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Applied Mathematics & Information Sciences

SLOWING LIGHT CONTROL FOR A SOLITON-PAIR

Nadia Boutabba, Hichem Eleuch

Published Apr 4, 2013• 7 citations
Publisher

Abstract

We investigate the propagation of a soliton-pair in 3-level atomic system out of resonance. We present an explicit analytical expression of the soliton-pair shape. We show that the speed of the soliton-pair can be controlled. Furthermore, we derive a condition for completely stopping the light.
DOI
10.12785/amis/070433

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In the framework of the nonlinear lambda model we investigate propagation of solitons in atomic vapors and Bose-Einstein condensates. We show how the complicated nonlinear interplay between fast solitons and slow-light solitons in the lambda-type media points to the possibility to create optical gates and, thus, to control the optical transparency of the lambda-type media. We provide an exact analytic description of decelerating, stopping and reaccelerating of slow-light solitons in atomic media in the nonadiabatic regime. Dynamical control over slow-light solitons is realized via a controlling field generated by an auxiliary laser. For a rather general time dependence of the field; we find the dynamics of the slow-light soliton inside the medium. We provide an analytical description for the nonlinear dependence of the velocity of the signal on the controlling field. If the background field is turned off at some moment of time, the signal stops. We find the location and shape of the spatially localized memory bit imprinted into the medium. We discuss physically interesting features of our solution, which are in a good agreement with recent experiments.
We investigate propagation of a slow-light soliton in Λ-type media such as atomic vapours and Bose–Einstein condensates. We show that the group velocity of the soliton monotonically decreases with the intensity of the controlling laser field, which decays exponentially after the laser is switched off. The shock wave of the vanishing controlling field overtakes the slow soliton and stops it, while the optical information is recorded in the medium in the form of spatially localized polarization. In the strongly nonlinear regime we find an explicit exact solution describing the whole process.
In the framework of the nonlinear Λ model, propagation of solitons was analysed in atomic vapours and Bose-Einstein condensates. The complicated nonlinear interplay between fast and slow-light solitons in a Λ-type medium was shown to facilitate control of its optical transparency and formation of optical gates. An exact analytical description was given for the deceleration, stopping and revival of slow-light solitons in the experimentally relevant non-adiabatic regime. A stopping slow-light soliton imprints a localized immobile polarization pattern in the medium, which, as explicitly demonstrated here, can be used as a bit of readable optical memory. The whole process can be controlled with the background field and an auxiliary laser field. The latter regulates the signal velocity, while the slow-light soliton can be stopped by switching off the former. The location and shape of the imprinted memory bit were also determined. With few assumptions characteristic of slow light, the Λ model was reduced to a simpler nonlinear model that also describes two-dimensional dilatonic gravity. Exact solutions could now be derived also in the presence of relaxation. Spontaneous decay of the upper atomic level was found to be strongly suppressed, and the spatial form of the decelerating slow-light soliton was preserved, even if the optical relaxation time was much shorter than the typical time scale of the soliton. The effective relaxation coefficient of the slow-light soliton was significantly smaller than that of an arbitrary optical pulse. Such features are obviously of great importance when this kind of system is applied, in practice, to information processing. A number of experimentally observable properties of the solutions reported were found to be in good agreement with recent experimental results, and a few suggestions are also made for future experiments.