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arXiv:quant-ph/0406231 · Physical Review A

Nonlinear interaction of light with a Bose-Einstein condensate: Methods to generate sub-Poissonian light

Ilya P Vadeiko, A. V. Prokhorov, Andrei V. Rybin, Sergei M Arakelyan

Published Jul 6, 2005• 14 citations
arXivHTMLPDF

Abstract

We consider a $\ensuremath{\Lambda}$-type model of the Bose-Einstein condensate of sodium atoms interacting with the light. Coefficients of the Kerr nonlinearity in the condensate can achieve large and negative values, providing the possibility for effective control of group velocity and dispersion of the probe pulse. We find a regime when the observation of the ``slow'' and ``fast'' light propagating without absorption becomes achievable due to the strong nonlinearity. An effective two-level quantum model of the system is derived and studied. Our approach is based on a possibility of establishing a connection of the underlying algebra with the $su(2)$ algebra within the formalism of the polynomial algebras of excitations (PAE). We propose an efficient way for the generation of sub-Poissonian fields in the Bose-Einstein condensate at time-scales much shorter than the characteristic decay time in the system. We show that the quantum properties of the probe pulse can be controlled in BEC by the classical coupling field.

DOI
10.1103/physreva.72.013804

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We consider a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type model of the Bose-Einstein condensate of sodium atoms interacting with the light. Coefficients of the Kerr nonlinearity in the condensate can achieve large and negative values, providing the possibility for effective control of group velocity and dispersion of the probe pulse. We find a regime when the observation of the slow'' and fast'' light propagating without absorption becomes achievable due to the strong nonlinearity. An effective two-level quantum model of the system is derived and studied. Our approach is based on a possibility of establishing a connection of the underlying algebra with the su(2)su(2)su(2) algebra within the formalism of the polynomial algebras of excitations (PAE). We propose an efficient way for the generation of sub-Poissonian fields in the Bose-Einstein condensate at time-scales much shorter than the characteristic decay time in the system. We show that the quantum properties of the probe pulse can be controlled in BEC by the classical coupling field.
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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.
A quantum theory of the interaction of the atomic Bose condensate with external optical fields has been developed for a two-beam Λ-scheme close to resonance. Regimes have been obtained where the coefficients of Kerr nonlinearity and nonlinear absorption reach giant values and even become negative, which gives rise to the effect of nonlinear electromagnetically induced transparency. The possibility of the efficient generation of quadrature-squeezed light under the condition of the nonlinear compensation of optical losses has been shown.
We propose a method to control the optical transparency of a Bose–Einstein condensate with working energy levels of the Λ-type. The reported effects are essentially nonlinear and are considered in the framework of an exactly solvable model describing the interaction of light with a Λ-type medium. We show how the complicated nonlinear interplay between fast and slow solitons in the Λ-type medium points to a possibility to create optical gates as well as to a possibility to store optical information.
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.