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Physical Review A

Radiation-matter oscillations and spectral line narrowing in field-correlated four-wave mixing. II. Experiment

Mark A. Dugan, A. C. Albrecht

Published Apr 1, 1991• 48 citations
Publisher

Abstract

New radiation-matter phenomena in four-wave mixing spectroscopies, given a theoretical basis in the preceding paper [Dugan and Albrecht, Phys. Rev. A 43, 3877 (1991)], are examined experimentally here. A new class of Rabi detuning oscillations is recorded in interferometric coherent Stokes Raman scattering (CSRS). Two identical nanosecond incoherent light fields are mutually delayed, while simultaneously mixing in a nonlinear medium with a narrow-band field of a different color. Spectral filtering of the CSRS signal is essential. From such signals the frequencies and the dephasing rate constants can be a measure of the Raman-active vibrations in both the electronic ground state and the electronic excited state of the scattering chromophore. In principle, analogous probing of vibronic transitions is possible. Detuning oscillations for multimode systems are presented. It is shown how they are transformed into quantum beats, exactly those seen with femtosecond CSRS, when the narrow-band field is made broad and/or the detection is ``white.'' Finally, an example of the sub-Raman linewidth spectral feature, predicted in the preceding paper, is presented. It determines a Raman frequency, but does not carry its linewidth.

DOI
10.1103/physreva.43.3922

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The theoretical basis for new signal transients and spectral features generated in field-correlated four-wave mixing spectroscopies is developed. Special attention is given to those signal responses that are sensitive to phase or amplitude correlation among the input driving fields, and not simply their intensity correlation. Thus the cases of incoherent broadband excitation and of coherent short-pulsed excitation will be discussed and compared. Applications to the coherent Raman spectroscopies, both electronically nonresonant and full resonant, are analyzed. Novel interferometric oscillatory behavior is exposed in terms of radiation-matter detuning beats and matter-matter bilevel and trilevel quantum beats. In addition, new resonances are found that have submaterial linewidths and detuning parameters that lock onto the mode frequency of the driven chromophore. These spectral features are members of a class of bichromophore resonant line shapes arising from nonlinear mixing with correlated driving fields. Analytic results are presented and modeled to anticipate experimental results presented in the following paper [Phys. Rev. A 43, 3922 (1991)].

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Resonance-enhanced four-wave-mixing processes were studied in molecular iodine by detection of a wave generated at frequency ${\mathrm{\ensuremath{\omega}}}_{3}$=2${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$ for a wide range of Raman frequencies (${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$). On the basis of known spectroscopic constants of the two electronic states involved, the electronic ground state ${\mathit{X}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ and the electronic excited state ${\mathit{B}}^{3}$${\mathrm{\ensuremath{\Pi}}}_{\mathit{u}0}^{+}$, an interpretation of the spectral features in terms of three essentially different four-wave-mixing processes is given. Resonance enhancement through bound states with discrete energy levels and the enhancement effect by dissociative continuum states are considered. In addition to resonance-enhanced coherent anti-Stokes Raman-scattering (CARS) processes, in which the Raman resonances are in the electronic ground state, two resonant schemes are identified in ${\mathrm{I}}_{2}$, in which Raman resonances in an excited state are probed: excited-state parametric and nonparametric CARS. The latter process is an example of electronic population transfer in a four-wave-mixing cycle.

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Summary form only given. Nonlinear techniques using broadband light have been developed and applied for studying dephasing processes, population and orientational dynamics of molecules. These techniques are based on the fact that in wave-mixing processes one may have the time resolution determined by the laser coherence time instead of the laser pulse duration. One limiting factor of the measurement sensitivity is a constant signal (pedestal), which is present even when the delay time between the exciting broadband beams is substantially longer than their coherence time and relaxation time under study. A technique has been developed, which uses not "white" detection, but spectral filtering in field-correlated four-wave mixing, the so called interferometric four-wave mixing (IFWM), which gives a signal that reveals oscillatory modulation, enabling us to discriminate it more easily from the pedestal. The technique allows to determine rather precisely the frequency of a molecular vibration and its dephasing time, as well as to study damped molecular rotations in liquids. We report the first measurements of population relaxation rates affected by stimulated emission in the presence of the pump field applying the IFWM technique.

