transitions between degenerate angular-momentum sublevels in an atom that is subject to collinear electric and magnetic fields that rotate adiabatically. The origin of the effects becomes clear when eigenstates of the total Hamiltonian, which includes the rotating fields, are calculated. The total Hamiltonian removes the degeneracy, and the eigenstates are in some cases linear combinations of the angular-momentum sublevels. Thus a system prepared in a specific sublevel may not remain in that sublevel, and the transition probability is exactly that given by an analysis of the geometric phase.

Physical Review A•Nov 1, 1990•2 citations

Molecular Kramers degeneracy and non-Abelian adiabatic phase factors

C. Alden Mead

For a molecular system with an odd number of electrons, the electronic Hamiltonian possesses a twofold Kramers degeneracy for all nuclear configurations. It is shown that this leads to a non-Abelian gauge-field term in the effective nuclear Hamiltonian, with permissible gauge transformations belonging to SU(2). This should lead to observable effects analogous to the Berry phase for the nondegenerate case. In particular, an atom in a slowly rotating electric field exhibits changes in its component of angular momentum along the field because of the non-Abelian phase factor.

Physical Review Letters•Jul 13, 1987•121 citations

Berry phases and optical spectra of atoms placed in an external adiabatically varying electric field

V I Matveev, M.M. Musakhanov

The behaviour of an atom placed in an external adiabatically cone-rotating constant electric field is considered. Taking into account the Berry phase in this problem is shown to be necessary. The radiation spectrum for this atom in such a field is obtained and photon polarizations are considered. The Berry phases are shown to be easily observable during optical transitions in atoms placed in an external varying electric field.

Journal of Physics B Atomic Molecular and Optical Physics•May 14, 1991•7 citations

Berry's Phase Effects in Spin Precession of Relativistic Neutral Particle in Slowly Changing Magnetic Field

Chang-Pu Sun, Lin-Zhi Zhang

By making use of the adiabatic approximate method, we derive the spin rotation formula of a relativistic neutral particle propagating in a slowly changing magnetic field, which involves the effects of the Berry's phases. In the non–relativistic limit, the Berry's phases result in an additional rotation in OVV spin rotation.

Communications in Theoretical Physics•Dec 1, 1989•1 citation

Inclusion of Berry's phase into an impact treatment of self-broadening of the Lyman- α line in an external slowly rotating electric field

R. Ciuryło, Michał Słowiński, Józef Szudy +1 more

The intensity distribution in the core region of the Lyman-$\ensuremath{\alpha}$ line of hydrogen perturbed by neutral hydrogen atoms in the presence of an external cone-rotating electric field has been evaluated using an impact approximation. It was found that the line shape in this region can be described as the sum of four Lorentzian profiles representing contributions coming from transitions between various Stark and Berry sublevels of the resonance and ground states of the hydrogen atom. The effects due to Berry's phase are shown to produce a Lorentzian-shaped feature on each side of the Lyman-$\ensuremath{\alpha}$ line, with maxima located at frequencies linearly dependent on the angular frequency with which the electric field rotates about the laboratory fixed $z$ axis, as well as on the cosine of the polar angle that the field makes with respect to this axis. The remaining two Lorentzian profiles are due to the Stark effect, and their maxima are located on both sides of the Lyman-$\ensuremath{\alpha}$ line at frequencies corresponding to the Stark shift.

Physical Review A•Aug 31, 2018•0 citations

Berry's phase in the two-level model

A.C. Aguiar Pinto, M. Moutinho, M. T. Thomaz

We study the adiabatic evolution of a two-level model in the presence of an external classical electric field. The coupling between the quantum model and the classical field is taken in the electric dipole approximation. In this regime, we show the absence of geometric phases in the interacting two-level model in the presence of any periodic real time-dependent classical electric field. We obtain a conservative scalar potential in the calculation of Berry's phases of the instantaneous eigenstates of the model. For complex electric fields, we recover the existence of geometric phases. In particular, the geometric phases of the instantaneous eigenstates of the model in the presence of a positive or of a negative frequency component of the monochromatic electric field differ by an overall sign. As a check on our results, we map this interacting two-level model onto a spin-1/2 model under the action of a classical magnetic field. We confirm that the first one acquires Berry's phase only in the rotating wave approximation [RWA].

arXiv:0904.1774•Brazilian Journal of Physics•Jun 1, 2009•5 citations
We observe that the non-Abelian Berry’s potential can appear in the atomic system under the slowly rotating electric field (Stark effect). We calculate Berry’s phase using the perturbation theory in the weak external electric field. To elaborate the nature of non-Abelian character, we demonstrate the change of states during the adiabatic transportation for a particular set of paths.
The full effect of adiabatically varying Hamiltonians on systems prepared in eigenstates of the stationary Hamiltonian often includes geometric Berry's phases. For degenerate systems these effects may result in transitions between distinct degenerate eigenstates that can be described in terms of a non-Abelian gauge potential. I demonstrate the explicit dynamic origin of such transitions between degenerate angular-momentum sublevels in an atom that is subject to collinear electric and magnetic fields that rotate adiabatically. The origin of the effects becomes clear when eigenstates of the total Hamiltonian, which includes the rotating fields, are calculated. The total Hamiltonian removes the degeneracy, and the eigenstates are in some cases linear combinations of the angular-momentum sublevels. Thus a system prepared in a specific sublevel may not remain in that sublevel, and the transition probability is exactly that given by an analysis of the geometric phase.
For a molecular system with an odd number of electrons, the electronic Hamiltonian possesses a twofold Kramers degeneracy for all nuclear configurations. It is shown that this leads to a non-Abelian gauge-field term in the effective nuclear Hamiltonian, with permissible gauge transformations belonging to SU(2). This should lead to observable effects analogous to the Berry phase for the nondegenerate case. In particular, an atom in a slowly rotating electric field exhibits changes in its component of angular momentum along the field because of the non-Abelian phase factor.
The intensity distribution in the core region of the Lyman-$\ensuremath{\alpha}$ line of hydrogen perturbed by neutral hydrogen atoms in the presence of an external cone-rotating electric field has been evaluated using an impact approximation. It was found that the line shape in this region can be described as the sum of four Lorentzian profiles representing contributions coming from transitions between various Stark and Berry sublevels of the resonance and ground states of the hydrogen atom. The effects due to Berry's phase are shown to produce a Lorentzian-shaped feature on each side of the Lyman-$\ensuremath{\alpha}$ line, with maxima located at frequencies linearly dependent on the angular frequency with which the electric field rotates about the laboratory fixed zzz axis, as well as on the cosine of the polar angle that the field makes with respect to this axis. The remaining two Lorentzian profiles are due to the Stark effect, and their maxima are located on both sides of the Lyman-$\ensuremath{\alpha}$ line at frequencies corresponding to the Stark shift.
We study the adiabatic evolution of a two-level model in the presence of an external classical electric field. The coupling between the quantum model and the classical field is taken in the electric dipole approximation. In this regime, we show the absence of geometric phases in the interacting two-level model in the presence of any periodic real time-dependent classical electric field. We obtain a conservative scalar potential in the calculation of Berry's phases of the instantaneous eigenstates of the model. For complex electric fields, we recover the existence of geometric phases. In particular, the geometric phases of the instantaneous eigenstates of the model in the presence of a positive or of a negative frequency component of the monochromatic electric field differ by an overall sign. As a check on our results, we map this interacting two-level model onto a spin-1/2 model under the action of a classical magnetic field. We confirm that the first one acquires Berry's phase only in the rotating wave approximation [RWA].