Two-state model of a general Heun class with periodic level-crossings
- Авторы: Saget G.1, Ishkhanyan А.2,3, Leroy C.1, Ishkhanyan Т.1,2,4
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Учреждения:
- Laboratoire Interdisciplinaire Carnot de Bourgogne
- Institute for Physical Research
- Armenian State Pedagogical University
- Moscow Institute of Physics and Technology
- Выпуск: Том 52, № 4 (2017)
- Страницы: 324-334
- Раздел: Article
- URL: https://journals.rcsi.science/1068-3372/article/view/228494
- DOI: https://doi.org/10.3103/S1068337217040041
- ID: 228494
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Аннотация
A specific constant-amplitude periodic level-crossing model of the semi-classical quantum time-dependent two-state problem that belongs to a general Heun class of field configurations is presented. The exact analytic solution for the probability amplitude, generally written for this class in terms of the general Heun functions, in this specific case admits series expansion in terms of the incomplete Beta functions. Terminating this series results in an infinite hierarchy of finite-sum closedform solutions each standing for a particular two-state model, which generally is only conditionally integrable in the sense that for these field configurations the amplitude and phase modulation functions are not varied independently. However, there exists at least one exception when the model is unconditionally integrable, that is the Rabi frequency and the detuning of the driving optical field are controlled independently. This is a constant-amplitude periodic level-crossing model, for which the detuning in a limit becomes a Dirac delta-comb configuration with variable frequency of the levelcrossings. The exact solution for this model is derived, the Floquet exponents are determined and study of the population dynamics in the system for various regions of the input parameters is done.
Об авторах
G. Saget
Laboratoire Interdisciplinaire Carnot de Bourgogne
Email: tishkhanyan@gmail.com
Франция, Dijon
А. Ishkhanyan
Institute for Physical Research; Armenian State Pedagogical University
Email: tishkhanyan@gmail.com
Армения, Ashtarak; Yerevan
C. Leroy
Laboratoire Interdisciplinaire Carnot de Bourgogne
Email: tishkhanyan@gmail.com
Франция, Dijon
Т. Ishkhanyan
Laboratoire Interdisciplinaire Carnot de Bourgogne; Institute for Physical Research; Moscow Institute of Physics and Technology
Автор, ответственный за переписку.
Email: tishkhanyan@gmail.com
Франция, Dijon; Ashtarak; Dolgoprudny