Conference on Lasers and Electro-Optics•Jan 1, 2000•0 citations
New radiation-matter phenomena in four-wave mixing spectroscopies, given a theoretical basis in the preceding paper [Dugan and Albrecht, Phys. Rev. A 43, 3877 (1991)], are examined experimentally here. A new class of Rabi detuning oscillations is recorded in interferometric coherent Stokes Raman scattering (CSRS). Two identical nanosecond incoherent light fields are mutually delayed, while simultaneously mixing in a nonlinear medium with a narrow-band field of a different color. Spectral filtering of the CSRS signal is essential. From such signals the frequencies and the dephasing rate constants can be a measure of the Raman-active vibrations in both the electronic ground state and the electronic excited state of the scattering chromophore. In principle, analogous probing of vibronic transitions is possible. Detuning oscillations for multimode systems are presented. It is shown how they are transformed into quantum beats, exactly those seen with femtosecond CSRS, when the narrow-band field is made broad and/or the detection is ``white.'' Finally, an example of the sub-Raman linewidth spectral feature, predicted in the preceding paper, is presented. It determines a Raman frequency, but does not carry its linewidth.
The theoretical basis for new signal transients and spectral features generated in field-correlated four-wave mixing spectroscopies is developed. Special attention is given to those signal responses that are sensitive to phase or amplitude correlation among the input driving fields, and not simply their intensity correlation. Thus the cases of incoherent broadband excitation and of coherent short-pulsed excitation will be discussed and compared. Applications to the coherent Raman spectroscopies, both electronically nonresonant and full resonant, are analyzed. Novel interferometric oscillatory behavior is exposed in terms of radiation-matter detuning beats and matter-matter bilevel and trilevel quantum beats. In addition, new resonances are found that have submaterial linewidths and detuning parameters that lock onto the mode frequency of the driven chromophore. These spectral features are members of a class of bichromophore resonant line shapes arising from nonlinear mixing with correlated driving fields. Analytic results are presented and modeled to anticipate experimental results presented in the following paper [Phys. Rev. A 43, 3922 (1991)].
The delayed or time-domain four-wave-mixing experiment is treated in the regime of intense near-resonant pulses. The interaction with the radiation during both pump and probe pulses is considered to all powers of the electric field amplitude. Analytical results are obtained for an effective four-level system. These include the dependence of the coherence amplitudes on the ratio of the pump-field intensities when there is a large vibrational discrepancy between ground and excited electronic states and a general solution for the unitary time development during the probe pulse. For the first time, delayed coherent anti-Stokes Raman scattering is detected from highly dilute (10-ppm) guest molecules. Illustrative examples are presented for the system of pentacene in benzoic acid at low temperature. Vibronic-free induction decay and the effect of field inhomogeneity across the beam profile are found to be essential for understanding the observed intensity and spectral distribution of the signal beam in the region of optimum pulse intensity.
The theory for temporally multidimensional, electronically resonant four-wave-mixing (FWM) spectroscopy based on broadband light interferometry is developed. Both homodyne and heterodyne detection are considered. Upon spectrally resolving the signal, the electronic Bohr frequency is seen to be extremely down-converted, even to zero frequency, but only with homodyne detection. These very low frequency fringes, referred to as radiation difference oscillations, are well known in the interferometric coherent Raman broadband light spectroscopies. Such low frequency fringes permit interferometry in the optical region using Nyquist criteria corresponding to far infrared sampling rates. Possible applications are illustrated by simulations of the two-dimensional third order signals from an electronic two-level system in a variety of ``baths.'' It is seen how homogeneous and inhomogeneous line-shaping mechanisms manifest themselves differently and revealingly in the free induction decay, the photon echo decay and their cross term components of the FWM signal.
