Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond

Eliahu Cohen, Hugo Larocque, Frédéric Bouchard, Farshad Nejadsattari, Yuval Gefen, Ebrahim Karimi

Research output: Contribution to journalReview articlepeer-review

208 Scopus citations

Abstract

Whenever a quantum system undergoes a cyclic evolution governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov–Bohm phase and the Pancharatnam and Berry phase, but both earlier and later manifestations exist. Although traditionally attributed to the foundations of quantum mechanics, the geometric phase has been generalized and become increasingly influential in many areas from condensed-matter physics and optics to high-energy and particle physics and from fluid mechanics to gravity and cosmology. Interestingly, the geometric phase also offers unique opportunities for quantum information and computation. In this Review, we first introduce the Aharonov–Bohm effect as an important realization of the geometric phase. Then, we discuss in detail the broader meaning, consequences and realizations of the geometric phase, emphasizing the most important mathematical methods and experimental techniques used in the study of the geometric phase, in particular those related to recent works in optics and condensed-matter physics.

Original languageEnglish
Pages (from-to)437-449
Number of pages13
JournalNature Reviews Physics
Volume1
Issue number7
DOIs
StatePublished - 1 Jul 2019

Bibliographical note

Publisher Copyright:
© 2019, The Publisher.

Funding

This work was supported by Canada Research Chair (CRC), Canada Foundation for Innovation (CFI), Canada First Excellence Research Fund (CFREF) Program, DFG grants no. MI 658/10-1, no. RO 2247/8-1 and CRC 183, Leverhulme Trust and the Italia-Israel project QUANTRA.

FundersFunder number
Canada Research Chair
Canada Foundation for Innovation
Deutsche Forschungsgemeinschaft
Canada First Research Excellence Fund

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