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arXiv:physics/0309017 · Journal of the Optical Society of America B

Nonlinear absorption and refraction in near-detuned rubidium vapor

Colin F. McCormick, Daniel R. Solli, R. Y. Chiao, J. Miguel Hickmann

Published Dec 1, 2003• 18 citations
arXivHTMLPDF

Abstract

Using the z-scan technique, we have measured the self-induced absorptive and refractive nonlinear behavior of hot atomic rubidium vapor within the Doppler profile of the D2 line. We observe large nonlinear amplitude and phase effects with only tens of microwatts of incident power. Our results are in good agreement with numerical calculations based on an analytic model of a Doppler-broadened two-level system.

DOI
10.1364/josab.20.002480

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Using the z-scan technique, we have measured the self-induced absorptive and refractive nonlinear behavior of hot atomic rubidium vapor within the Doppler profile of the D2 line. We observe large nonlinear amplitude and phase effects with only tens of microwatts of incident power. Our results are in good agreement with numerical calculations based on an analytic model of a Doppler-broadened two-level system.
Atomic vapors make flexible and useful nonlinear optical media when light is detuned far from resonances. However, few direct measurements of their nonlinear coefficients have been performed to date. We present a measurement of the Kerr coefficient for various detunings to both the red and blue of the D2D2D2 line in hot atomic rubidium vapor. Saturation effects complicate the interpretation of the standard z-scan method, but a simple saturation model agrees well with our data. We find values of ${n}_{2}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{-}7}{\mathrm{cm}}^{2}/\mathrm{W}$ for 1 GHz detunings from the D2D2D2 line.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale micro-electro-mechanical system (MEMS) cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing very good quantitative agreement. A Kerr nonlinear refractive index n2 of up to −1.2×10−4 cm2/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale MEMS cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing excellent quantitative agreement. A Kerr nonlinear refractive index n2n_2n2​ of up to 10−410^{-4}10−4 cm2^22/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.
We report the measurement of the Kerr nonlinear refractive index of the rubidium vapor via the high sensitivity z-scan method by using an optical frequency comb. The novel self-focusing and self-defocusing effects of the vapor are presented with red and blue detunings of the laser frequency. The optical nonlinear characteristics of the rubidium vapor are clearly interpreted under different experimental parameters. Furthermore, the Kerr nonlinear refractive index n2 is obtained from the measured dispersion curve, and it basically occurs on the order of 10−6 cm2/W. The evolutions of the Kerr nonlinear coefficient n2 with the laser power and frequency detuning, respectively, are studied. To the best of our knowledge, the use of pulsed lasers to measure the Kerr nonlinear refractive index n2 of atomic vapor has not been reported yet. The direct measurement of the Kerr nonlinear coefficient will greatly help us understand and optimize nonlinear optical processes and find its more potential applications in quantum optics.
The Kerr nonlinear index of refraction for rubidium atoms is measured by using an optical ring cavity with and without electromagnetically induced transparency (EIT). Significant enhancement and inhibition of the Kerr nonlinear index is observed near resonance with EIT. The nonlinear index of refraction is measured as functions of probe and coupling frequency detunings, respectively, with and without the presence of EIT. A simple theoretical calculation including Doppler broadening is presented and is found to be in good qualitative agreement with the experimentally measured results.