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Nonlinear Schrödinger equation and semiclassical description of the microwave-to-optical frequency conversion based on the Lamb–Retherford experiment

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Abstract

It is shown that Lamb–Retherford experiment can be completely described within the framework of classical field theory without using such concepts as discrete states of the atom and jump-like electron transitions between them. The rate of stimulated decay of the metastable state of a hydrogen atom in an external periodic electric field is determined. The dependence of this rate on the frequency and amplitude of the external electric field, as well as on the parameters of the atom, is obtained. It is shown that the maximum value of the stimulated decay rate of the metastable state of a hydrogen atom is achieved at a frequency of an external electric field equal to the frequency shift corresponding to either the fine structure of the hydrogen atom or the Lamb shift. Using the Lamb–Retherford idea, a direct method of the microwave-to-optical frequency conversion is suggested. A theory of this conversion is developed, and the intensity of optical emission induced by microwave radiation is calculated.

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Acknowledgements

This work was done on the theme of the State Task No. AAAA-A17-117021310385-6. Funding was provided in part by the Tomsk State University competitiveness improvement program.

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  1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Vernadskogo Ave., 101/1, Moscow, Russia, 119526

    Sergey A. Rashkovskiy

  2. Tomsk State University, 36 Lenina Avenue, Tomsk, Russia, 634050

    Sergey A. Rashkovskiy

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Correspondence to Sergey A. Rashkovskiy.

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Rashkovskiy, S.A. Nonlinear Schrödinger equation and semiclassical description of the microwave-to-optical frequency conversion based on the Lamb–Retherford experiment. Indian J Phys 94, 161–174 (2020). https://doi.org/10.1007/s12648-019-01476-w

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  • DOI: https://doi.org/10.1007/s12648-019-01476-w

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