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Physical Review A

Saturation-induced distortion of four-wave-mixing spectra in a two-level system

A. D. Wilson‐Gordon, Harry Friedmann

Published Oct 1, 1988• 16 citations
Publisher

Abstract

It is shown that saturation causes the three-peaked four-wave-mixing (FWM) signal at frequency 2${\ensuremath{\omega}}_{1}$-${\ensuremath{\omega}}_{2}$, obtained from the interaction of a two-level system with a ``probe'' laser of varying frequency ${\ensuremath{\omega}}_{2}$ and a ``pump'' laser of fixed frequency ${\ensuremath{\omega}}_{1}$, to become asymmetrical on increasing the probe-laser intensity. Whereas saturation peaks occur in the population-inversion spectrum at one-photon and multiphoton resonances, this is not so for the FWM spectrum, where often the peaks correspond to nothing more than minima in the population-inversion spectrum.

DOI
10.1103/physreva.38.4087

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Summary form only given. It is well-known that the steady-state four-wave mixing (FWM) spectrum, obtained when a two-level atomic system interacts with a coherent pump of arbitrary intensity and a weak probe, is symmetrical and consists of three peaks: a central peak and two Rabi sidebands. Previously, we showed for temporally nonoverlapping pulses, that the spectrum becomes extremely asymmetrical and that only the Rabi sideband near the resonance frequency survives, in the case where the probe precedes the pump. For the opposite case, where the pump precedes the probe, no FWM spectrum is obtained at all. It should be noted that these results hold true provided the pump and probe pulses are much shorter than the transverse relaxation time T/sub 2/ and the pump-probe time delay /spl Delta/t/sub 0/ (/spl Delta/t/sub 0/<0 when the probe precedes the pump). We have also shown that T/sub 2/ can be determined from the slope of the semilog plot of the FWM intensity, near the resonance sideband, versus the pump-probe time delay /spl Delta/t/sub 0/ (for the case /spl Delta/t/sub 0/<0).

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Physical Review A•Oct 1, 1983•30 citations
It is shown that saturation causes the three-peaked four-wave-mixing (FWM) signal at frequency 2\ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​-\ensuremathω2{\ensuremath{\omega}}_{2}\ensuremathω2​, obtained from the interaction of a two-level system with a probe'' laser of varying frequency ${\ensuremath{\omega}}_{2}$ and a pump'' laser of fixed frequency \ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​, to become asymmetrical on increasing the probe-laser intensity. Whereas saturation peaks occur in the population-inversion spectrum at one-photon and multiphoton resonances, this is not so for the FWM spectrum, where often the peaks correspond to nothing more than minima in the population-inversion spectrum.
Summary form only given. It is well-known that the steady-state four-wave mixing (FWM) spectrum, obtained when a two-level atomic system interacts with a coherent pump of arbitrary intensity and a weak probe, is symmetrical and consists of three peaks: a central peak and two Rabi sidebands. Previously, we showed for temporally nonoverlapping pulses, that the spectrum becomes extremely asymmetrical and that only the Rabi sideband near the resonance frequency survives, in the case where the probe precedes the pump. For the opposite case, where the pump precedes the probe, no FWM spectrum is obtained at all. It should be noted that these results hold true provided the pump and probe pulses are much shorter than the transverse relaxation time T/sub 2/ and the pump-probe time delay /spl Delta/t/sub 0/ (/spl Delta/t/sub 0/<0 when the probe precedes the pump). We have also shown that T/sub 2/ can be determined from the slope of the semilog plot of the FWM intensity, near the resonance sideband, versus the pump-probe time delay /spl Delta/t/sub 0/ (for the case /spl Delta/t/sub 0/<0).
We predict that the four-wave mixing (FWM) excitation spectrum for a two-level system becomes extremely asymmetrical when steady-state excitation is replaced by pulsed excitation, using temporally nonoverlapping probe and pump pulses. We also show that when a resonant probe pulse precedes the detuned pump pulse, the FWM signal may become more intense than when the pulses overlap. These effects are attributed to free-induction decay (FID): the coherence induced in the two-level system by a short resonant probe pulse survives the pulse (FID) and replaces it in producing a strong nonlinear signal on interaction with the strong pump pulse. Moreover, by plotting the FWM signal intensity as a function of the delay between the probe and pump pulses, an efficient method is proposed for determining short transverse relaxation times or fast chemical reaction rates.
The influence of the high-pump-field intensity saturation and dynamic Stark effects on the resonant nearly degenerate four-wave-mixing signal (${\mathrm{\ensuremath{\omega}}}_{3}$=2${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$) is studied in a frequency space defined by the pump- and probe-field frequencies, ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$, respectively. Variable inhomogeneous widths have been considered ranging from extremely narrow (homogeneous distribution) to extremely wide. Remarkable differences between nearly homogeneously broadened systems and extreme inhomogeneous ones are exhibited. It is shown, for the situation of homogeneous broadening, that the spectra carried on with fixed probe and fixed pump frequency values have substantial differences in shape. These differences disappear in the situation of extreme inhomogeneous broadening. Fixed-pump-frequency resonant and fixed-probe-frequency nonresonant spectra are proposed as very convenient tools to yield useful evidence about the width of the inhomogeneous molecular distribution.
We have calculated the interference spectra of a single electron in the excited state of a four-level atom interacting with three laser fields, where two of them are on two-photon resonance with the three levels forming a `Λ' scheme while the third laser operates between the second ground and the second excited states of the atom. It is shown that in the low-intensity limit of all three laser fields, the third laser field destroys the destructive interference that occurs between the spontaneous radiative decay and the process arising from the combined field of all the three laser fields. The result is that the overall intensity of the peak at the centre of the line depends on the strength of the third laser field and it takes negative values indicating that light amplification without population inversion (LAWI) is likely to occur at the one-photon frequency. The antisymmetric two-photon state of the two lower levels as well as the two-photon process, where one laser photon is absorbed and another laser photon is emitted simultaneously by the second excited state of the atom, is found to exhibit LAWI at the one-photon frequency. The derived results are graphically presented and discussed.
An analytic nonperturbative treatment of degenerate four-wave mixing is presented to study Zeeman-coherence effects in phase conjugation. The counterpropagating pump waves are taken to be orthogonally circularly polarized and interact with different Zeeman sublevels. The nonlinear medium is modeled in terms of a homogeneously broadened, folded three-level system. Particular attention is paid to the phase-conjugate spectrum obtained by varying the Larmor frequency associated with the Zeeman splitting. A level-crossing resonance is found to occur in the saturation regime and manifests itself as a narrow peak or dip depending on various level decay rates. Even for a purely absorptive system, the Zeeman coupling of the ground-state degenerate sublevels is shown to produce significant phase-conjugate reflectivities at pump intensities much lower than those required for a two-level system.