Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Mathematics

Exact Solutions of the Bloch Equations of a Two-Level Atom Driven by the Generalized Double Exponential Quotient Pulses with Dephasing

Sofiane Grira, Nadia Boutabba, Hichem Eleuch

Published Jun 17, 2022• 5 citations
Publisher

Abstract

We theoretically investigate a two-level atom driven by a time-dependent external field with a generalized double exponential temporal shape, in the presence of dephasing. Therefore, we provide exact analytical solutions for the population inversion, the real and the imaginary parts of the coherence for a family of chirped and time-dependent laser waveforms. We demonstrate that the remaining atomic population inversion can be controlled by the manipulation of the pulse’s shape structure.

DOI
10.3390/math10122105

Related papers

Atomic population inversion in a two-level atom for shaped and chirped laser pulses: Exact solutions of Bloch equations with dephasing

Sofiane Grira, Nadia Boutabba, Hichem Eleuch

We perform a theoretical analysis of the Bloch equations of a two-level atom with dephasing. Exact analytical solutions with two different chirped and time-dependent detuned laser pulses are derived. The atomic population inversion as well as the coherence are explored for different initial populations. We show that the stationary population inversion can be controlled.

Results in Physics•Jun 5, 2021•3 citations

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

Sofiane Grira, Nadia Boutabba, Hichem Eleuch

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.

Mathematics•May 4, 2023•1 citation

Atomic population inversion and absorption dispersion-spectra driven by modified double-exponential quotient pulses in a three-level atom

Nadia Boutabba, Sofiane Grira, Hichem Eleuch

In this study, we control a three-level atomic system using a typical strong control field with a modified quotient double exponential form (modified QEXP). The considered atomic configuration is a V-type three-level system in which QEXP is applied between the ground and excited states. Atomic population inversion can be achieved by selecting specific shaped pulses. In addition, we control the temporal atomic coherence of the system for a spectrum of waveforms and derive both absorption and dispersion spectra. Compared to a continuous wave control field, the proposed modified QEXP pulse achieves an electromagnetically induced transparency window in the absorption spectrum.

Results in Physics•Apr 4, 2021•12 citations

Exact solution of the Bloch equations for the nonresonant exponential model in the presence of dephasing

Kaloyan N. Zlatanov, G. S. Vasilev, Peter A. Ivanov +1 more

An exact analytic solution is presented for a two-state quantum system driven by a time-dependent external field with an exponential temporal shape in the presence of dephasing. In the absence of dephasing the model reduces to the well-known Demkov model originally introduced in slow atomic collisions. The solution is expressed in terms of the generalized hypergeometric function ${}_{1}{F}_{2}(a;{b}_{1},{b}_{2};x)$. Various limiting cases are examined in the limits of weak and strong dephasing, strong driving field, and exact resonance.

Physical Review A•Oct 6, 2015•12 citations

Exact solution of the optical Bloch equation for the Demkov model

G. S. Vasilev, Peter A. Ivanov, Nikolay V. Vitanov

An exact analytic solution is presented for coherent resonant excitation of a two-state quantum system driven by a time-dependent pulsed external field described by Demkov model in the presence of dephasing.

arXiv:1402.5648•Feb 23, 2014•0 citations

Analysis of a q-deformed hyperbolic short laser pulse in a multi-level atomic system

Nadia Boutabba, Sofiane Grira, Hichem Eleuch

A fast laser pulse with a q-deformed hyperbolic function shape is investigated in a Multi-level atomic system. Therefore, we first derive the exact solution of the Bloch equations describing a two-level atom excited by a q-deformed laser pulse with dephasing and time-dependent detuning. Next, we analyze the dynamic of the atomic population inversion at resonance and off-resonance of a Rubidium 87 three-level atom driven by a classical weak field and a strong q-deformed control laser. Finally, in order to get a deeper insight of the probe field's absorption and dispersion properties, we investigate the coherence's dependence on the q-deformation. Our work demonstrates that, the dynamic of the atomic system can be fully controlled through the manipulation of the asymmetry scaling parameter q of the q-deformed hyperbolic laser wave-form.

Scientific Reports•Jun 3, 2022•13 citations
We theoretically investigate a two-level atom driven by a time-dependent external field with a generalized double exponential temporal shape, in the presence of dephasing. Therefore, we provide exact analytical solutions for the population inversion, the real and the imaginary parts of the coherence for a family of chirped and time-dependent laser waveforms. We demonstrate that the remaining atomic population inversion can be controlled by the manipulation of the pulse’s shape structure.
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.
In this study, we control a three-level atomic system using a typical strong control field with a modified quotient double exponential form (modified QEXP). The considered atomic configuration is a V-type three-level system in which QEXP is applied between the ground and excited states. Atomic population inversion can be achieved by selecting specific shaped pulses. In addition, we control the temporal atomic coherence of the system for a spectrum of waveforms and derive both absorption and dispersion spectra. Compared to a continuous wave control field, the proposed modified QEXP pulse achieves an electromagnetically induced transparency window in the absorption spectrum.
An exact analytic solution is presented for a two-state quantum system driven by a time-dependent external field with an exponential temporal shape in the presence of dephasing. In the absence of dephasing the model reduces to the well-known Demkov model originally introduced in slow atomic collisions. The solution is expressed in terms of the generalized hypergeometric function 1F2(a;b1,b2;x){}_{1}{F}_{2}(a;{b}_{1},{b}_{2};x)1​F2​(a;b1​,b2​;x). Various limiting cases are examined in the limits of weak and strong dephasing, strong driving field, and exact resonance.
A fast laser pulse with a q-deformed hyperbolic function shape is investigated in a Multi-level atomic system. Therefore, we first derive the exact solution of the Bloch equations describing a two-level atom excited by a q-deformed laser pulse with dephasing and time-dependent detuning. Next, we analyze the dynamic of the atomic population inversion at resonance and off-resonance of a Rubidium 87 three-level atom driven by a classical weak field and a strong q-deformed control laser. Finally, in order to get a deeper insight of the probe field's absorption and dispersion properties, we investigate the coherence's dependence on the q-deformation. Our work demonstrates that, the dynamic of the atomic system can be fully controlled through the manipulation of the asymmetry scaling parameter q of the q-deformed hyperbolic laser wave-form.