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 language | English |
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Pages (from-to) | 437-449 |
Number of pages | 13 |
Journal | Nature Reviews Physics |
Volume | 1 |
Issue number | 7 |
DOIs | |
State | Published - 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.
Funders | Funder number |
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Canada Research Chair | |
Canada Foundation for Innovation | |
Deutsche Forschungsgemeinschaft | |
Canada First Research Excellence Fund |