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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Density matrix description of light storage and speed reduction in the sodium atom

Abu Mohamed Alhasan, Jan Fiutak

Published Nov 18, 2003• 2 citations
Publisher

Abstract

The time dependent solution of the density matrix is analyzed for the two-color light excitation of the sodium atom for the D1 transition. The light storage effect and the slowing down of the light are investigated in terms of the populations, the dipole moment and the Raman coherences.
DOI
10.1117/12.544418

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Atomic coherence effects within the sodium D1{\mathit{D}}_{1}D1​ line are shown to lead to the suppression of optical pumping, to the switching of light on and off when the coherence effects are turned on and off, and especially to lasing without inversion.
A quantum-electrodynamic (QED) description of the resonant interaction of monochromatic light with the 32{3}^{2}32S1/2{\mathit{S}}_{1/2}S1/2​(F'=2)\ensuremath{\rightarrow}32{3}^{2}32P3/2{\mathit{P}}_{3/2}P3/2​(F=3,2,1) hyperfine transitions of the sodium D2{D}_{2}D2​ line is formulated in terms of the Heisenberg atomic operator. Off-diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences, and certain state coherences form a closed subset of the total system of equations. This subset is small enough to be computed numerically. The results of calculations with this model are compared with three previously developed semiclassical descriptions using the density operator. One of the semiclassical models was developed to describe the interaction of weak light with the atomic transition while another is suitable in the case of high-intensity light. For both \ensuremath{\pi} and \ensuremath{\sigma} excitation it is shown that the QED calculated values for the time-averaged, excited-level population probability converge to those of each of the semiclassical models in the appropriate limit of light intensity. For homogeneous broadening, results show that the optimum light intensity to obtain the largest fraction of atoms in the 32{3}^{2}32P3/2{P}_{3/2}P3/2​ level after transversing a 1-mm-diam laser beam is 1.15 mW/mm2{\mathrm{mm}}^{2}mm2 for \ensuremath{\pi} excitation and 1.43 mW/mm2{\mathrm{mm}}^{2}mm2 for \ensuremath{\sigma} excitation.
For pt. I see ibid. p. 231, 1994. We consider optical pumping in the multilevel sodium D 1 manifold by several coherent light fields. Coherence between atomic states is taken into account by solving the complete density matrix equations. The manifestation of population trapping and the variation of transmitted light intensity are predicted numerically and verified experimentally for the sodium D 1 line. The influence of relaxation and Doppler broadening is elucidated. The interaction of a strong and a weak field is shown to create electromagnetically induced transparency.