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arXiv:1411.1824 · Journal of Optics

Reversible self–Kerr nonlinearity in an N-type atomic system through a switching field

Xu Yang, Kang Ying, Yueping Niu, Shangqing Gong

Published Mar 27, 2015• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2040-8978/17/4/045505

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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.
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${}^{\ensuremath{-}6}$ to 4 \ifmmode\times\else\texttimes\fi{} 10${}^{\ensuremath{-}6}$ 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 theoretically investigate the linear and nonlinear optical properties of a five-level atomic system interacting with multiple electromagnetic fields. The relevant optical Bloch equations are numerically solved via iterative formalism to procure first- and third-order susceptibilities. Our numerical computations reveal that the switching field’s strength can be used as a knob to get either single or multiple transparency windows. It is also identified that colossal Kerr nonlinearity exists within the optical EIT dips. Furthermore, we found that the position, sign and magnitude of self-Kerr index can be manipulated by merely adjusting the Rabi frequency of switching field. We also resort to double dressed state mechanism in order to justify our numerical results. Our findings are of particular interest in multi-channel communication, quantum computation and designing of optical devices.
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.
Abstract We propose to utilize a five-level Λ − Ξ system to achieve large self-Kerr nonlinearity under multiphoton resonance conditions. Using a density matrix formulation along with an iterative perturbation technique, analytic expressions of linear and nonlinear susceptibilities are derived for stationary as well as for moving atoms. Variation of first- and third-order susceptibilities with respect to frequency and intensity of switching field is then discussed. The dressed-state picture is employed to explain the amplitude and position of each peak in linear and nonlinear absorption profiles. It is found that under slow light conditions, large controllable Kerr nonlinearity with reduced linear and nonlinear absorption is achieved by properly adjusting the strength and detunings of strong electromagnetic (e.m.) fields. Our numerical results also reveal that the Kerr nonlinear index of our considered system is greater than that of existing three-level Λ and four-level N systems. Finally, it is substantiated that self-Kerr nonlinearity is proliferated by taking the Doppler effect into account.
In this paper, we propose an analytical model to study the effect of Doppler broadening on self-Kerr nonlinearity in a five-level ladder-type atomic system. First- and third-order susceptibilities and the self-Kerr nonlinear coefficient are found as the function of temperature and parameters of laser fields. The analytical model is applied to hot $^{85}{\rm Rb}$85Rb and $^{87}{\rm Rb}$87Rb atoms, and it is shown that under the electromagnetically induced transparency (EIT) effect, the self-Kerr nonlinear coefficient is enhanced around three transparent spectral regions. When the temperature of atomic vapor increases (i.e., Doppler width increases), the depth and width of the EIT windows decrease accordingly, and therefore the amplitude of the Kerr nonlinear coefficient decreases significantly. In addition, because the frequency gaps between hyperfine levels of upper excited state ${{5\rm D}_{5/2}}$5D5/2 of $^{85}{\rm Rb}$85Rb atoms are much smaller than those of $^{87}{\rm Rb}$87Rb atoms, the EIT windows as well as the nonlinear dispersion curves for $^{85}{\rm Rb}$85Rb atoms are closer than those for $^{87}{\rm Rb}$87Rb atoms as the Doppler effect presents. The analytical results agree well with the experimental observation when reducing to a three-level atomic system. The analytical model can be used to easily fit the experimental observations of self-Kerr nonlinearity in a five-level atomic system under different temperature conditions and apply to a variety of applications relating to all-optical-switching techniques.
We derive a cross-Kerr type effective Hamiltonian for the four-level atom interacting with three electromagnetic fields in the N-configuration. When the atom has relaxed into the ground state a cross-Kerr nonlinearity arises between two weak probe fields. As a development on earlier work we show in general that the atom will also display a linear and self-Kerr response. However, if certain resonance conditions are satisfied then the linear and self-Kerr interactions will vanish. The electrical susceptibilities of the probe transitions are also explored and it is shown that a large, pure cross-Kerr nonlinearity can be generated with vanishing absorption of both probe fields.