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Physical Review A

High-resolution studies of collision-induced population grating resonances in optical four-wave mixing in sodium vapor

Lewis J. Rothberg, N. Bloembergen

Published Nov 1, 1984• 36 citations
Publisher

Abstract

Optical four-wave mixing resonances in sodium vapor induced by collisions with inert buffer gases (He, Ar, Xe, ${\mathrm{N}}_{2}$) are characterized at high resolution ( 5 MHz) using lasers tuned near the $D$ lines of Na. These resonances are interpreted in terms of coherent scattering from a population grating established by collisional absorption of the incident radiation. The roles of homogeneous and inhomogeneous contributions to the resonance line shapes are clarified. The line shapes exhibit structure sharper than the predicted linewidth, that characteristic of the $3P$-to-$3S$ transition rate. We show that this is caused by collision-induced optical pumping which introduces the ground-state lifetime into the grating relaxation physics. These long-lived gratings are exemplified dramatically by experiments in the presence of ${\mathrm{N}}_{2}$ which collisionally quenches the Na $3P$ states. Similar results are obtained in Xe where it is argued that excimer formation with the $3P$ states plays a role in the population dynamics. Model calculations of the effects of sodium level degeneracy on the grating dynamics are presented to support these conclusions. Finally we present data illustrating interference between the collision-induced population grating resonances detailed here and collision-induced coherent Raman resonances between Zeeman sublevels of the ground state.

DOI
10.1103/physreva.30.2327

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Effects of state-specific reservoir coupling on four-wave-mixing spectroscopy.

Jing Liu

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 ($\delta$ = 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 $\delta$ = 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 $\delta$ = 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.

•Jan 1, 1989•0 citations
Optical four-wave mixing resonances in sodium vapor induced by collisions with inert buffer gases (He, Ar, Xe, N2{\mathrm{N}}_{2}N2​) are characterized at high resolution ( 5 MHz) using lasers tuned near the DDD lines of Na. These resonances are interpreted in terms of coherent scattering from a population grating established by collisional absorption of the incident radiation. The roles of homogeneous and inhomogeneous contributions to the resonance line shapes are clarified. The line shapes exhibit structure sharper than the predicted linewidth, that characteristic of the 3P3P3P-to-3S3S3S transition rate. We show that this is caused by collision-induced optical pumping which introduces the ground-state lifetime into the grating relaxation physics. These long-lived gratings are exemplified dramatically by experiments in the presence of N2{\mathrm{N}}_{2}N2​ which collisionally quenches the Na 3P3P3P states. Similar results are obtained in Xe where it is argued that excimer formation with the 3P3P3P states plays a role in the population dynamics. Model calculations of the effects of sodium level degeneracy on the grating dynamics are presented to support these conclusions. Finally we present data illustrating interference between the collision-induced population grating resonances detailed here and collision-induced coherent Raman resonances between Zeeman sublevels of the ground state.
Near-resonant four-wave light mixing in Na vapor with inert buffer gases reveals collision-induced coherences when the difference frequency between two incident light beams equals the hyperfine splitting or the Zeeman splitting between two states of the 32S3^{2}S32S ground-state manifold. The Doppler broadening of the corresponding resonances decreases with increasing buffer-gas pressure. The width of the resonances becomes significantly narrower than the spontaneous linewidth of the near-resonant intermediate state and is determined by spin-exchange collisions between ground-state atoms. The dependence of the intensity of these collision-induced resonances on buffer-gas pressure and detuning from one-photon resonances is measured. Selection rules for various polarizations of the incident light fields and directions of an externally applied magnetic field are established.
Collision-enhanced Hanle resonances in the 3 2S1/2^{2}S_{1/2}2S1/2​ electronic ground state of Na atoms have been studied in a phase-conjugate four-wave light-mixing geometry. Narrow resonances in zero magnetic field have been observed at very high inert-buffer-gas pressures, with a width of 21 mG, or less than 10 kHz, full width at half-maximum. The intensity and the width of these resonances has been studied as a function of buffer-gas pressure, of alkali-metal vapor pressure, of detuning from the D1{D}_{1}D1​ and D2{D}_{2}D2​ Na resonances, and of the intensity of the incident light beams. Saturation phenomena and power broadening are observed. The results are explained theoretically in terms of transversely pumped optical gratings. The equivalence of this description with collision-induced coherence gratings in the limit of low light intensities is demonstrated.
We present experimental data showing destruction of degenerate four-wave-mixing signals by collisions at extremely low pressures of added buffer gases (\ensuremath{\sim}100 mtorr). These experiments are performed on the $3s^{2}S_{\frac{1}{2}}(F=2)\ensuremath{-}3p^{2}P_{\frac{3}{2}}(F=3)$ transition of the D2{D}_{2}D2​ line in atomic sodium for which, in the absence of buffer gases, the lower state is not optically pumped to the 3s2S12(F=1)3s^{2}S_{\frac{1}{2}}(F=1)3s2S21​​(F=1) ground state. However, using a simple rate equation model we are able to qualitatively explain the observed behavior by showing that state-changing collisions have the effect of generating a collision-induced optical pumping. This transfers the F=2F=2F=2 ground-state population to the F=1F=1F=1 ground state, thus reducing the density of atoms available for generating a signal.
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.