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Optics Letters

Level-splitting effects in resonant four-wave mixing

Sergei A Babin, Sergey I. Kablukov, U. Hinze, E. Tiemann, B. Wellegehausen

Published Jan 15, 2001• 17 citations
Publisher

Abstract

Resonant spectral structures of four-wave mixing (FWM) in molecular sodium are investigated. For a double- ? configuration with strong-weak-strong-weak fields, split components in FWM spectra induced by the strong pump fields are observed. It is shown that the split components merge into a single peak for a certain ratio of the strong field intensities. A correlation between the level-splitting effects and the saturation behavior of the FWM signal is experimentally demonstrated.

DOI
10.1364/ol.26.000081

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Resonant spectral structures of four-wave mixing (FWM) in molecular sodium are investigated. For a double- ? configuration with strong-weak-strong-weak fields, split components in FWM spectra induced by the strong pump fields are observed. It is shown that the split components merge into a single peak for a certain ratio of the strong field intensities. A correlation between the level-splitting effects and the saturation behavior of the FWM signal is experimentally demonstrated.
Investigations of resonant spectral structures of four wave mixing (FWM) in molecular sodium are presented. For a double- (Lambda) configuration with strong-weak-strong-weak fields, split components in FWM spectra induced by the strong pump fields are observed. It is shown, that the split components merge into a single peak for a certain ratio of the strong field intensities. A strong correlation between the level splitting effect and saturation behavior of the FWM-signal is experimentally demonstrated.
The explicit solution is obtained for Raman four-wave mixing ω4=ω1−ω2+ω3\omega_4=\omega_1-\omega_2+\omega_3ω4​=ω1​−ω2​+ω3​ of two strong fields E1,E3E_1, E_3E1​,E3​ and two weak fields E2,E4E_2, E_4E2​,E4​ in a four-level system with the large Doppler broadening. The resonance of the mixing coefficient vs intensity is found near equal Rabi frequencies of strong fields and interpreted as an intersection of quasi-energy levels. Up to 6 peaks appear in the dependence of conversion coefficient on the detuning of the probe field. An unexpected additional pair of peaks is a result of averaging over velocities and disappears at low temperature. The effects allow explaining saturation behavior in recent experiments on the mixing in sodium molecular vapor.
A nonperturbative semiclassical theory is presented for the treatment of four-wave mixing (FWM) in a four-level system. This treatment is based on a transformation to a generalized rotating frame followed by a numerical diagonalization of the resulting time-independent Hamiltonian. For strong fields, all resonant frequencies are shifted from the atomic (molecular) frequencies. Lines are split up in a way similar to the ac Stark effect for a two-level system, and for even stronger fields, the effect of stirring is observed for the first time in four-wave mixing. In addition, a new extra resonance appears which is induced by the saturating field. This field-induced resonance is the new member in the family of extra resonances (pressure induced, or stochastic fluctuation induced), and it should be observed whenever saturating fields interact with a multilevel atomic or molecular system.
An explicit solution is obtained for the four-wave mixing ω 4 =ω 1 −ω 2 +ω 3 of two strong fields E 1 , E 3 and two weak fields E 2 , E 4 in a four-level system with large Doppler broadening. Resonance of the intensity dependence of the mixing coefficient is found around equal Rabi frequencies, E 1 · d 1 = E 3 · d 3 , where d 1,3 are the dipole moments of the corresponding transitions. The effect is interpreted as a crossing of quasi-energy levels. Up to 6 peaks appear in the dependence of the conversion coefficient on the detuning of the probe field E 2 . The unexpected additional pair of peaks is a consequence of averaging over velocities. The results permit interpretation of the saturation behavior found in recent experiments on mixing in sodium vapor.
A nonperturbative theoretical study of four-wave-mixing processes in four-level systems is presented. Using the density-matrix formalism, numerical results are obtained for two arbitrarily intense pump fields with the third field a weak probe. The fourth wave, radiated by the system, is obtained analytically for some special cases. We find, for different frequency detunings, Rabi frequencies, and relaxation rates that the line shapes exhibit: (i) dynamic Stark splitting and shifting, and merging of resonances; (ii) power broadening with two-photon antiresonance behavior resulting from a destructive interference between different contributions to the optical polarization; and (iii) extra resonances induced by field intensities and saturation processes.
Degenerate four-wave mixing (DFWM) line shapes are investigated in sodium vapor near the D(2) resonance line using nearly Fourier-transform-limited pulses. At low pump intensities sub-Doppler resolution is obtained. When the Rabi frequency associated with the pump intensity becomes comparable with the ground-state hyperfine frequency separation of sodium, each component of the double-peaked DFWM spectrum splits further into two components. An adiabatic-following model explains the near-resonant intensity dependence of the DFWM signal. A qualitative explanation of the observed splitting is also given.