Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

QUANTUM JAYNES–CUMMINGS MODEL FOR A TWO-LEVEL SYSTEM WITH EFFECTS OF PARAMETRIC TIME-DEPENDENCES
Mounira Berrehail^a, Nadjet Benchiheub^a, Salah Menouar^b, and Jeong Ryeol Choi^c
^aDepartment of Material Sciences, University of Bordj Bou Arreridj, Bordj Bou Arreridj 34000, Algeria
^bLaboratory of Optoelectronics and Compounds (LOC), Department of Physics, Faculty of Science,
University of Ferhat Abbas Setif 1, Setif 19000, Algeria
^cDepartment of Nanoengineering, Kyonggi University, Yeongtong-gu, Suwon, Gyeonggi-do 16227, Republic of Korea
Email: choiardor@hanmail.net

Received 20 December 2021; accepted 15 February 2022

An approach to exact quantum solutions of the time-dependent two energy level Jaynes–Cummings model with an imaginary photon process is represented in this work. The Lewis–Riesenfeld invariant treatment and the unitary transformation method are used for this purpose. The original Schrödinger equation is reduced to an equivalent solvable one through unitary transformations by using suitable unitary operators. The reduced equation corresponds to a simpler Hamiltonian which is written as a linear combination of the generators of the reduced-dimensional SU(2) algebra. A Hermitian invariant operator is constructed based on the same algebraic formulation and its instantaneous eigenfunctions are obtained. By utilizing such eigenfunctions, the complete quantum wave functions of the system are evaluated. Such wave functions are necessary when we analyze the quantum characteristics of the system.

Keywords: time-dependent two-level atom, Jaynes–Cummings model, unitary transformation, invariant theory, SU(2) algebra
PACS: 03.65.Ge, 03.65.Ca, 03.65.Fd

KVANTINIS JAYNES–CUMMINGS MODELIS DVIEJŲ LYGMENŲ SISTEMAI SU PARAMETRINIŲ LAIKINIŲ PRIKLAUSOMYBIŲ REIŠKINIAIS
Mounira Berrehail^a, Nadjet Benchiheub^a, Salah Menouar^b, Jeong Ryeol Choi^c

^aBordž Bu Areridžo universiteto Medžiagų mokslo departamentas, Alžyras
^bSetifo Ferhato Abaso universiteto Mokslo fakultetas, Alžyras
^cKiongi universiteto Nanoinžinerijos departamentas, Korėjos Respublika

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