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Optics Letters

Extra resonances in degenerate four-wave mixing triggered by pressure-induced decay of the lower state

A. D. Wilson‐Gordon, Harry Friedmann

Published Dec 1, 1983• 20 citations
Publisher

Abstract

By using the Schenzle-Brewer model, in which the ground state of a two-level system also has a finite lifetime, it is shown that two pressure-induced extraresonant degenerate four-wave mixing signals are obtained. The first extra resonance is similar to that predicted and observed by Bogdan et al. [Opt. Lett. 6, 82, 348 (1981)]. It is characterized by a linewidth equal to the inverse lifetime of the upper state and appears only in the presence of collisional redistribution. The second extra resonance is characterized by a linewidth equal to the inverse lifetime of the ground state and does not depend on collisional redistribution for its appearance.

DOI
10.1364/ol.8.000617

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Extraresonances in degenerate four-wave mixing induced by sequential decay

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Collisionally induced coherent signals and collisional redistribution

M. Dagenais

It is demonstrated that, in the presence of collisions and for nonresonant lasers, it is energetically possible to access resonantly excited states and induce a coherence between the states. This situation cannot arise in the absence of collisions if the starting state does not decay. This explains why, when collisions are introduced, a new signal can be generated in a wave-mixing type of experiment. The collisionally induced generation of a coherent signal is intimately related to the process of collisional redistribution. It is shown that all the collisionally induced coherent signals that have been reported up to now involve putting real populations in the excited states. This fact has not always been fully appreciated. No resonance between unpopulated states can exist. The time dependence of these new coherent signals is briefly discussed. In the case of a Raman resonance between equally populated states, it is pointed out that new coherent pathways of equal importance should be considered for explaining the experimental results. A new pressure-induced signal in four-wave mixing is also discussed. It is called "collisionally triggered two-photon quasiresonant coherent signal."

Physical Review A•Aug 1, 1982•23 citations
By using the Schenzle-Brewer model, in which the ground state of a two-level system also has a finite lifetime, it is shown that two pressure-induced extraresonant degenerate four-wave mixing signals are obtained. The first extra resonance is similar to that predicted and observed by Bogdan et al. [Opt. Lett. 6, 82, 348 (1981)]. It is characterized by a linewidth equal to the inverse lifetime of the upper state and appears only in the presence of collisional redistribution. The second extra resonance is characterized by a linewidth equal to the inverse lifetime of the ground state and does not depend on collisional redistribution for its appearance.
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.
It is shown that intense collisionless Rayleigh-type extraresonant signals in degenerate four-wave mixing (DFWM) can be obtained when the $| a 〉\ensuremath{\rightarrow}| b 〉$ transition which produces the DFWM signal is coupled to another transition ($ | a 〉\ensuremath{\rightarrow}| d 〉$) which is excited near-resonantly by an additional laser beam. Two effects contribute to the Rayleigh-type extraresonant signal at ${\ensuremath{\omega}}_{2}={\ensuremath{\omega}}_{1}$. The first effect is resonance-enhanced three-photon scattering (TPS), which leads to the population of state ∣b〉| b 〉∣b〉 and consequently contributes a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$, the off-diagonal density-matrix element, which is characterized by the linewidth (1T1)ba{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}(T1​1​)ba​, the inverse lifetime of the state ∣b〉| b 〉∣b〉. The second effect derives from the effective lifetime acquired by the ground state ∣a〉| a 〉∣a〉 due to its strong coupling to state ∣d〉| d 〉∣d〉. This leads to a term in ${\ensuremath{\rho}}_{\mathrm{ba}}$ characterized by a linewidth 12(1T1)da\frac{1}{2}{(\frac{1}{{T}_{1}})}_{\mathrm{da}}21​(T1​1​)da​, which is half the inverse lifetime of the state ∣d〉| d 〉∣d〉. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\gg}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the TPS effect dominates and the extraresonant DFWM signal is narrow and intense. When ${(\frac{1}{{T}_{1}})}_{\mathrm{da}}\ensuremath{\simeq}{(\frac{1}{{T}_{1}})}_{\mathrm{ba}}$, the signal is less intense and interference between the two effects is evident.
A theory of four-wave mixing including effects of velocity-changing collisions is presented. Three fields with frequencies \ensuremath{\omega}, \ensuremath{\omega}, and \ensuremath{\omega}+\ensuremath{\delta} are incident on a vapor of ``two-level'' atoms having upper state b and lower state a. Two of the fields are counterpropagating and the third (of frequency \ensuremath{\omega}+\ensuremath{\delta}) makes a small angle with one of the others. The frequency \ensuremath{\omega} is a nearly resonant (inside the Doppler width) with the a-b transition frequency. The phase-conjugate signal emitted at frequency \ensuremath{\omega}-\ensuremath{\delta} is calculated as a function of \ensuremath{\delta}. Using a simple collision model in which collisions are phase interrupting in their effect on atomic coherence and velocity-changing in their effect on level populations, we discuss the conditions under which resonances characterized by the upper or lower radiative and collision rates can be observed. Assuming that the total (a+b) state population is conserved in the absence of collisions, it is shown that velocity-changing collisions can ``open'' the system and lead to a resonance characterized by the lower-state width (convoluted with the residual Doppler width). With increasing pressure, the width of this induced resonance structure decreases monotonically. For sufficiently high pressure, the collisional redistribution of velocity classes is complete---the system ``recloses'' and the narrow resonance disappears. The interplay of the collision-induced opening, line narrowing, and reclosing of the system is discussed, as is the relationship of these narrow resonances to the so-called pressure-induced extra resonances of Bloembergen and co-workers [Indian J. Pure Appl. Phys. 16, 151 (1978); Phys. Rev. Lett. 46, 111 (1981)].
Using both a bare-atom and dressed-atom picture of atom-field interactions, we present a theory of the pressure-induced resonances that can arise when four radiation fields interact with a three-level quantum system. The four fields drive two coupled atomic transitions which share a common level, the levels being arranged in a ``ladder'' scheme. As the field frequencies are varied, certain resonant structures in the excitation spectrum of the upper state population appear only in the presence of collisions. The resonant structures result from processes that have been referred to in the past as collisionally aided radiative excitation (CARE) and pressure-induced extra resonances in four-wave mixing (PIER4). We show that both CARE- and PIER4-type resonances have a common origin, which can be linked to conservation of energy. In contrast to conventional PIER4 signals, line shapes calculated in this work result from a ``single atom'' rather than a collective emission. Moreover, the signals vanish unless the applied fields are relatively coherent, again in contrast to conventional PIER4.
It is demonstrated that, in the presence of collisions and for nonresonant lasers, it is energetically possible to access resonantly excited states and induce a coherence between the states. This situation cannot arise in the absence of collisions if the starting state does not decay. This explains why, when collisions are introduced, a new signal can be generated in a wave-mixing type of experiment. The collisionally induced generation of a coherent signal is intimately related to the process of collisional redistribution. It is shown that all the collisionally induced coherent signals that have been reported up to now involve putting real populations in the excited states. This fact has not always been fully appreciated. No resonance between unpopulated states can exist. The time dependence of these new coherent signals is briefly discussed. In the case of a Raman resonance between equally populated states, it is pointed out that new coherent pathways of equal importance should be considered for explaining the experimental results. A new pressure-induced signal in four-wave mixing is also discussed. It is called "collisionally triggered two-photon quasiresonant coherent signal."