Abstract
We present a new exactly integrable time-dependent constant-amplitude level-crossing two-state quantum model for which the detuning of the excitation laser field varies with time over a restricted interval. This field configuration is a member of one of the eleven independent classes of general Heun two-state models. We prove that this is the only non-classical unconditionally solvable field configuration among the general Heun classes, solvable in terms of finite sums of Gauss hypergeometric functions. Each of the two fundamental solutions that compose the general solution of the problem is written as an irreducible linear combination of two ordinary hypergeometric functions.
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REFERENCES
Ishkhanyan, A.M. Shahverdyan, T.A., and Ishkhanyan, T.A., Eur. Phys. J. D, 2015, vol. 69, p. 10.
Shore, B.W., The Theory of Coherent Atomic Excitation, New York: Wiley, 1990.
Ronveaux, A., Heun’s Differential Equations, London: Oxford University Press, 1995.
Slavyanov, S.Yu. and Lay, W., Special functions, Oxford: Oxford University Press, 2000.
Olver, F.W.J., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (eds.), NIST Handbook of Mathematical Functions, New York: Cambridge University Press, 2010.
Ishkhanyan, T.A., Shahverdyan, T.A., and Ishkhanyan, A.M., Advances in High Energy Physics, 2018, vol. 2018, id 4263678.
Ishkhanyan, A.M., Theor. Math. Phys., 2020, vol. 202, p. 1.
Melikdzhanian, D.Yu. and Ishkhanyan, A.M., J. Math. Anal. Appl., 2021, vol. 499, id 125037.
Ishkhanyan, A.M., Constructive Approximation, 2019, vol. 49, p. 445.
Demkov, Yu.N. and Kunike, M., Vestn. Leningr. Univ. Fis. Khim., 1969, vol. 16, p. 39.
Suominen, K.A. and Garraway, B.M., Phys. Rev. A, 1992, vol. 45, p. 374.
Slater, L.J., Generalized hypergeometric functions, Cambridge: Cambridge University Press, 1966.
Bambini, A. and Berman, P.R., Phys. Rev. A, 1981, vol. 23, p. 2496.
Hioe, F.T. and Carroll, C.E., Phys. Rev. A, 1985, vol. 32, p. 1541.
Ishkhanyan, A.M., Opt. Commun., 2000, vol. 176, p. 155.
Ishkhanyan, A.M., J. Phys. A, 2000, vol. 33, p. 5539.
Nakamura, H., Nonadiabatic Transition NJ, Hackensack: World Scientific, 2002.
Landau, L.D., Phys. Z. Sowjetunion, 1932, vol. 2, p. 46.
Zener, C., Proc. R. Soc. London, Ser. A, 1932, vol. 137, p. 696.
Majorana, E., Nuovo Cimento, 1932, vol. 9, p. 43.
Stückelberg, E.C.G., Helv. Phys. Acta., 1932, vol. 5, p. 369.
Ishkhanyan, A.M. and Grigoryan, A.E., J. Phys. A, 2014, vol. 47, id 465205.
Shahverdyan, T.A., Ishkhanyan, T.A., Grigoryan, A.E., and Ishkhanyan, A.M., J. Contemp. Phys., 2015, vol. 50, p. 211.
Saget, G., Ishkhanyan, A.M., Leroy, C., and Ishkhanyan, T.A., J. Contemp. Phys., 2017, vol. 52, p. 324.
Ishkhanyan, T.A., J. Contemp. Phys., 2019, vol. 54, p. 17.
Ishkhanyan, T.A., Papoyan, A.V., Ishkhanyan, A.M., and Leroy, C., Las. Phys. Lett., 2020, vol. 17, p. 106001.
Funding
The research was supported by the Russian-Armenian University, the Armenian Science Committee (SC Grant No. 20RF-171 and Grant No. 21SC-BRFFR-1C021) and the Armenian National Science and Education Fund (ANSEF Grant No. PS-2520).
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Translated by A.M. Ishkhanyan
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Shahverdyan, T.A., Ishkhanyan, T.A. & Ishkhanyan, A.M. A New Level-Crossing Two-State Model Solvable in Terms of Hypergeometric Functions. J. Contemp. Phys. 56, 291–296 (2021). https://doi.org/10.3103/S1068337221040150
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DOI: https://doi.org/10.3103/S1068337221040150