Pulse Propagation Through a medium Consists of Two Three-Level Atoms | ||||
| Al-Azhar Bulletin of Science | ||||
| Article 7, Volume 32, Issue 2-B, December 2021, Page 33-43 PDF (665.96 K) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/absb.2021.100248.1145 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Rasha N. Rabea  1; Mervat A. Eldeberky1; Mohamed M. A. Ahmed2
| ||||
| 1Mathematics Department, Faculty of Science (Girls Branch), Al-Azher University, Nasr City 11884, Cairo, Egypt. | ||||
| 2Mathematics Department, Faculty of Science (Boys Branch) , Al-Azher University, Nasr City 11884, Cairo, Egypt. | ||||
| Abstract | ||||
| The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon. | ||||
| Keywords | ||||
| Pulse propagation; semi-classical approach; Maxwell Bloch equations; non-linear equations; density matrix | ||||
| References | ||||
|
[1] Chen X. The Geometric tradition and the wave theory of light. l st ed. Springer Science + Business Media Dordrech. Kluwer Academic; (2000).
[2] Allen L, Eberly J H. Optical reasonance and two-level atom. 8th ed. John Weily, New York; 1987.
[3] Cook R J, Shore B. Coherent dynamics of N-level atoms and molecules. III. An analytically soluble periodic case. J Phys Rev A. 1979; 20 : 539. doi.org/10.1103/PhysRevA.20.539.
[4] Hioe F T, Eberly H J. Nonlinear constants of motion for three-level quantum systems. Phys Rev Lett . 1982; 4 : 25. doi.org/10.1103/PhysRevA.25.2168.
[5] Nath M R, Sen S. Dynamics of cascade three level system interacting with the classical and quantized field. Pramana J. Phys. 2003; 61 :1089. doi.org/10.1007/BF02704404.
[6] Dalton B J, Garraway BM. Non-Markovian decay of a three-level cascade atom in a structured reservoir, Phys. Rev. A. 2003; 68 : 33809. doi.org/10.1103/PhysRevA.68.033809.
[7] Shchedrin G, O’Brien C, Rostovtsev Y, Scully MO. Analytic solution and pulse area theorem for three-level atoms, Phys. Rev. A. 2015; 92 :063815. doi.org/10.1103/PhysRevA.92.063815.
[8] Grira S, Eleuch H. Solitary waves propagation in three-level atomic media. J. Phys. Conf. Ser. 2019; 1411: 012018. Doi:10.1088/1742-6596/1411/1/012018
[9] Groves E, Clader, Eberly JH. Jaynes–Cummings theory out of the box, J. Phys. B: At. Mol. Opt. Phys. 2013; 46 : 224005. https://doi.org/10.1088/0953-4075/46/22/224005.
[10] Urchueguia J F, Espinosa V, Valcarcel G.J. De. Nonlinear dynamics of a class-a two-photon laser with injected signal in cascade systems. J. Mod. Opt. 1999; 46 : 1483. https://doi.org/10.1080/09500349908231349.
[11] McGloin D, Dunn M H, Fulton D J. Polarization effects in electromagnetically induced transparency. Phys. Rev. A. 2000; 62 : 53802. doi.org/10.1103/PhysRevA.62.053802.
[12] Rooijakkers W, Hogervorst W, Vassen W. Laser cooling, friction, and diffusion in a three-level cascade system. Phys. Rev. A. 1997; 56 : 3083. doi.org/10.1103/PhysRevA.56.3083.
[13] Grischkowsky D, Loy M M T, Liao P F. Adiabatic following model for two-photon transitions: nonlinear mixing and pulse propagation. Phys. Rev . A. 1975, 12 : 2514. doi.org/10.1103/PhysRevA.12.2514.
[14] Scully M O, Zubairy M S. Quantum optics. 1st ed. United kingdom at University press, Cambredge; 1999.
[15] Meystre P. Semiclassical Atom–Light Interaction. Quantum Optics. Springer; 2021. doi.org/10.1007/978-3-030-76183-72021.
[16] Konopnicki M J, Eberly J H. Simultaneous propagation of short different-wavelength optical pulses, Phsyics A. 1981; 24 : 2567. doi.org/10.1103/PhysRevA.24.2567.
[17] Bullough R K, Caudrey P D, Eilbeck D C. A general theory of self-induced transparency, Opto-electronics. 1974; 6 : 121. doi.org/10.1007/BF01421994. | ||||
|
Statistics Article View: 163 PDF Download: 127 |
||||
