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Chinese Physics Letters

Trichromatic Manipulation of Kerr Nonlinearity in a Three-Level A Atomic System

Hongju Guo, Niu Yue-Ping, Wang Li-chun, Jin Shi-Qi, Gong Shang-Qing

Published Oct 1, 2008• 6 citations
Publisher

Abstract

Trichromatic manipulation of Kerr nonlinearity in a three-level A atomic configuration is investigated theoretically. It is shown that for a weak monochromatic probe Held, the enhanced Kerr nonlinearity can be achieved in multiple separate transparent windows due to interference effect of multiple two-photon Raman channels. Furthermore, the property of Kerr nonlinearity can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump Geld compared to the central component.

DOI
10.1088/0256-307x/25/10/037

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Trichromatic manipulation of Kerr nonlinearity in a three-level A atomic configuration is investigated theoretically. It is shown that for a weak monochromatic probe Held, the enhanced Kerr nonlinearity can be achieved in multiple separate transparent windows due to interference effect of multiple two-photon Raman channels. Furthermore, the property of Kerr nonlinearity can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump Geld compared to the central component.
We study the dependence of absorption and dispersion spectra on amplitudes and phases of the driving fields in multiple electromagnetically induced transparency. For this purpose we consider trichromatic excitation in a three-level Λ atomic system, in which a trichromatic control laser and a monochromatic probe laser are applied to two different transitions, respectively. We numerically calculate the absorption and dispersion spectra. Two characteristic features are found. Firstly, the central transparency can be made to appear or to disappear by utilizing the amplitudes and phases of the driving components. Secondly, so long as we fix the sum of two relative phases of two sideband excitation components to the central component, the absorption and dispersion spectra keep their own lineshapes unchanged no matter how we vary the respective relative phases.
We proposed a model for manipulating giant cross-Kerr nonlinearity in an atomic gaseous medium consisting of six-level inverted-Y systems. The absorption, dispersion, and cross-Kerr nonlinear coefficients of the medium are derived as analytical functions of the parameters of probe, coupling, and signal fields. It is shown that the cross-Kerr nonlinearity is enhanced significantly in three transparent windows under electromagnetically induced transparency (EIT). Furthermore, the cross-Kerr nonlinearity can be manipulated between positive and negative values by controlling intensity and/or frequency of the coupling laser. Such controllable giant cross-Kerr nonlinearity with the analytical interpretation is convenient to find experimental parameters and is useful for studying applications of controllable multi-channel quantum phase gates.
Sideband manipulation of population inversion in a three-level A atomic configuration is investigated theoretically. Compared with the case of a nearly monochromatic field, a population inversion between an excited state and a ground state has been found in a wide sideband intensity range by increasing the difference in frequency between three components. Furthermore, the population inversion can be controlled by the sum of the relative phases of the sideband components of the trichromatic pump field with respective to the phase of the central component. Changing the sum phase from 0 to π, the population inversion between the excited state and the ground state can increase within nearly half of the sideband intensity range. At the same time, the sideband intensity range that corresponds to the system exhibiting inversion ρ 00 > ρ 11 also becomes wider evidently.
We study the nonlinear effect in a three-level atomic system in Λ configuration. As two or more fields are confined within the common electromagnetically induced transparency (EIT) window, they directly disturb EIT dark state at the same time, which leads to the self- and cross-Kerr nonlinear interactions. Our scheme is different from the existed schemes based on three-level or multilevel systems only existing single type of nonlinear interactions. In the common EIT windows, the self- and cross-Kerr nonlinearities are established with suppressed linear absorption and our scheme can be generalized polychromatic Kerr nonlinearity. Because the atoms are almost trapped in the ground states and the atom population becomes unchanged, the scheme is robust to the atomic spontaneous emission. Our scheme is a promising avenue for preparation of squeezing and entanglement .
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.
A theoretical investigation is carried out into the effect of spontaneously generated coherence on the Kerr nonlinearity of general three-level systems of Lambda, ladder, and V-shape types. It is found, with spontaneously generated coherence present, that the Kerr nonlinearity can be clearly enhanced. In the Lambda- and ladder-type systems, the maximal Kerr nonlinearity increases and at the same time enters the electromagnetically induced transparency window as the spontaneously generated coherence intensifies. As for the V-type system, the absorption property is significantly modified and therefore enhanced Kerr nonlinearity without absorption occurs for certain probe detunings. We attribute the enhancement of Kerr nonlinearity mainly to the presence of an extra atomic coherence induced by the spontaneously generated coherence.