Berry and Pancharatnam topological phases of atomic and optical systems
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Theoretical and experimental studies of Berry and Pancharatnam phases are reviewed. Basic elements of differential geometry necessary for understanding the topological nature of these phases are presented. The basic theory analysed by Berry in relation to magnetic monopoles is presented. The theory is generalized to nonadiabatic processes and to noncyclic Pancharatnam phases. Different systems are discussed including polarization optics, n -level atomic systems, neutron interferometry and molecular topological phases.
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The Berry phase provides a natural geometrical formalism that describes variations of the light polarization along the propagation trajectory.
“The Berry phase provides a natural geometrical formalism that describes variations of the light polarization along the propagation trajectory (see reviews [4 -7] and original papers [8 -20]).”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [7]
In the generic case of an elliptical polarization, Eq. (3.28) describes the same turn of the polarization ellipse on angle Φ_B with its eccentricity conserved.
“In the generic case of an elliptical polarization, Eq. (3.28) describes the same turn of the polarization ellipse on angle B Φ with its eccentricity conserved, Fig. 1 [4 -20,59].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [7]
The Berry connection determines the natural parallel transport of the polarization vector e over the unit t-sphere.
“In this manner, polarization vector e is tangent to this sphere, and the Berry connection determines the natural parallel transport of e over the 2 S sphere, Fig. 2 [1 -7,9,13 -15,44,84 -90].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [7]
For a cyclic evolution in momentum space, the Berry phase equals the solid angle cut by the contour Γ.
“For a cyclic evolution in momentum space (which corresponds to a ray trajectory with the coincident input and output directions of propagation), the Berry phase (3.26) equals [4 -20]”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [7]
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Ben-Aryeh, Y. (2023) · doi:10.1364/opticaopen.23641206.v1
Self-citationGeometric phases for a thermal two-dimensional mixed spin 1/2 systemPreprint
Ben-Aryeh, Y. (2023) · doi:10.1364/opticaopen.23641206
Self-citationBen-Aryeh, Y. (2025) · International Journal of Thermodynamics · doi:10.5541/ijot.1395683
Self-citationGuoxia, 韩. H., Yanbin, 马. M., Biao, 檀. T., Yihan, 田. T., Feiyang, 张. Z., & Xianghua, 于. Y. (2026) · Acta Optica Sinica · doi:10.3788/aos251329
Spin-orbit interactions of light
Bliokh, K. Y., Rodriguez-Fortuno, F. J., Nori, F., & Zayats, A. V. (2015) · arXiv
- Authors
- Ben-Aryeh, Y.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Corresponding author
- Ben-Aryeh, Y
- ORCID
- Ben-Aryeh, Y
- Venue
- Journal of Optics B: Quantum and Semiclassical Optics
- Publisher
- IOP Publishing
- Published
- 2004-03-26
- Volume
- 6
- Issue
- 4
- Pages
- R1-R18
- ISSN
- 1464-4266 (ISSN-L)
- 1741-3575
- OpenAlex
- W2044873176
- Cited by
- 40
- References
- 214
- Citations by year
- 2026: 2 · 2025: 1 · 2023: 7 · 2021: 1 · 2020: 2 · 2019: 2 · 2018: 2 · 2017: 1 · 2015: 1 · 2014: 1 · 2013: 4 · 2012: 3
- FWCI
- 1.43
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Optics B Quantum and Semiclassical Optics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Keywords
- Berry phase, Pancharatnam phase, topological phases, differential geometry, magnetic monopoles, nonadiabatic processes, polarization optics, neutron interferometry
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