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Physical Review A

Modified self-Kerr-nonlinearity in a four-level N -type atomic system

Jiteng Sheng, Xihua Yang, Haibin Wu, Min Xiao

Published Nov 10, 2011• 104 citations
Publisher

Abstract

The self-Kerr-nonlinearity of a four-level $\mathsf{N}$-type atomic system is studied both experimentally and theoretically. The self-Kerr-nonlinear coefficient ${n}_{2}$ of the probe beam is greatly enhanced near atomic resonance, and can be dramatically modified by changing the switching laser power. With an increasing switching laser power, the slope of the Kerr nonlinear coefficient ${n}_{2}$ around the atomic resonance changes from negative to positive, and the value of ${n}_{2}$ varies from \ensuremath{\sim}--4 \ifmmode\times\else\texttimes\fi{} 10${}^{\ensuremath{-}6}$ to 4 \ifmmode\times\else\texttimes\fi{} 10${}^{\ensuremath{-}6}$ cm${}^{2}$/W at certain near-resonant probe frequency detunings. Such controllable Kerr nonlinearity can find applications in optoelectronic devices, such as all-optical switching and logic gates.

DOI
10.1103/physreva.84.053820

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The self-Kerr-nonlinearity of a four-level N\mathsf{N}N-type atomic system is studied both experimentally and theoretically. The self-Kerr-nonlinear coefficient n2{n}_{2}n2​ of the probe beam is greatly enhanced near atomic resonance, and can be dramatically modified by changing the switching laser power. With an increasing switching laser power, the slope of the Kerr nonlinear coefficient n2{n}_{2}n2​ around the atomic resonance changes from negative to positive, and the value of n2{n}_{2}n2​ varies from \ensuremath{\sim}--4 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−6{}^{\ensuremath{-}6}\ensuremath−6 to 4 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−6{}^{\ensuremath{-}6}\ensuremath−6 cm2{}^{2}2/W at certain near-resonant probe frequency detunings. Such controllable Kerr nonlinearity can find applications in optoelectronic devices, such as all-optical switching and logic gates.
We investigate the self–Kerr nonlinearity of a four-level N-type atomic system in 87 Rb and observe its reversible property with a unidirectional increase in the switching field. For a laser arrangement in which the probe field interacts with the middle two states, the slope and the sign of the self–Kerr nonlinearity around the atomic resonance not only can be changed from negative to positive but also can be changed to negative again with a unidirectional increase in the switching field. Numerical simulations are consistent with the experimental results, and dressed state analysis is presented to explain the experimental results.
We study enhancement of cross-Kerr nonlinearity in four-level N-type atomic system by the analytical method. The results apply to the 87Rb atoms and show that in the presence of the EIT effect (i.e., the presence of coupling laser field), the Kerr nonlinear coefficient is enhanced several order of magnitudes (about 10-6 cm2/W) around the EIT window. That is, on the Kerr nonlinear graph the two positive and negative values are found on both sides of the resonant frequency. The amplitude and sign of the Kerr nonlinear coefficient can be controlled versus the intensity or frequency of the coupling laser field. Analytical results are useful for experimental observation and related applications.
Summary form only given. The reduced absorption and enhanced nonlinearity in a three-level electromagnetically induced transparency (EIT) system are very important in achieving an effective all-optical switching action. The Kerr-nonlinear index of refraction of a three-level EIT medium can be greatly enhanced near resonance due to atomic coherence induced in such a system in comparison with a two-level atomic system, as we have shown by using an optical ring cavity. Both the magnitude and sign of the Kerr-nonlinear index change dramatically for different frequency detunings of the controlling (or coupling) or cavity (or probe) field. Bistability and dynamic instability occur when such a three-level /spl Lambda/-type EIT system is placed inside an optical ring cavity and the controlling and cavity input intensities to exceed certain threshold values. In this paper, we present a recent experimental demonstration of controlling the cavity output intensity by modulating the frequency detuning of the controlling beam.
We propose to use a five-level cascade system to enhance self-Kerr nonlinearity under an electromagnetically induced transparency (EIT) condition. Using density-matrix theory, an expression of the self-Kerr nonlinear coefficient for a weak probe light is derived. Variations of the self-Kerr coefficient with respect to the frequency and intensity of a strong coupling light are investigated. The Kerr nonlinearity is basically modified and enhanced greatly in the spectral regions corresponding to EIT transparent windows. Furthermore, the sign, slope, and magnitude of the self-Kerr coefficient can be controlled with the frequency and intensity of the coupling light. Such a controllable Kerr nonlinearity can find interesting applications in optoelectronic devices working with low light intensity at multiple frequencies.