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Physical Review Letters

Decay induced narrow resonances in backward nearly degenerate four-wave mixing spectroscopy

Jing Liu, J. T. Remillard, Duncan G. Steel

Published Aug 17, 1987• 8 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.59.779

Related papers

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

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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 ($\delta$ = 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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Collisionless extraresonances (ER) in degenerate four-wave mixing (DFWM) are predicted when the upper state \ensuremath{\Vert}b〉 of the \ensuremath{\Vert}a〉\ensuremath{\rightarrow}\ensuremath{\Vert}b〉 transition, excited by near-resonant incident laser beams, decays to the lower state \ensuremath{\Vert}a〉 both directly (\ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉) and via one or two intermediate states: \ensuremath{\Vert}b〉\ensuremath{\rightleftarrows}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉 or \ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}c〉\ensuremath{\rightarrow}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉. The width of the new ER, which depends on the relative decay rates in the cascade process, may be very narrow leading to very strong DFWM signals. Dephasing collisions affect the intensity of the new ER and also produce the usual, pressure-induced ER.

Physical Review A•Mar 1, 1986•14 citations
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 \ensuremathγsp{\ensuremath{\gamma}}_{\mathrm{sp}}\ensuremathγsp​, and the two states decay to the reservoir at \ensuremathγ1{\ensuremath{\gamma}}_{1}\ensuremathγ1​ and \ensuremathγ2{\ensuremath{\gamma}}_{2}\ensuremathγ2​. If \ensuremathγ1{\ensuremath{\gamma}}_{1}\ensuremathγ1​ and \ensuremathγ2{\ensuremath{\gamma}}_{2}\ensuremathγ2​ 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 \ensuremathγ1{\ensuremath{\gamma}}_{1}\ensuremathγ1​ is oberved as a result of the effect of the additional excited-state decay on the magnitude of the ground-state probability amplitude.
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.
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.
Collisionless extraresonances (ER) in degenerate four-wave mixing (DFWM) are predicted when the upper state \ensuremath{\Vert}b〉 of the \ensuremath{\Vert}a〉\ensuremath{\rightarrow}\ensuremath{\Vert}b〉 transition, excited by near-resonant incident laser beams, decays to the lower state \ensuremath{\Vert}a〉 both directly (\ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉) and via one or two intermediate states: \ensuremath{\Vert}b〉\ensuremath{\rightleftarrows}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉 or \ensuremath{\Vert}b〉\ensuremath{\rightarrow}\ensuremath{\Vert}c〉\ensuremath{\rightarrow}\ensuremath{\Vert}d〉\ensuremath{\rightarrow}\ensuremath{\Vert}a〉. The width of the new ER, which depends on the relative decay rates in the cascade process, may be very narrow leading to very strong DFWM signals. Dephasing collisions affect the intensity of the new ER and also produce the usual, pressure-induced ER.