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Physical Review A

Sub-Doppler resolution in strongly saturated copropagating degenerate four-wave mixing

Yehiam Prior, E. Yarkoni

Published Dec 1, 1983• 12 citations
Publisher

Abstract

The observation of a new type of saturation effects in degenerate four-wave mixing in Na vapor is reported. The experimental configuration is neither counterpropagating nor velocity selective, and yet sub-Doppler high-resolution lines are observed at the atomic-transition frequencies, and at the weighted center of a Doppler-broadened distribution. These new features are the result of an interplay between absorption and saturation, and the inhomogeneous broadening is essential for their existence.

DOI
10.1103/physreva.28.3689

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Xuemei Cheng, Haowei Chen, Jian Wang +4 more

Resolutions of degenerate four-wave mixing with forward and phase-conjugate configurations (FDFWM and PCDFWM) are investigated and compared theoretically and experimentally in hot rubidium (Rb) atomic vapor. The theoretical simulations indicate that PCDFWM is of much higher resolution than FDFWM. The resolution of PCDFWM is less dependent on Doppler broadening. The experimental results are in good agreement with the theoretical expectation. PCDFWM can resolve the hyperfine transitions and crossover resonances of 87Rb which cannot be achieved by FDFWM. Additionally, with sample temperature increasing, the linewidth of FDFWM spectrum obviously broadens. In comparison, no obvious broadening can be observed in the PCDFWM spectrum.

Chinese Physics Letters•Jul 1, 2012•2 citations
The observation of a new type of saturation effects in degenerate four-wave mixing in Na vapor is reported. The experimental configuration is neither counterpropagating nor velocity selective, and yet sub-Doppler high-resolution lines are observed at the atomic-transition frequencies, and at the weighted center of a Doppler-broadened distribution. These new features are the result of an interplay between absorption and saturation, and the inhomogeneous broadening is essential for their existence.
We present a theoretical study of phase-conjugate (PC) emission by backward degenerate four-wave mixing (DFWM) processes in a resonant gas medium. In this study, high-intensity (pump) saturation and Doppler broadening are simultaneously taken into account. We develop a general formalism to deal with the saturation effects in the case of a three-level atom (with degenerate frequencies) and obtain analytical expressions of the PC field amplitude (after integration over the velocity distribution) under the following conditions: (1) the probe beam and one of the pump beams have intensities weak enough to be treated at the lowest perturbation order, whereas the other pump intensity is arbitrarily high; (2) the probe crosses the standing pump wave at grazing incidence. It is shown that the saturation induced by the forward pump (copropagating with the probe beam) leads to entirely different behavior of the nonlinear susceptibility from that induced by the backward pump (counterpropagating with the probe beam). This saturation anisotropy is specific to the inhomogeneous broadening of the gas medium, which is also responsible for the frequency splitting experimentally observed in the intensity line shape of the PC emission for large pump intensities. At saturation, this splitting is theoretically shown to be proportional to the Rabi frequency, with a proportionality coefficient critically dependent on the relaxation processes; in the case of a single-relaxation model, the splitting is equal to 1.5 times the Rabi frequency. The PC intensity line shape is demonstrated to be of dispersive origin in the case of backward saturation, whereas for forward saturation, narrow structures are predicted in both real and imaginary parts of the nonlinear susceptibility, also leading to the intensity line-shape splitting. One also finds that the reflectivity of PC mirrors based on resonant DFWM strongly depends on the origin of the saturation. For a saturating forward pump, the PC emission intensity tends toward zero with increasing pump intensities, and it reaches a finite (nonzero) limit in the case of backward saturation. Most of these predictions have been observed experimentally [ BlochD., Phys. Rev. Lett.49, 719 ( 1982)].
We present in this paper a theory of the saturation effects in degenerate four-wave mixing which makes use of the dressed-atom method. We mainly study the case of a Doppler-broadened line, but several results can be applied to the case of nearly degenerate four-wave mixing for a Doppler-free medium. We show that a close relationship does exist between the two problems : the generated beam is mainly created when the detuning between two incident beams is equal to the Rabi frequency. In the degenerate case, this condition is fulfilled by two velocity groups because of the Doppler shift. We analytically calculate the lineshapes for two-level atoms in the case of forward saturation (the intense pump beam propagates in the same direction than the probe beam) and in the case of backward saturation (the intense pump beam and the probe beam propagate in opposite directions). We also study collisional effects and the influence of the intensity of the weak pump beam when perturbation theory can no longer be applied.
Resolutions of degenerate four-wave mixing with forward and phase-conjugate configurations (FDFWM and PCDFWM) are investigated and compared theoretically and experimentally in hot rubidium (Rb) atomic vapor. The theoretical simulations indicate that PCDFWM is of much higher resolution than FDFWM. The resolution of PCDFWM is less dependent on Doppler broadening. The experimental results are in good agreement with the theoretical expectation. PCDFWM can resolve the hyperfine transitions and crossover resonances of 87Rb which cannot be achieved by FDFWM. Additionally, with sample temperature increasing, the linewidth of FDFWM spectrum obviously broadens. In comparison, no obvious broadening can be observed in the PCDFWM spectrum.