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

Slow-light solitons and shape-preserving pulses

Ulf Leonhardt, Luciana C. Dávila Romero

Published Feb 9, 2006• 1 citation
Publisher

Abstract

The physics of slow-light propagation in atomic Lambda systems is described by the theory of integrable systems, which allows the existence of solitons. Slow-light solitons are stable polarization structures that propagate through the atomic medium at a controllable speed. They represent generalizations of the experimentally demonstrated slow-light pulses in atomic media where one light polarization dominates the other, the probe, and controls its group velocity. In the general case, the overall intensity controls the speed of the entire polarization structure. For zero detuning between light and atoms, even more general shape-preserving pulses exist. Quantum fluctuations of slow-light pulses can be stored in atomic media. In the case of solitons, these are fluctuations of the soliton parameters.

DOI
10.1117/12.660191

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The physics of slow-light propagation in atomic Lambda systems is described by the theory of integrable systems, which allows the existence of solitons. Slow-light solitons are stable polarization structures that propagate through the atomic medium at a controllable speed. They represent generalizations of the experimentally demonstrated slow-light pulses in atomic media where one light polarization dominates the other, the probe, and controls its group velocity. In the general case, the overall intensity controls the speed of the entire polarization structure. For zero detuning between light and atoms, even more general shape-preserving pulses exist. Quantum fluctuations of slow-light pulses can be stored in atomic media. In the case of solitons, these are fluctuations of the soliton parameters.
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.
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.
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.
Abstract This paper describes the dynamics of solitonic pulse propagation in a closed loop quantum system comprised of five atomic energy levels. In this system four higher energy levels with four control laser fields form a closed ring-shape loop which is coherently coupled to a ground level state by a tunable probe laser field. Although the propagation of an intense probe pulse suffers losses and broadening in linear regime, there exist specific conditions where the probe pulse is found to become robust during its propagation. We attribute this regime to the formation of an optical soliton with a slow group velocity because of the balance between the dispersion and Kerr optical nonlinearity. Results obtained are based on the theoretical model using the coupled Maxwell–Bloch equations for the nonlinear propagation.
Coherent interactions of laser light with atomic ensembles allow one to modify dispersive properties of a medium and lead to new optical phenomena. Studies of the controlled light propagation and storing in such media have recently become a dynamically developing field of research motivated both by the fundamental character of the processes and by potential applications. This article briefly reviews basic theoretical approach to the dynamics of the propagation of laser pulses in optically modified media. The method and the physical processes are discussed that allow one to slow down the group velocity of laser pulse to zero (stopping of light), to transfer the state of a light pulse to atomic coherences and to restore the pulse. The interpretation of these phenomena in the formalism of dark-state polaritons is presented. Examples of possible coherent manipulations on a stored light are also discussed.