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Physical Review A

Effects of radiative decay in four-wave-mixing spectroscopy: Narrow resonances produced by nonconservation of population, alignment, and orientation

P. R. Berman, Duncan G. Steel, G. Khitrova, Jing Liu

Published Jul 1, 1988• 61 citations
Publisher

Abstract

We present experimental and theoretical results describing the presence of radiative-decay-induced narrow resonances in systems which do not conserve population, alignment, or orientation. We show how spectroscopic line-shape analysis of the nonlinear response can be used to determine all of the relaxation parameters characterizing a two-level atom.

DOI
10.1103/physreva.38.252

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The Journal of Chemical Physics•Mar 15, 1996•46 citations
We present experimental and theoretical results describing the presence of radiative-decay-induced narrow resonances in systems which do not conserve population, alignment, or orientation. We show how spectroscopic line-shape analysis of the nonlinear response can be used to determine all of the relaxation parameters characterizing a two-level atom.
We present results showing narrow resonant behavior in a collisionless four-wave mixing interaction in atomic sodium. In a two-level system the excited state radiatively decays to the ground state at rate ${\ensuremath{\gamma}}_{\mathrm{sp}}$, and the two states decay to the reservoir at ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$. If ${\ensuremath{\gamma}}_{1}$ and ${\ensuremath{\gamma}}_{2}$ equal the transit time, the resonance width is determined by the total decay rate out of state 2. In the presence of additional excited-state decay to another state, a narrow resonance with width ${\ensuremath{\gamma}}_{1}$ is oberved as a result of the effect of the additional excited-state decay on the magnitude of the ground-state probability amplitude.
We have measured the atomic lifetime of the argon 2 p 4 level by the laser-induced-fluorescence spectroscopy to be 30.5 ns. This contradicts the recent measurement using the high-frequency plused electron-beam excitation. We conjecture that, in their experiment, the radiation trapping not only affects the decay of the upper-level population but also relaxes the alignment initially produced by the electron-collision excitation in the upper-level population. Thus, the directly observed decay of the emission-line intensity is different from the decay of the upper-level population. We have observed the radiative relaxation of alignment on the neon 2 p 2 level which is a complementary effect to coherence narrowing.
The purpose of this research is to study the dynamic behavior of a resonant system using four-wave-mixing spectroscopy (FWM). From this study, we have obtained rich information about the FWM spectral response of systems which have different state-specific reservoir couplings. Atomic sodium (Na) is used as our model system. It is shown that the FWM spectral response depends strongly on how each level couples to the vacuum radiation field (through spontaneous emission). This effect is illustrated in the line shape obtained from a nearly degenerate FWM (NDFWM) experiment for a simple two-level system in Na. A narrow spike on top of a wide resonance is observed at zero pump-probe detuning (δ\deltaδ = 0) when the upper-state decay rate $\gamma\sb2$ to the reservoir is larger than the lower-state decay rate $\gamma\sb1$. The width of the spike is 2$\gamma\sb1$ and the width of the wide resonance is determined by the total upper-level decay rate (2$\gamma\sbsp{2}{\rm t}$). From the NDFWM spectrum, all the decay rates characterizing a two-level system may be measured directly. If magnetic substate degeneracy is included, the NDFWM line shape has contributions arising from orientation and alignment gratings, as well as from population gratings. For a two-level system closed with respect to population, the orientation or alignment gratings may contribute a narrow resonance at δ\deltaδ = 0 in the NDFWM response. These features are demonstrated for the first time by using NDFWM. Reservoir coupling can also occur through collisions with externally added gas. Collisions can cause a closed two-level system to become open, resulting in NDFWM spectra that show a narrow resonance at δ\deltaδ = 0 with a width below the residual Doppler width (Dicke narrowing). This is also the first time that Dicke narrowing has been observed in population terms. Finally, we present a calculation of the NDFWM response for strong degenerate pump fields and a weak probe field. We compare the differences between NDFWM spectra of closed two- and three-level systems in the presence of strong pumps.
It is shown that, as a result of the atomic recoil associated with the absorption and emission of radiation, resonances can appear in nonlinear spectroscopy. The theory is illustrated by calculating the line shapes associated with nearly degenerate four-wave mixing and pump-probe spectroscopy when laser fields interact with an ensemble of two-level atoms. The recoil-induced resonances should be observable for atoms cooled below the Doppler limit of laser cooling, and the line shapes may provide a means for measuring the velocity distribution of these cooled atoms.
We present a combined theoretical and experimental study on the effects of different population, orientation, and alignment relaxation rates in resonant four-wave mixing (RFWM). Signal generation in RFWM can be viewed as the formation of and scattering from laser-induced population, orientation, and alignment gratings. We show that the relative contributions from the upper-state and lower-state population, orientation, and alignment gratings to the observed output signal can be changed by varying the polarizations of the three input fields. A theory is developed to account for these changes in collisional environments where the three multipole moments of the total angular momentum distribution, i.e., the population, the orientation, and the alignment, relax unequally. This theory is applied to the OH radical in an atmospheric-pressure H2/O2/He flame for which we have measured the line profiles using high-resolution degenerate and nearly degenerate four-wave mixing. We find that orientation and alignment gratings relax more rapidly than population gratings for low rotational levels of OH in the presence of He but at essentially the same rate for high rotational levels. A discussion is presented of the importance of this effect in the interpretation of RFWM experiments.