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Frontiers in Optics

Frequency Shift in Two Symmetric Four-Wave Mixing in Rubidium Vapor

A. A. C. de Almeida, A. S. Alvarez, S. S. Vianna

Published Jan 1, 2020• 0 citations
Publisher

Abstract

Two symmetrical forward four-wave mixing processes in rubidium vapor present an opposing frequency shift. We model the effect with an anomalous refractive index due to the nonlinear interaction of the incident fields in the medium.
DOI
10.1364/fio.2020.jth4a.18

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Abstract We report experimental and theoretical results of two symmetrical signals of degenerate four-wave mixing generated in rubidium vapor. Both nonlinear signals are induced by two almost copropagating laser beams, with k ⃗ a and k ⃗ b wave-vectors, and detected simultaneously in the 2 k ⃗ a − k ⃗ b and 2 k ⃗ b − k ⃗ a directions. In each direction, we observe a single peak when the two beams are tuned on the closed transition 85 Rb 5 S 1/2 ( F = 3) → 5 P 3/2 ( F = 4). The excitation spectra reveal a small frequency separation between the two peaks, which is explained when propagation effects are taken into account. Furthermore, our theoretical analysis shows that a correct description of the frequency position of each peak is achieved with a variable refractive index for both lasers, in which the scanning laser experiences an anomalous window in the refractive index near resonance.
We present new results on the coherent control of a four-wave mixing signal in rubidium vapor involving Rydberg levels. By varying the relative polarizations of the laser beams responsible for the nonlinear process, we control atomic excitation routes and thus quantum interference in the medium. We observed interference fringes as a function of the relative polarizations and further developed a theoretical model based on the density-matrix formalism that is in very good agreement with our experimental results.
We investigate experimentally and theoretically nondegenerate four-wave mixing in rubidium vapor using a diamond configuration (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​ 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.
Multiphoton processes in dense atomic vapors such as four-wave mixing or coherent blue light generation are typically viewed from single-atom perspective. Here we study the surprisingly important effect of phase matching near two-photon resonances that arises due to spatial extent of the atomic medium within which the multiphoton process occurs. The non-unit refractive index of the atomic vapor may inhibit generation of light in nonlinear processes, significantly shift the efficiency maxima in frequencies and redirect emitted beam. We present these effects on an example of four-wave mixing in dense rubidium vapors in a double-ladder configuration. By deriving a simple theory that takes into account essential spatial properties of the process, we give precise predictions and confirm their validity in the experiment. The model allows us to improve on the geometry of the experiment and engineer more efficient four-wave mixing.