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- Title
Exact Solutions of the Bloch Equations to the Asymmetric Hyperbolic Cosine Pulse with Chirped Frequency.
- Authors
Grira, Sofiane; Boutabba, Nadia; Eleuch, Hichem
- 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.
- Subjects
BLOCH equations; NUCLEAR magnetic resonance; EXCITED states; LASER pumping; NUCLEAR magnetic resonance spectroscopy; ANALYTICAL solutions
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 9, p2159
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11092159