Three-pulse four-wave mixing (FWM) is used here to study and control laser excitation processes. For general laser excitation processes, after a molecule interacts resonantly with a laser pulse, the molecule has a probability of being in the ground or in the excited state. Control over this process depends on the phase and amplitude of the electric fields that interact with the molecular system. Here we show how three-pulse FWM can be used to control the excitation of iodine molecules. Depending on the time delay between the first two pulses, the observed signal reflects the dynamics of the ground or excited state. A theoretical formalism based on the density matrix formulation is presented and solved for a four-level system. Experiments are found to be in excellent agreement with the theory. The influence of linear chirp on three-pulse FWM experiments is explored. Spectrally dispersed three-pulse FWM is found to be extremely useful for studying the effect of chirp on laser excitation of molecular systems. Experimental demonstrations of these effects are included.
Three-pulse four-wave mixing (FWM) is used here to study and control laser excitation processes. For general laser excitation processes, after a molecule interacts resonantly with a laser pulse, the molecule has a probability of being in the ground or in the excited state. Control over this process depends on the phase and amplitude of the electric fields that interact with the molecular system. Here we show how three-pulse FWM can be used to control the excitation of iodine molecules. Depending on the time delay between the first two pulses, the observed signal reflects the dynamics of the ground or excited state. A theoretical formalism based on the density matrix formulation is presented and solved for a four-level system. Experiments are found to be in excellent agreement with the theory. The influence of linear chirp on three-pulse FWM experiments is explored. Spectrally dispersed three-pulse FWM is found to be extremely useful for studying the effect of chirp on laser excitation of molecular systems. Experimental demonstrations of these effects are included.
Control of coherence and population transfer between the ground and excited states is reported using three-pulse four-wave mixing. The inherent vibrational dynamics of the system are utilized in timing the pulse sequence that controls the excitation process. A slight alteration in the pulse sequence timing causes a change in the observed signal from coherent vibration in the ground state to coherent vibration in the excited state. This control is demonstrated experimentally for molecular iodine. The theoretical basis for these experiments is discussed in terms of the density matrix for a multilevel system.
The role of four-wave mixing (FWM) techniques in coherent control is considered from the point of view of some of the most important developments in this field over the past years, namely multiphoton excitation, pump-dump methods, interference between coherent pulses, chirped laser pulses, and optimal control. FWM techniques provide a powerful platform for combining coherently multiple laser pulses. We explore the effectiveness of these techniques in controlling chemical reactions. The phase relationship between the pulses is maintained by detecting the signal in a phase-matching direction. The results presented show control over the observed dynamics from ground and excited state populations. The FWM signal results from the polarization of the sample following three different electric field interactions. The virtual echo sequence is achieved by the interactions of the sample with three consecutive electric fields characterized by exp[i(kx-w t)], exp[-i(kx-w t)] and exp[i(kx-w t)]. This sequence allows control over the observed ground or excited state dynamics. With the photon echo pulse sequence, characterized by interactions with exp[-i(kx-w t)], exp[i(kx-w t)], and exp[i(kx-w t)], we find that control of ground and excited state populations is not achieved.
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
Coherent control of quantum phenomena can be achieved by using phase- and amplitude modulated laser pulses. With a self-learning loop, which combines a femtosecond pulse shaper, an optimization algorithm and an experimental feedback signal, it is possible to automatically steer the interaction between system and electric field. This approach allows control even without any knowledge of the Hamiltonian. We have successfully implement this learning loop for the coherent control of the nonresonant two-photon excitation in sodium. New solutions for 'bright' and 'dark' pulses could be designed for this two-photon resonance without previous knowledge of the resonances. In a further experiment we combined the self-learning loop with degenerate four-wave-mixing spectroscopy in order to study the influence of phase and amplitude modulated pulses on the molecular FWM response of the prototype system K2. The obtained control pulses typically show a complex structure which hides the responsible physical mechanism. In order to extract the applied mechanism the concept of parameterization has been introduced which allows the learning algorithm to optimize already known control processes. Therefore the control of vibrational wavepacket motion in the electronic ground and excited state could be attributed to chirped pulse excitation, impulsive Raman excitation by pulse trains and phase-related double pulses representing the well-known Tannor-Rice-Kosloff control scheme.
We will demonstrate that four-wave mixing with linearly chirped (phase-modulated) pulses is a unique tool for obtaining information on the dynamics and level structure of a system. Especially, it will be shown that the transient-grating-scattering type of experiment with chirped pulses provides an immediate answer to the question of whether the dynamics of a system occurs on a fast and/or slow time scale. In addition, we present compelling evidence that chirped four-wave mixing in a molecular system is a viable method for measuring excited-state vibrational frequencies. Double-sided Feynman diagrams are used for a third-order perturbative calculation of two-level four-wave-mixing effects and chirped coherent Raman scattering. The diagrams provide a visual representation of the quantum-mechanical pathways that the system can take as a result of the different field interactions. The number of quantum-mechanical pathways that contribute to the signal is shown to depend on the chirp rate compared to the time scale(s) of the system dynamics. A stochastic model is used to describe the optical dynamics of the system. The resulting expressions for the third-order nonlinear polarization are so complex that numerical calculations are necessary to simulate the time dependence of the optical response. It will also be shown that our theoretical results in the appropriate limits converge to those obtained for impulsive or continuous-wave excitation.
Mechanisms and optimal experimental conditions in coherent control still intensely stimulate debates. In this work, a phase-only control mechanism in an open quantum system is investigated experimentally and numerically. Several parameterizations for femtosecond pulse shaping (combination of chirp and multipulses) are exploited in transient absorption of a prototype organic molecule to control population and vibrational coherence in ground and excited states. Experimental results are further numerically simulated and corroborated with a four-level density-matrix model, which reveals a phase-only control mechanism based on the interaction between the tailored phase of the excitation pulse and the induced transient absorption. In spite of performing experiment and numerical simulations in the linear regime of excitation, the control effect amplitude depends non-linearly on the excitation energy and is explained as a pump-dump control mechanism. No evidence of single-photon control is observed with the model. Moreover, our results also show that the control effect on the population and vibrational coherence is highly dependent on the spectral detuning of the excitation spectrum. Contrary to the popular belief in coherent control experiments, spectrally resonant tailored excitation will lead to the control of the excited state only for very specific conditions.