We present an analysis of two experimental approaches to controlling the directionality of molecular rotation with ultrashort laser pulses. The two methods are based on the molecular interaction with either a pair of pulses (a ``double-kick'' scheme) or a longer pulse sequence (a ``chiral-pulse-train'' scheme). In both cases, rotational control is achieved by varying the polarization of and the time delay between the consecutive laser pulses. Using the technique of polarization-sensitive resonance-enhanced multiphoton ionization, we show that both methods produce significant rotational directionality. We demonstrate that increasing the number of excitation pulses supplements the ability to control the sense of molecular rotation with quantum-state selectivity, i.e., predominant excitation of a single rotational state. We also demonstrate the ability of both techniques to generate counterrotation of molecular nuclear-spin isomers (here, ortho- and para-nitrogen) and molecular isotopologs (here,
14N
2 and
15N
2).
We investigate theoretically the ability of an optical centrifuge - a laser pulse whose linear polarization is rotating at an accelerated rate, to control molecular rotation in the regime when the rigid-rotor approximation breaks down due to coupling between the vibrational and rotational degrees of freedom. Our analysis demonstrates that the centrifuge field enables controlled excitation of high rotational states while maintaining relatively low spread along the vibrational coordinate. We contrast this to the rotational excitation by a linearly polarized Gaussian pulse of equal spectral width and pulse energy which, although comparable to the centrifuge-induced rotation, is unavoidably accompanied by a substantial broadening of the vibrational wavepacket.
We have theoretically investigated the vibrational population transfer in the presence of manifolds of rotational levels in a model 15-level
Li2 molecular system by stimulated Raman adiabatic passage with intense unchirped femtosecond laser pulses. We have considered five rotational levels
Jg=0,2,…,8 associated with the initial vibrational level
vg=0 of the ground electronic state $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$, five rotational levels
Ji=1,3,…,9 associated with the vibrational level
vi=1 of the intermediate excited electronic state $A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}$, and five rotational levels
Jf=0,2,…,8 associated with the final target vibrational levels
vf=1,2 of the $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$ state of the
Li2 alkali dimer. The pump and Stokes laser pulses are taken to have the same temporal (Gaussian) shapes, pulse widths, and linear parallel polarizations. The laser wavelengths are in the (visible) range of 700--740 nm. The (peak) intensities of the pulses are of the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{12}--2.5\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{W}/{\text{cm}}^{2}$ and the pulse widths are of the order of 20--50 fs. We have solved the 15 coupled time-dependent Schr\"odinger equations to study the population transfer to the target-excited vibrational levels. We have observed that, even with ``mushrooming'' of closely spaced rotational levels, efficient and selective population transfer to excited vibrational levels in
Li2 alkali dimer can be achieved for counterintuitive pulse sequence by controlling the pump and Stokes laser parameters. We have endeavored to explain the results within the framework of adiabatic picture.
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.
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
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.