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International Journal of Theoretical Physics

, Volume 57, Issue 5, pp 1391–1403 | Cite as

On the Transition Probability for the Near or Exact Resonance with the RWA

  • Dafa Li
  • Meng Zhao
  • Shuwang Li
Article

Abstract

Rotating wave approximation (RWA) has been used to evaluate the transition probability and solve the Schrödinger equation approximately in quantum optics. Examples include the invalidity of the traditional adiabatic condition for the adiabaticity invoking a two-level coupled system near resonance. Here, using a two-state system driven by an oscillatory force, we derive the exact transition probability by solving the Schrödinger equation analytically for a general wave function. Our results reveal that the application of the RWA may lead to false conclusions on the transition probability for the near resonance with weak coupling, especially when the coupling strength is about a half of the transition frequency. We also investigate conditions for which RWA may work or fail.

Keywords

RWA (rotating wave approximation) The Schrödinger equation Transition probability Near resonance Weak coupling 

Notes

Acknowledgments

S. Li thanks the stimulating discussion with Prof. Z. Sullivan at the Physics Department of Illinois Institute of Technology. D. Li thanks Man-Hong Yung and Yanjun Hao for their discussion. All authors thank the reviewer for his useful suggestions. This work was supported by NSFC (Grant No. 10875061) and Tsinghua National Laboratory for Information Science and Technology.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.Center for Quantum Information Science and TechnologyTsinghua National Laboratory for Information Science and Technology (TNList)BeijingChina
  3. 3.Department of Applied MathematicsIllinois Institute of TechnologyChicagoUSA

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