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

Jing Liu

Published Jan 1, 1989• 0 citations
OpenAlex

Abstract

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.

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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 γ\sb2\gamma\sb2γ\sb2 to the reservoir is larger than the lower-state decay rate γ\sb1\gamma\sb1γ\sb1. The width of the spike is 2γ\sb1\gamma\sb1γ\sb1 and the width of the wide resonance is determined by the total upper-level decay rate (2γ\sbsp2t\gamma\sbsp{2}{\rm t}γ\sbsp2t). 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.
In this paper we present theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrary strong pump field drives a given transition and a probe (weak) field drives the same transition. We have studied the influence of level degeneracy and field polarization on pump-probe and four-wave mixing signals. Our results indicate that for some closed systems (no population loss to the reservoir) it is possible to observe resonances that are characterized by the ground state width. Previous calculations indicate that for a nondegenerate system this resonance can appear only for an open system, the so-called "pressure induced resonances.”1 Our result, which contradicts this conclusion, can be understood by noting the fact that there are in general three irreducible tensor2 (in general) contributions to the line shape (K = 0 population, K = 1 orientation, and K = 2 alignment). Thus, even if the system is closed for the population it may still remain open for orientation or alignment; this effect is responsible for the narrow resonance. Specific calculations are presented for J = 1/2 → 1/2 and J = 1→2 transitions.
We discuss the effects of population pulsations on the spectral response of backward nearly degenerate four-wave mixing (NDFWM). We include the effects of state-specific decay and spontaneous emission on both two-level and inverted-v-type three-level systems. We compare the results with experiments in both the gas phase and the condensed phase that show ultranarrow resonances. In addition, we examine the response in the presence of strong pump fields. We show that in a simple two-level system, the NDFWM response results in an ac-Stark splitting of the spectral response, whereas in a simple three-level system with decay to a metastable state, a single narrow resonance is observed, which broadens in the presence of strong pumps.
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 report a series of measurements of the nearly degenerate four-wave-mixing response in atomic sodium in the presence of a helium buffer gas. The results show the line shape associated with both the ground-state and excited-state dynamics. The line shape evolves as a function of pressure from a dip at a pressure of 0 Torr to a spike at a few Torr due to the presence of collisions. The width of the spike is determined by residual Doppler broadening. At higher pressure (\ensuremath{\ge}10 Torr), the width of the spike is further narrowed below the residual Doppler width. The additional reduction is due to a form of Dicke narrowing associated with the dynamics of the lower- and upper-level excitations. The results are in qualitative agreement with a perturbation solution of the density-matrix equations which include the effects of velocity-changing collisions and state-changing collisions.
This paper presents perturbation calculations using the density matrix to describe the nearly degenerate four-wave-mixing spectral response in resonant systems subject to state-specific reservoir coupling. The calculations provide physical insight into the origin of narrow resonances observed in recent experimental work in atomic sodium and ultranarrow resonances in crystals. The calculations are for systems which are homogeneously broadened as well as systems which are inhomogeneously broadened due to velocity effects or random crystal fields. The calculations show that it is possible to eliminate the effects of either kind of broadening and measure the decay rate of the dipole coherence as well as the decay rates of both states of the transition. Furthermore, the calculations indicate that the method of cross-correlated optical fields which was used to eliminate the effects of laser jitter in longitudinal relaxation rate measurements could be extended to the measurements of slow dephasing rates in crystals.
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.