Nonrelativistic limit in the2+1Dirac oscillator: A Ramsey-interferometry effect
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We study the nonrelativistic limit of a paradigmatic model in relativistic quantum mechanics, the two-dimensional Dirac oscillator. Remarkably, we find a different kind of Zitterbewegung which persists in this nonrelativistic regime, and leads to an observable deformation of the particle orbit. This effect can be interpreted in terms of a Ramsey-interferometric phenomenon, allowing an insightful connection between relativistic quantum mechanics and quantum optics. Furthermore, subsequent corrections to the nonrelativistic limit, which account for the usual spin-orbit Zitterbewegung, can be neatly understood in terms of a Mach-Zehnder interferometer.
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Earlier work has shown that relativistic dynamics can be studied in systems that are intrinsically non-relativistic, including atomic gases, trapped ions, and graphene layers.
“It has been noted in earlier works on atomic gases [1][2][3], trapped ions [4,5], and also in layers of graphene [6,7], that it is indeed possible to study relativistic dynamics for systems which are inherently non-relativistic.”
From Atomic Zitterbewegung (2008) · cites this paper as [4]
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Zitterbewegung of electrons in graphene in a magnetic field
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- Authors
- Bermudez, A., Martin-Delgado, M. A., & Luis, A.
- Affiliations
- Universidad Complutense de Madrid (ES)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2008-03-18
- Volume
- 77
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1967929728
- Cited by
- 63
- References
- 29
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 4 · 2023: 3 · 2022: 1 · 2021: 4 · 2020: 6 · 2019: 1 · 2018: 1 · 2017: 3 · 2016: 4 · 2015: 6 · 2014: 7 · 2013: 3 · 2012: 7
- FWCI
- 1.94
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Library Open Repository (Universidad Complutense Madrid) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Dirac oscillator, non-relativistic limit, Zitterbewegung, Ramsey interferometry, spin-orbit coupling, Mach-Zehnder interferometer, relativistic quantum mechanics, two-dimensional Dirac equation
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