The four-wave mixing produced with two ultrashort phase-locked !-3! laser pulses propagating coherently in a two-level system in the infrared spectral region is shown to depend on the pulses relative phase. The Maxwell-Bloch equations are solved beyond the rotating-wave approximation to account for field frequencies which are largely detuned from the atomic resonance. The relative phase dominating the efficiency of the coupling to the 5! anti-Stokes Raman component is determined by sign of the total ac Stark shift induced in the system, in such a way that the phase influence disappears precisely where the ac Stark effect due to both pulses is compensated. This fundamental quantum interference effect can be the basis for nonlinear ultrafast optical spectroscopy techniques. Phenomena arising from the coherent control of nonlinear interactions are of importance in fields as diverse as optoelectronics and materials research, in high harmonic generation, in photoionization or molecular dissociation, and in biological applications such as spectroscopy and imaging, among others [1, 2, 3, 4, 5, 6, 7]. Optical quantum coherent control is based on the fact that the phases of interfering transition amplitudes in light-matter interactions can be controlled through the optical phase of coherent light sources that drive the interaction, in such a way that the transition rates to final states and the dynamics at various stages of the process can be modified [1]. In a recent paper [8], a theoretical investigation on the quantum coherent control of the optical transient four-wave mixing of two intense phase-locked femtosecond laser pulses of central angular frequencies ω and 3ω propagating in a two-level atom (TLA) was reported. It was shown how the nonlinear (χ (3) ) coupling to the antiStokes Raman field at frequency 5ω depends critically on the initial relative phase φ of the propagating pulses. In Ref. [8], the study was centered to intense pulses in the visible and ultraviolet spectral regions, with frequencies at resonance or lower than the atomic transition. The phenomena observed in [8], however, can be scaled to various laser and material parameters. In the infrared spectral range, for instance, experiments on ultrafast molecular dynamics are frequently performed by help of twocolor pump probe nonlinear spectroscopy techniques. In this type of studies, due to the high intensities inherent to ultrashort (subpicosecond) pulses, nonlinear effects such as stimulated Raman processes may become important and are often utilized as a complementary tool to gain information [9]. In this Letter, we address the conditions for quantum coherent control of transient four-wave mixing interactions with two phase-locked ω-3ω femtosecond laser pulses in the mid-IR spectral region. Our purpose is to reveal the basic physics for a strict two-level medium and to this end the Maxwell-Bloch TLA will be considered. We will study pulses with a duration of 300 fs (with a w 5w
Resonance-enhanced four-wave-mixing processes were studied in molecular iodine by detection of a wave generated at frequency ${\mathrm{\ensuremath{\omega}}}_{3}$=2${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$ for a wide range of Raman frequencies (${\mathrm{\ensuremath{\omega}}}_{1}$-${\mathrm{\ensuremath{\omega}}}_{2}$). On the basis of known spectroscopic constants of the two electronic states involved, the electronic ground state X1{\mathit{X}}^{1}X1${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}^{+}$ and the electronic excited state B3{\mathit{B}}^{3}B3${\mathrm{\ensuremath{\Pi}}}_{\mathit{u}0}^{+}$, an interpretation of the spectral features in terms of three essentially different four-wave-mixing processes is given. Resonance enhancement through bound states with discrete energy levels and the enhancement effect by dissociative continuum states are considered. In addition to resonance-enhanced coherent anti-Stokes Raman-scattering (CARS) processes, in which the Raman resonances are in the electronic ground state, two resonant schemes are identified in I2{\mathrm{I}}_{2}I2​, in which Raman resonances in an excited state are probed: excited-state parametric and nonparametric CARS. The latter process is an example of electronic population transfer in a four-wave-mixing cycle.
Summary form only given. Nonlinear techniques using broadband light have been developed and applied for studying dephasing processes, population and orientational dynamics of molecules. These techniques are based on the fact that in wave-mixing processes one may have the time resolution determined by the laser coherence time instead of the laser pulse duration. One limiting factor of the measurement sensitivity is a constant signal (pedestal), which is present even when the delay time between the exciting broadband beams is substantially longer than their coherence time and relaxation time under study. A technique has been developed, which uses not "white" detection, but spectral filtering in field-correlated four-wave mixing, the so called interferometric four-wave mixing (IFWM), which gives a signal that reveals oscillatory modulation, enabling us to discriminate it more easily from the pedestal. The technique allows to determine rather precisely the frequency of a molecular vibration and its dephasing time, as well as to study damped molecular rotations in liquids. We report the first measurements of population relaxation rates affected by stimulated emission in the presence of the pump field applying the IFWM technique.