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Introduction to the Rotating Wave Approximation (RWA): Two Coherent Oscillations
International College of Arts and Sciences, Yokohama City University, Yokohama, Japan
- 1 International College of Arts and Sciences, Yokohama City University, Yokohama, Japan
Journal of Modern Physics·Volume 08 (2017)·Pages 2042–2058·Published 9 November 2017·DOI10.4236/jmp.2017.812124
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Abstract
In this note, I introduce a mysterious approximation called the rotating wave approximation (RWA) to undergraduates or non-experts who are interested in both Mathematics and Quantum Optics. In Quantum Optics, it plays a very important role in order to obtain an analytic approximate solution of some Schr Ö dinger equation, while it is curious from the mathematical point of view. I explain it carefully with two coherent oscillations for them and expect that they will overcome the problem in the near future.
KeywordsQuantum OpticsRabi ModelRotating Wave ApproximationCoherent Oscillation
- Green, H.S. (1965) Matrix Mechanics. P. Noordhoff Ltd., Groningen.
- Dirac, P. (1958) The Principles of Quantum Mechanics. 4th Edition, Oxford University Press.
- Peres, A. (1995) Quantum Theory: Concepts and Methods. Kluwer Academic Publishers, Dordrecht.
- Hosoya, A. (1999) Lectures on Quantum Computation (in Japanese), SGC Library 4. Saiensu-sha Co., Ltd. Publishers, Tokyo.
- Fujii, K., et al. (2010) Treasure Box of Mathematical Sciences (in Japanese). Yusei-sha, Tokyo.
- Schleich, W.P. (2001) Quantum Optics in Phase Space. WILEY-CH, Berlin. https://doi.org/10.1002/3527602976
- Jaynes, E.T. and Cummings, F.W. (1963) Comparison of Quantum and Semiclassical Radiation Theories with Applications to the Beam Maser. Proceedings of the IEEE, 51, 89-109. https://doi.org/10.1109/PROC.1963.1664
- Fujii, K. and Suzuki, T. (2011) An Approximate Solution of the Jaynes-Cummings Model with Dissipation. International Journal of Geometric Methods in Modern Physics, 8, 1799-1814. arXiv: 1103.0329[math-ph]. https://doi.org/10.1142/S0219887811005944
- Fujii, K. and Suzuki, T. (2012) An Approximate Solution of the Jaynes-Cummings Model with Dissipation II: Another Approach. International Journal of Geometric Methods in Modern Physics, 9, Article ID: 1250036, arXiv: 1108.2322[math-ph]. https://doi.org/10.1142/S0219887812500363
- Larson, J. (2013) On the Rotating Wave Approximation in the Adiabatic Limit. Physica Scripta, 2013, Article ID: 014040, arXiv: 1208.1891[quant-ph]. https://doi.org/10.1088/0031-8949/2013/T153/014040
- Law, C.K. (1994) Effective Hamiltonian for the Radiation in a Cavity with a Moving Mirror and a Time-Varying Dielectric Medium. Physical Review A, 49, 309. https://doi.org/10.1103/PhysRevA.49.433
- Dodonov, A.V. and Dodonov, V.V. (2012) Approximate Analytical Results on the Cavity Casimir Effect in the Presence of a Two-Level Atom. Physical Review A, 85, Article ID: 063804, arXiv: 1112.0523[quant-ph]. https://doi.org/10.1103/PhysRevA.85.015805
- Fujii, K. and Suzuki, T. (2013) An Approximate Solution of the Dynamical Casimir Effect in a Cavity with a Two-Level Atom. International Journal of Geometric Methods in Modern Physics, 10, Article ID: 1350035, arXiv: 1209.5133[quant-ph]. https://doi.org/10.1142/S0219887813500357
- Fujii, K. and Suzuki, T. (2014) Rotating Wave Approximation of the Law's Effective Hamiltonian on the Dynamical Casimir Effect. International Journal of Geometric Methods in Modern Physics, 11, 1450003, arXiv: 1209.5133[quant-ph]. https://doi.org/10.1142/S0219887814500030