Topological phase evolving from the orbital angular momentum of ‘coiled’ quantum vortices
Abstract
The propagation of a scalar field that satisfies the Schrodinger equation in a coiled helical potential well is studied. It is demonstrated that on propagation the scalar wave acquires an additional phase whose value is determined only by geometric parameters of the helix. It is established that this geometric phase is proportional to the orbital angular momentum of the particle and the solid angle subtended by the trajectory of the state on the orbital Poincare sphere. It is shown that this phase increment takes place for any state with well-defined orbital angular momentum and can be obtained through a simple rotational transformation of the Schrodinger equation into some effective rotating frame. A possible way of detection of such a phase in an interferometric experiment is also discussed. A connection is made with the propagation of optical vortices in coiled few-mode optical fibres.
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It is this rotation that causes the spin Hall effect.
“It is this rotation that causes the spin Hall effect [135].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [135]
The Berry phase and spin Hall effect allow immediate generalizations to the case of higher-order beams with vortices bearing intrinsic orbital angular momentum.
“Likewise the angular Doppler shift [72 -80] and the Imbert -Fedorov shift [124 -129], the Berry phase and spin Hall effect allow immediate generalizations to the case of higher-order beams with vortices bearing intrinsic orbital angular momentum [119,130 -135] (see also [84,90]).”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [135]
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- Authors
- Alexeyev, C. N., & Yavorsky, M. A.
- Affiliations
- Taurida National V.I. Vernadsky University (UA)
- Venue
- Journal of Optics A: Pure and Applied Optics
- Publisher
- IOP Publishing
- Published
- 2006-07-13
- Volume
- 8
- Issue
- 9
- Pages
- 752-758
- ISSN
- 1464-4258 (ISSN-L)
- 1741-3567
- OpenAlex
- W1968389518
- Cited by
- 28
- References
- 52
- Citations by year
- 2026: 4 · 2024: 4 · 2023: 2 · 2022: 3 · 2021: 3 · 2019: 1 · 2016: 1 · 2015: 1 · 2012: 2
- FWCI
- 1.51
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Optics A Pure and Applied Optics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- topological phases, Berry phase, orbital angular momentum, quantized vortices, Schrödinger equation, solid angle, rotating frame, optical vortices
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