Quantum mechanics with a momentum-space artificial magnetic field

The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study systems directly relevant to ultracold gases and photonics. G...

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Bibliographic Details
Published in:Physical review letters 2014-11, Vol.113 (19), p.190403-190403, Article 190403
Main Authors: Price, Hannah M, Ozawa, Tomoki, Carusotto, Iacopo
Format: Article
Language:English
Subjects:
Dynamical systems
Dynamics
Energy bands
Exchanging
Magnetic fields
Magnetism
Mathematical analysis
Quantum mechanics
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Summary:The Berry curvature is a geometrical property of an energy band which acts as a momentum space magnetic field in the effective Hamiltonian describing single-particle quantum dynamics. We show how this perspective may be exploited to study systems directly relevant to ultracold gases and photonics. Given the exchanged roles of momentum and position, we demonstrate that the global topology of momentum space is crucially important. We propose an experiment to study the Harper-Hofstadter Hamiltonian with a harmonic trap that will illustrate the advantages of this approach and that will also constitute the first realization of magnetism on a torus.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.113.190403