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Physical Review A

Nondegenerate four-wave mixing in rubidium vapor: The diamond configuration

F. E. Becerra, R. T. Willis, S. L. Rolston, Luis A. Orozco

Published Jul 23, 2008• 65 citations
Publisher

Abstract

We investigate experimentally and theoretically nondegenerate four-wave mixing in rubidium vapor using a diamond configuration ($5{S}_{1/2}$, $5{P}_{1/2}$, $5{P}_{3/2}$, and $6{S}_{1/2}$ levels). We model this process of three classical fields interacting with a four-level atomic system with the Schr\"odinger equation. The experimental results are in good agreement with theoretical predictions for the generated light as a function of detuning.

DOI
10.1103/physreva.78.013834

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We investigate the transient response of the generated light from four-wave mixing (FWM) in the diamond configuration using a step-down field excitation. The transients show fast decay times and oscillations that depend on the detunings and intensities of the fields. A simplified model taking into account the thermal motion of the atoms, propagation, absorption, and dispersion effects shows qualitative agreement with the experimental observations with the energy levels in rubidium (5S1/25{S}_{1/2}5S1/2​, 5P1/25{P}_{1/2}5P1/2​, 5P3/25{P}_{3/2}5P3/2​, and 6S1/26{S}_{1/2}6S1/2​). The atomic polarization comes from all the contributions of different velocity classes of atoms in the ensemble modifying dramatically the total transient behavior of the light from FWM.
We develop a model to calculate nonlinear polarization in a nondegenerate four-wave mixing in diamond configuration which includes the effects of hyperfine structure and Doppler broadening. We verify the model against the experiment with 52S1/2,52P3/2,52D3/25{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2},5{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2},5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2}52S1/2​,52P3/2​,52D3/2​, and 52P1/25{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}52P1/2​ levels of rubidium 85. Treating the multilevel atomic system as a combination of many four-level systems we are able to express the nonlinear susceptibility of a thermal ensemble in a low-intensity regime in terms of Voigt-type profiles and obtain an excellent conformity of theory and experiment within this complex system. The agreement is also satisfactory at high intensity and the analytical model correctly predicts the positions and shapes of resonances. Our results elucidate the physics of coherent interaction of light with atoms involving higher excited levels in vapors at room temperature, which is used in an increasing range of applications.
We present measurements of the resonance structure for nondegenerate four-wave mixing (4WM) in the diamond configuration in a warm atomic vapor of rubidium. We show that a narrow sub-Doppler feature exists and can be understood as a result of velocity-class selection. We measure the efficiency of the 4WM process and show it to be on the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Our observations are consistent with the results of a theoretical treatment based on the semiclassical Maxwell-Bloch equations for the system with the appropriate coupling values derived from the experimental values in Rb.