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Quantum Electronics and Laser Science Conference

Light guiding light: nonlinear refraction in rubidium vapour

J.A. Andersen, M. E. J. Friese, Z. Ficek, P. D. Drummond, N. R. Heckenberg, Halina H. Rubinsztein-Dunlop, Andrew G. Truscott

Published Nov 13, 2002• 0 citations
Publisher

Abstract

Summary form only given. We have extended previous theory to account for the hyperfine structure of the rubidium D lines, the presence of both major isotopes of rubidium and the possibility of tuning both the probe and the pump relative to their respective lines. To do this, we have developed a master equation, this time for the five (rather than three) atomic energy levels of both major isotopes of rubidium, which we can solve for a steady state, accounting for Doppler shifts.

DOI
10.1109/qels.2001.961961

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Summary form only given. We have extended previous theory to account for the hyperfine structure of the rubidium D lines, the presence of both major isotopes of rubidium and the possibility of tuning both the probe and the pump relative to their respective lines. To do this, we have developed a master equation, this time for the five (rather than three) atomic energy levels of both major isotopes of rubidium, which we can solve for a steady state, accounting for Doppler shifts.
Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.
We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2% for the D2 line at 16.5 degrees C.
We have developed a rubidium atomic-beam light source that emits Rb lines with a Doppler width of only 0.0015 cm−1. When the light from this source was measured with a scanning Fabry–Perot interferometer and the data were reduced by digital computer utilizing numerical deconvolution techniques, we were able to determine a hyperfine level splitting in natural rubidium as small as 0.0014 cm−1 with an uncertainty of 0.0001 cm−1. We have measured the relative intensities and positions of 19 of the 20 hfs components of the two resonance lines, 7800 and 7974 Å, of natural Rb. From these data, we calculate isotope shifts σ87−σ85 = 0.00268 cm−1 for 52P32 and σ87′−σ85′ = 0.00259 cm−1 for 52P12.
Abstract. We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2 % for the D2 line at 16.5 ◦ C. PACS numbers: 32.70.-n, 32.70.Fw, 42.62.FiAbsolute Rb absorption 2 1.
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.