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Cited by 101Quantum Mechanics and ApplicationsTopological Materials and PhenomenaQuantum Mechanics and Non-Hermitian Physics

Topological phases in quantum mechanics and polarization optics

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Vinitskiĭ, S I, Derbov, V L, Dubovik, Vladimir M, Markovski, B L, Stepanovskiĭ, Yu P·1990·Soviet Physics Uspekhi
DOI 10.1070/pu1990v033n06abeh002598
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Abstract

A mathematical treatment is presented of the known Berry, Wilczek-Zee, Aharonov-Anandan, and Pancharatnam topological phases, and simple illustrative examples of their quantum mechanics are presented. The continuity and connection is traced among the various phases, while filling the gap involved with the forgotten works of S. M. Rytov and V. V. Vladimirskiĭ in polarization optics. A set of current experiments in polarization optics where the topological phases are measured is discussed in detail. Additional information on recently obtained results involving manifestations of geometrical phases in quantum mechanics and other fields of physics is contained in the Appendix and in the studies cited there.

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Crossref · 10.1070/pu1990v033n06abeh002598

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  • In the simplest case of total reflection from an interface, the reflected beam acquires a helicity-dependent shift (the Imbert-Fedorov shift).

    “In the simplest case of total reflection from the interface, the reflected beam acquires the helicity-dependent shift”

    From Spin–orbit interactions of light (2015) · cites this paper as [75]

    Section 3.1 discusses polarization changes at a reflecting interface, while Section 3.6 describes a helicity-dependent phase and a shift of interference fringes after multiple reflections. Neither passage addresses a spatial shift of a beam reflected from a single interface; searches for the Imbert–Fedorov effect and reflected-beam displacement found no such passage in our copy. (LLM, conf=0.73)

    Experimental — accuracy not yet measured

  • 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 [5]

  • 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 [5]

  • 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 [5]

  • 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 [5]

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Authors
Vinitskiĭ, S. I., Derbov, V. L., Dubovik, V. M., Markovski, B. L., & Stepanovskiĭ, Y. P.
Affiliations
Saratov State University (RU)
ORCID
Derbov, V L
Venue
Soviet Physics Uspekhi
Publisher
Uspekhi Fizicheskikh Nauk (UFN) Journal
Published
1990-06-30
Volume
33
Issue
6
Pages
403-428
ISSN
0038-5670 (ISSN-L)
DOI
10.1070/pu1990v033n06abeh002598
OpenAlex
W1987329343
Cited by
101
References
15
Citations by year
2026: 3 · 2025: 2 · 2024: 2 · 2023: 9 · 2022: 7 · 2021: 4 · 2020: 2 · 2019: 3 · 2018: 5 · 2017: 3 · 2016: 6 · 2015: 1 · 2014: 2 · 2013: 5 · 2012: 1
FWCI
1.10
Type
journal article
Language
en
Open access
Locations
Soviet Physics Uspekhi (publishedVersion)
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
topological phases, Berry phase, Aharonov-Anandan phase, Pancharatnam phase, polarization optics

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