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Physical Review A

Electromagnetically-induced-transparency-enhanced Kerr nonlinearity: Beyond steady-state treatment

L. Deng, M. G. Payne, W. R. Garrett

Published Jul 9, 2001• 16 citations
Publisher

Abstract

A time-dependent perturbation calculation for a four-level system is presented. A resonantly enhanced Kerr nonlinearity is produced with a combination of long, short, and delayed laser pulses in the presence of electromagnetically induced transparency. We show the enhanced Kerr nonlinearity and vanishingly small linear susceptibility due to the induced transparency, both are favorable for cross-phase modulation. In addition, we show that possible constructive and destructive interference between different excitation pathways could also lead to enhancement and suppression of the Kerr nonlinearity.

DOI
10.1103/physreva.64.023807

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A time-dependent perturbation calculation for a four-level system is presented. A resonantly enhanced Kerr nonlinearity is produced with a combination of long, short, and delayed laser pulses in the presence of electromagnetically induced transparency. We show the enhanced Kerr nonlinearity and vanishingly small linear susceptibility due to the induced transparency, both are favorable for cross-phase modulation. In addition, we show that possible constructive and destructive interference between different excitation pathways could also lead to enhancement and suppression of the Kerr nonlinearity.
We report an experimental observation of large Kerr nonlinearity with vanishing linear susceptibilities in coherently prepared four-level rubidium atoms. Quantum coherence and interference manifested by electromagnetically induced transparency suppress the linear susceptibilities and greatly enhance the nonlinear susceptibilities at low light intensities. The measured Kerr nonlinearity is comparable in magnitude to the linear dispersion in a simple two-level system and is several orders of magnitude greater than the Kerr nonlinearity of a conventional three-level scheme under similar conditions.
A theoretical investigation was carried out into the program for enhancing the Kerr nonlinearity by interacting double dark states resonances.Using density-matrix equations and perturbative iterative method,the dependence of the real part of the third-order susceptibility on the variation of the additional coherent driving field detuning was derived.It is found that the maximal Kerr nonlinearity induced by interacting dark resonances increases with increment of the detuning and enters gradually the electromagnetically induced transparency window,in which the corresponding linear absorption vanishes,moreover,by utilizing the dressed state theory,physical mechanisms for the results were presented.The realization of the giant Kerr nonlinearity with vanishing absorption is possible in a generic four-level system with double dark resonances.
We investigate a four-level double-Λ atomic scheme interacting with four laser fields, a weak probe field, a weak signal field and two driven fields, in a closed-loop configuration. We study the Kerr nonlinearity associated with cross-phase modulation based on electromagnetically induced transparency. Our results show, in this closed-loop system, that the strength of cross-phase modulation and two-photon absorption are dependent critically on the relative phase between the excitation paths. By choosing the parameters appropriately, large cross-phase modulation can be achieved within a wide transparency window, while two-photon absorption is cancelled completely. The strength of cross-phase modulation can be enhanced much more by decreasing the intensities of two driven fields.
We investigate a four-level double-Lambda atomic scheme interacting with four laser fields, a weak probe field, a weak signal field and two driven fields, in a closed-loop configuration. We study the Kerr nonlinearity associated with cross-phase modulation based on electromagnetically induced transparency. Our results show, in this closed-loop system, that the strength of cross-phase modulation and two-photon absorption are dependent critically on the relative phase between the excitation paths. By choosing the parameters appropriately, large cross-phase modulation can be achieved within a wide transparency window, while two-photon absorption is cancelled completely. The strength of cross-phase modulation can be enhanced much more by decreasing the intensities of two driven fields.
A scheme for large enhancement of the third-order nonlinearity in a four-level system with double dark resonances is proposed. We obtain an analytical expression for the linear susceptibility and nonlinear susceptibility of a weak probe field and show that the properties of double electromagnetically induced transparency and the Kerr nonlinearity can be modified significantly by changing the ratio of the two coupling fields. A physical understanding of our numerical results using the dressed-state approach is presented. The obtained large nonlinearity with vanishing absorption can be used to generate optical solitons, polarization phase gates and optical Kerr shutters.