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Frontiers in Optics

Dynamics of EIT-enhanced refractive-Kerr nonlinearity: Prospect for quantum-nonlinear-optics

Michael Vern Pack, Ryan M. Camacho, John C. Howell

Published Jan 1, 2006• 0 citations
Publisher

Abstract

For CW-EIT and pulsed signal fields, we predict and measure the rise-times of the EIT-Kerr-optical nonlinearity are proportional to the product of the optical-pumping rate and medium optical-thickness. A slow-light signal field overcomes some rise-time limitations.
DOI
10.1364/fio.2006.ftul6

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We present a theory describing the transients and rise times of the refractive Kerr nonlinearity which is enhanced using electromagnetically induced transparency (EIT). We restrict our analysis to the case of a pulsed signal field with continuous-wave EIT fields, and all fields are well below saturation. These restrictions enable the reduction of an EIT Kerr, four-level, density-matrix equation to a two-level Bloch-vector equation which has a simple and physically intuitive algebraic solution. The physically intuitive picture of a two-level Bloch vector provides insights that are easily generalized to more complex and experimentally realistic models. We consider generalization to the cases of Doppler broadening, many-level EIT systems (we consider the D1D1D1 line of 87Rb^{87}\mathrm{Rb}87Rb), and optically thick media. For the case of optically thick media we find that the rise time of the refractive EIT Kerr effect is proportional to the optical thickness. The rise time of the refractive EIT Kerr effect sets important limitations for potential few-photon applications.
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We report observations of the dynamics of electromagnetically induced transparency (EIT) in a $\ensuremath{\Lambda}$ system when the ground states are Stark shifted. Interactions of this type exhibit large optical nonlinearities called Kerr nonlinearities, and have numerous applications. The EIT Kerr nonlinearity is relatively slow, which is a limiting factor that may make many potential applications impossible. Using rubidium atoms, we observe the dynamics of the EIT Kerr nonlinearity using a Mach-Zehnder interferometer to measure phase modulation of the EIT fields resulting from a pulsed signal beam Stark shifting the ground state energy levels. The rise times and transients agree well with theory.
It is now well understood that the characteristics of a nonlinear optical process are the result of the interplay of the linear and nonlinear susceptibilities. In general, as an atomic transition to the ground state is approached, the nonlinear susceptibility is resonantly enhanced, but, at the same time, the media exhibits a rapidly increasing refractive index and becomes opaque. During the last several years we have shown how electromagnetically induced transparency (EIT) may be used to dramatically solve this problem.