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Physical Review A

Phase coherence control and subcycle transient detection in nonlinear Raman scattering with ultrashort laser pulses

Aleksei M. Zheltikov

Published Nov 3, 2006• 21 citations
Publisher

Abstract

A model of two-level weakly interacting quantum systems is used to demonstrate that the phase of molecular vibrations excited through stimulated Raman scattering can be controlled by the relative phase of time-separated laser pulses, allowing synchronization and amplitude control of coherence excitation in a medium. For transients with a phase relaxation time less than the field cycle, the field half-cycle can serve as a subfemtosecond probe of coherent vibrations. In this regime, the high-frequency field-induced modulation of molecular dipole moments gives rise to a detectable modulation of the optical response of a medium at the frequency $2\ensuremath{\omega}$, $\ensuremath{\omega}$ being the frequency of the laser field.

DOI
10.1103/physreva.74.053403

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A model of two-level weakly interacting quantum systems is used to demonstrate that the phase of molecular vibrations excited through stimulated Raman scattering can be controlled by the relative phase of time-separated laser pulses, allowing synchronization and amplitude control of coherence excitation in a medium. For transients with a phase relaxation time less than the field cycle, the field half-cycle can serve as a subfemtosecond probe of coherent vibrations. In this regime, the high-frequency field-induced modulation of molecular dipole moments gives rise to a detectable modulation of the optical response of a medium at the frequency 2\ensuremathω2\ensuremath{\omega}2\ensuremathω, \ensuremathω\ensuremath{\omega}\ensuremathω being the frequency of the laser field.
We suggest that subfemtosecond pulses can be generated by using high-order stimulated Raman scattering when a Raman transition is driven by three intense single-mode laser beams with two different modulation frequencies. An oscillatory strong Raman coherence is established by the modulated molecular modulation. Numeric simulations based on the first fundamental vibrational Raman transition of gaseous and solid deuterium indicate that subfemtosecond pulses can be generated by Raman excitations with above, below, or opposite Raman detunings.
We study the generation of subfemtosecond pulses with the molecular coherence control in stimulated Raman scattering. We show analytically that the antiphased state temporally advances the higher frequencies with respect to the lower frequencies during a beating cycle. After some propagation distance, due to the dispersion and the difference between the antiphased and phased states in advancing high or low frequencies, the coherence is highest on the negative side of the detuning, when the two-photon Rabi frequency is about equal to the detuning. This asymmetry of the coherence magnitude with respect to the negative and positive sides of the Raman detuning is reflected in the behavior of the tuning characteristics of the high-order frequency components. When the Raman detuning is small, although the process is nonadiabatic, the subfemtosecond pulse generation may occur for both negative and positive sides of the detuning.
We have investigated the behavior of high-order stimulated Raman scattering in a highly-transient regime. We demonstrate efficient collinear generation of vibrational sidebands in molecular hydrogen and methane using two-color pumping with pulses of duration $\ensuremath{\tau}\ensuremath{\sim}100\phantom{\rule{0.3em}{0ex}}\mathrm{fs}$ tuned to a vibrational Raman transition. A Raman spectrum with a large bandwidth was observed, ranging from the IR to the UV. Under some conditions strong pump depletion was observed and up to five anti-Stokes sidebands were observed to have energies exceeding 10% of the transmitted pump pulse energies. A numerical simulation reproduces qualitatively and quantitatively the experimental results and allows us to explain key experimental features. The simulation also confirms that the molecular coherence in the medium is substantially increased by the two-color pumping and allows us to deduce values for the degree of material excitation. The use of this technique looks promising for efficient subfemtosecond pulse generation.
Subfemtosecond (sub-fs) pulses can be generated by cascade-stimulated Raman scattering in a Raman medium with modulated Raman excitations, driven by two sufficiently intense laser beams, one of which is amplitude modulated. The nonadiabatic Raman interaction establishes a strong modulated Raman coherence, which supports compression of the generated broadband Raman sidebands to a train of sub-fs pulses regardless of whether the carrier frequencies of the driving lasers are tuned above, below or on two-photon Raman resonance.
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
Unlike spontaneous Raman effect, nonlinear Raman scattering generates fields with a well-defined phase, allowing Raman signals from individual scatterers to add up into a highly directional, high-brightness coherent beam. Here, we show that the phase of coherent Raman scattering can be accurately controlled and finely tuned by using spectrally and temporally tailored optical driver fields. In our experiments, performed with spectrally optimized phase-tunable laser pulses, such a phase control is visualized through the interference of the coherent Raman signal with the field resulting from nonresonant four-wave mixing. This interference gives rise to Fano-type profiles in the overall nonlinear response measured as a function of the delay time between the laser pulses, featuring a well-resolved destructive-interference dip on the dark side of the Raman peak. This phase-control strategy is shown to radically enhance the coherent response from weak Raman modes, thus helping confront long-standing challenges in nonlinear Raman imaging and microspectroscopy.