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arXiv:1107.5768

Enhanced four-wave mixing via crossover resonance in cesium vapor

Thierry Passerat de Silans, C. S. L. Goncalves, D. Felinto, J. W. R. Tabosa

Published Jul 28, 2011• 0 citations
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Abstract

We report on the observation of enhanced four-wave mixing via crossover resonance in a Doppler broadened cesium vapor. Using a single laser frequency, a resonant parametric process in a double-$Λ$ level configuration is directly excited for a specific velocity class. We investigate this process in different saturation regimes and demonstrate the possibility of generating intensity correlation and anti-correlation between the probe and conjugate beams. A simple theoretical model is developed that accounts qualitatively well to the observed results.

DOI
10.48550/arxiv.1107.5768

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We report on the observation of enhanced four-wave mixing via crossover resonance in a Doppler broadened cesium vapor. Using a single laser frequency, a resonant parametric process in a double-ΛΛΛ level configuration is directly excited for a specific velocity class. We investigate this process in different saturation regimes and demonstrate the possibility of generating intensity correlation and anti-correlation between the probe and conjugate beams. A simple theoretical model is developed that accounts qualitatively well to the observed results.
We report on the observation of enhanced four-wave mixing via crossover resonance in a Doppler-broadened cesium vapor. Using a single laser frequency, a resonant parametric process in a double-Λ level configuration is directly excited for a specific velocity class. We investigate this process in different saturation regimes and demonstrate the possibility of generating intensity correlation and anticorrelation between the probe and conjugate beams. A simple theoretical model is developed that accounts qualitatively well to the observed results.
The evolution of enhanced four-wave mixing based on Raman coherence as the probe intensity increases is observed experimentally in an 85 R b atomic vapor system. We propose that for a Doppler-broadened Λ -type level system, the generated anti-Stokes field from one-photon resonance will be suppressed by the dressed-states resonance and can be controlled by the probe intensity, which influences the effective transverse relaxation rate of Raman coherence. When the probe field is not so weak, the double resonance for dressed states will greatly suppress the anti-Stokes emission at the central frequency, and the signal peak will be split. We show that this phenomenon is a result of the destructive polarization interference between atoms with different velocities from the two types of resonance. Based on our model, we present a new, to the best of our knowledge, interpretation of four-wave mixing enhancement in the conventional Λ -type electromagnetically induced transparency system.
An influence of nonlinear interference processes at quantum transitions in strong resonance electromagnetic fields on absorption, amplification and refractive indices as well as on four-wave mixing processes is investigated. Doppler broadening of the coupled transitions, incoherent excitation, relaxation processes, as well as power saturation processes associated with the coupled levels are taken into account. Both closed (ground state is involved) and open (only excited states are involved) energy level configurations are considered. Common expressions are obtained which allow to analyze the optical characteristics (including gain without inversion and enhanced refractive index at vanishing absorption) for various V, (Lambda) and H configurations of interfering transitions by a simple substitution of parameters. Similar expressions for resonant four-wave mixing (FWM) in Raman configurations are derived too. Crucial role of Doppler broadening is shown. Theory is applied for numerical analysis of some recent and potential experiments.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.
In this work, we present a set of experiments involving four-wave mixing processes in rubidium atoms. We employ several experimental configurations exploring two- and three-level systems in cascade or Λ configurations, all of which are in a copropagating geometry, to investigate different physical phenomena present in each scenario. In the first experiment, we combine a cw diode laser and a 1 GHz femtosecond pulse train to generate coherent blue light through the four-wave mixing process in hot rubidium vapor. The generated coherent signal is analyzed by scanning either the diode frequency or the repetition rate of the frequency comb. In both cases, the cw laser induces an Autler- Townes splitting with a wide separation in the doublet structure due to the configuration of copropagating fields. To model these results, we employ the density matrix formalism to write the Bloch equations and solve them numerically. The solutions allow us to explore other cases beyond those involving our experimental setup, comparing the response of the upper-level population and the generated signal coherence for homogeneously and non-homogeneously broadened systems. Moreover, in this same experiment, we also observed an unexpected interference effect between excitation routes of the four-wave mixing process when the repetition rate of the pulse train is scanned. The theoretical model demonstrates that the interfering effect appears only when the repetition rate is carefully chosen to produce a pair of modes of the frequency comb resonant with both one- and two-photon transitions for the same atomic velocity group. In the second experiment, still with a hot rubidium vapor, we explore two symmetrical degenerate four- wave mixing signals induced by two almost copropagating laser beams, with~ka and~kb wave-vectors, and detected simultaneously in the 2~ka −~kb and 2~kb −~ka directions. Each spectrum has a single peak with a short frequency separation between them, which our model indicates is due to the nonlinear behavior of the refractive indexes, a consequence of the high intensity of both input fields. Finally, we use the same experimental setup for the two symmetrical signals to study the field intensity fluctuations of the degenerate four-wave mixing signals and the transmission signals. In this case, the sample is an ensemble of cold rubidium atoms in a magneto-optical trap. There is an intensity- intensity cross-correlation between the signals due to the resonant phase-noise to amplitude-noise conversion. In this type of cold system, we can neglect the Doppler- broadening, allowing a straightforward study of the dependency of the correlations on the laser detuning. In these measurements, we observe a type of oscillation in the correlation curves that the theoretical model indicates to be connected with Rabi oscillations, revealed by the fluctuations long after the transient period.
We investigate Degenerate Four-Wave Mixing (DFWM) in a thermal cesium vapor using a nearly collinear, co-propagating geometry under deeply non-perturbative conditions (I≈150Is). While standard theoretical treatments that coherently average over the atomic velocity distribution predict a pronounced spectral dip at resonance, our experimental measurements consistently exhibit a single, smooth, Doppler-broadened profile. To resolve this discrepancy, we develop a non-perturbative theoretical model based on a spatial harmonic expansion of the optical Bloch equations, replacing the standard coherent integration with an incoherent summation over velocity classes. By combining this incoherent velocity averaging with a Beer-Lambert attenuation correction, our model accurately reproduces both the experimentally observed smooth spectral line shape and the sublinear power dependence characteristic of highly saturated multi-photon processes. These results suggest that non-homogeneous spatial dephasing processes in dense, highly saturated thermal media play an important role in the dynamics of the interaction.