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Optics Letters

Nondegenerate four-wave mixing in a double-? system under the influence of coherent population trapping

Baolong Lü, W. H. Burkett, Min Xiao

Published May 15, 1998• 144 citations
Publisher

Abstract

Nondegenerate four-wave mixing (NDFWM) in a double-L system of Rb atomic vapor was achieved for collinear pump fields. By comparison of different pump-probe configurations, direct experimental evidence of influence of coherent population trapping on the output power of the NDFWM signal was established. A maximal efficiency for generating the NDFWM signal exists for a moderate pump power in this double-L system.

DOI
10.1364/ol.23.000804

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The atomic coherence effect can be used in enhancing the efficiencies of nonlinear optical processes. Particularly, nondegenerate four-wave mixing (NDFWM) in multilevel systems has recently gained attention in connection with the advantage of using coherent population trapping (CPT) or electromagnetically induced transparency (EIT) to enhance the efficiency of generated signals. Generally speaking, linear absorption competes with the nonlinear signal generation at the exact one-photon resonance condition. However, the linear absorption can, in principle, be reduced or even eliminated by preparing the system in the CPT or EIT state. We report experimental demonstrations of NDFWM in several multi-level configurations in rubidium atomic vapor. In one of the double-/spl Lambda/ systems an unusual behavior of signal output power as a function of pump power, i.e. a maximum in the generated signal power is reached as the pump power increases, is experimentally observed. By comparing with several related /spl Lambda/ and double-/spl Lambda/ systems, we have concluded that CPT is the mechanism for this interesting effect.

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Acta Sinica Quantum Optica•Jan 1, 2010•0 citations
Nondegenerate four-wave mixing (NDFWM) in a double-L system of Rb atomic vapor was achieved for collinear pump fields. By comparison of different pump-probe configurations, direct experimental evidence of influence of coherent population trapping on the output power of the NDFWM signal was established. A maximal efficiency for generating the NDFWM signal exists for a moderate pump power in this double-L system.
The atomic coherence effect can be used in enhancing the efficiencies of nonlinear optical processes. Particularly, nondegenerate four-wave mixing (NDFWM) in multilevel systems has recently gained attention in connection with the advantage of using coherent population trapping (CPT) or electromagnetically induced transparency (EIT) to enhance the efficiency of generated signals. Generally speaking, linear absorption competes with the nonlinear signal generation at the exact one-photon resonance condition. However, the linear absorption can, in principle, be reduced or even eliminated by preparing the system in the CPT or EIT state. We report experimental demonstrations of NDFWM in several multi-level configurations in rubidium atomic vapor. In one of the double-/spl Lambda/ systems an unusual behavior of signal output power as a function of pump power, i.e. a maximum in the generated signal power is reached as the pump power increases, is experimentally observed. By comparing with several related /spl Lambda/ and double-/spl Lambda/ systems, we have concluded that CPT is the mechanism for this interesting effect.
The theory of nondegenerate four-wave mixing (NDFWM) in semiconductor lasers and amplifiers is presented with particular emphasis on the physical processes that lead to population pulsations. In the case of nearly degenerate four-wave mixing, modulation of the carrier density at the beat frequency Ω of the pump and probe waves creates a dynamic population grating whose effectiveness is governed by the spontaneous carrier lifetime τs. Such a grating affects both the gain and the refractive index of the probe wave. In particular, the probe gain exhibits features analogous to those observed in a detuned atomic system arising from the optical Stark effect. Both the gain grating and the index grating contribute to NDFWM, with the dominant contribution coming from the index grating. For detunings such that Ωτs ≫ 1, population pulsations correspond to modulation of the intraband population arising from spectral hole burning. Our results show that NDFWM is then limited by the phase-mismatch effects governed by the transit time τ rather than by the intraband population-relaxation time T1. Significant NDFWM is expected to occur for detunings up to about 300 GHz for typical transit-time values of 3 psec in semiconductor lasers.
By applying a strong coupling field between a lower state and the upper state of an allowed transition to ground, an enhancement of nondegenerate four wave mixing (NDFWM) with a resonantly enhanced third-order nonlinear susceptibility in a rare-earth doped fiber can be obtained. We have derived an expression for the third-order nonlinear susceptibility using quantum theory and discussed the conversion efficiency for NDFWM. The theoretical result shows that the conversion efficiency has a maximum value while the third-order nonlinear susceptibility shows constructive interference at the Rabi frequency Ω 23 = ±√Γ 2 Γ 3 . On account of phase-mismatch, the frequency conversion efficiency has a maximum value over a certain small range of frequency separation (such as 0 < Δ f < 30 GHz at the wavelength λ c = 1.55 μm), and the frequency conversion range increases with increase of the third-order nonlinear susceptibility.
We report an experimental observation of the enhancement of nondegenerate four-wave mixing (NDFWM) based on electromagnetically induced transparency (EIT) in a lambda-type three-level system of rubidium atoms. We measured both the linear susceptibility Im chi(D)((1)) (absorption) and the third-order nonlinear coefficient chi(D)((3)) separately for the NDFWM process at a low atomic density. We found that, owing to the EIT effect, the linear absorption term Im chi(D)((1)) is greatly reduced, while the nonlinear generation term chi(D)((3)) is resonantly enhanced, permitting us to observe a significant enhancement of the NDFWM signal in an optically dense medium.
We have observed four-wave mixing (FWM) of weak pumping in a resonance double-Λ system for the 5S1/2- 5P1/2transition of87Rb atoms. When three beams (CPT1, CPT2 and pump) were co-propagated in the double-Λ configuration composed of the common excited state 5P1/2(Fe=2) and the two ground state 5S1/2(Fg=1 and 2), we directly measured the generated FWM signal filtering the three beams using polarizer and etalon filters. The spectral width of FWM signal was measured to be ~10 kHz under the condition of coherent population trapping (CPT). Dependence of FWM signals on the intensities of the two beams related CPT and pump beam was investigated in detail.
The impact of the pump polarization during the Rb atom degenerate four-wave mixing process on the degenerate four-wave mixing signals is studied.In the experiment,a pump light and the probe light transmitted in the same direction into the air chamber Rb atoms,and the other pump light propagated through the atoms in the opposite direction.Then,by changing the polarization of the two pump lights,the four-wave mixing signal is observed.The result shows that when the two pump light polarization is parallel,a strong four-wave mixing signal can be observed.While the two pump light polarization is orthogonal to each other,the four-wave mixing signal disappear.The theoretical analysis indicates that the population grating induced by the pump beam interference is the physics mechanism of the degenerate four-wave mixing signal.