Unified treatment of the total angular momentum of single photons via generalized quantum observables
- Creators
- Motta, M.
- Guarnieri, G.
- Lanz, L.
- Hiesmayr, B.
Abstract
In this paper, we provide a consistent framework to address the notorious difficult decomposition of the single-photon total angular momentum (TAM) into a spin (SAM) and an orbital (OAM) component. We discuss the canonical decomposition into SAM and OAM components, which are the generators of internal and spatial rotations in the space of physical states. We find that those operators are mutually compatible but unsharp quantum observables, therefore Positive Operator-Valued Measures describe their joint measurements. We present another decomposition of the TAM, which we denote as a non-canonical one. The operators resulting from this decomposition are mutually incompatible but sharp quantum observables, thus Projector-Valued Measurements. This fact reflects their consistency with the transversality condition of single-photon wavefunctions, thus explains the underlying physics from a quantum information theoretic view. Furthermore, we discuss the implementations on joint measurements for both decompositions and provide an explicit calculation of all these quantities for circularly polarized Gaussian single-photon states. The difference between the canonical and non-canonical momenta leads to observable differences in higher-order statistical moments.
Additional Information
©2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 12 July 2018. Accepted 12 December 2018. Accepted Manuscript online 12 December 2018. Published 28 February 2019. GG's work at Trinity College Dublin is supported the ERC Starting Grant ODYSSEY (grant agreement n. 758403). BCH acknowledges gratefully the Austrian Science Fund (FWF-P26783). M M gratefully acknowledges support from the Simons Foundation.Attached Files
Published - Motta_2019_New_J._Phys._21_023017.pdf
Submitted - 1806.05479.pdf
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Additional details
- Eprint ID
- 93329
- Resolver ID
- CaltechAUTHORS:20190228-085142357
- 758403
- European Research Council (ERC)
- FWF-P26783
- FWF Der Wissenschaftsfonds
- Simons Foundation
- Created
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2019-02-28Created from EPrint's datestamp field
- Updated
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2022-07-12Created from EPrint's last_modified field