Exact Solutions of the Bloch Equations to the Asymmetric Hyperbolic Cosine Pulse with Chirped Frequency

Sofiane Grira (), Nadia Boutabba and Hichem Eleuch
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Sofiane Grira: Department of Mathematics and Statistics, Abu Dhabi University, Abu Dhabi 59911, United Arab Emirates
Nadia Boutabba: Institute of Applied Technology, Fatima College of Health Sciences, Abu Dhabi 24162, United Arab Emirates

Mathematics, 2023, vol. 11, issue 9, 1-10

Abstract: In this research study, we derive the exact solutions of the Bloch equations describing the dynamics of a two-level atom with dephasing. In the two-level atom, a strong laser pump couples a ground state to an upper excited state with a time-dependent Rabi-frequency. The exact solutions are given for the atomic population inversion and the real and imaginary parts of the coherence while the input pulse is an asymmetric hyperbolic cosine form. Additionally, the system is under a chirped detuning. The method of solving the Bloch equations analytically is a very tedious part of the research, and as far as we know, there are few exact solutions available in this field. Hence, our solutions might be of great interest to various research areas, including nuclear magnetic resonance, where analytical solutions to the Bloch equations play a major role in the study of the information on the state of the medium as determined by the NMR signals.

Keywords: atomic population control; two-level atom; exact solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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