Femtosecond time scale coherence

From a theoretical perspective, the object that is initially created in the excited state is a coherent superposition of all the wavefunctions encompassed by the broad frequency spread of the laser. Because the laser pulse is so short in comparison with the characteristic nuclear dynamical time scales of the motion, each excited wavefunction is prepared with a definite phase relation with respect to all the others in the superposition. It is this initial coherence and its rate of dissipation which determine all spectroscopic and collisional properties of the molecule as it evolves over a femtosecond time scale. For IBr, the nascent superposition state, or wavepacket, spreads and executes either periodic vibrational motion as it oscillates between the inner and outer turning points of the bound potential, or dissociates to form separated atoms, as indicated by the trajectories shown in Figure 1.3. 

I had the honor to review the field, as described by the title of this chapter. I would like to take this opportunity here to focus on some concepts that were essential in the development of femtochemistry reaction dynamics and control on the femtosecond time scale. The following is not an extensive review, as many books and articles have already been published [1-12] on the subject, but instead is a summary of our own involvement with the development of femtochemistry and the concept of coherence. Most of the original articles are given in a recent two-volume book that overviews the work at Caltech [5], up to 1994. 

In siammary, the preliminary results presented in this contribution already demonstrate that time resolving polarization spectroscopy offers a number of favourable and new features for direct observation of fast evolving events on a femtosecond time scale and detection of oscillations up to the THz-range. The described technique can be applied to free atoms, liquids and solids to measure coherent transients in groimd and excited states. Since the observed beats result from an atomic interference effect, narrow structures which may be hidden by inhomogeneous broadening mechanisms can still be resolved. 

Temporal coherence allows laser pulses to be tailored, providing the chemist with the opportunity to observe rapid changes down to the femtosecond time-scale. Using the technique of femtosecond excitation and probing, we now have the capability to study ultrafast reactions in real time. 

Transient gratings also can be examined on a femtosecond time scale as a function of the time between the two pulses that create the grating [117]. As our discussion in Sect. 11.3 suggests, the two radiatitm fields do not actually need to be present in the sample simultaneously the second field can interfere constructively or destructively with coherence generated by the first. This makes femtosecond transient-grating experiments potentially useful for exploring relaxations that destroy such coherence. However, photon-echo experiments provide a more thoroughly developed path to this end. 

A new area of research, femtochemistry, in the framework of which reactions are studied in the femtosecond time scale, has recently speared along with the term coherent elementary reactions in which phase characteristics of the motion of atoms in the molecular reacting system are taken into account. 

Under the simulation conditions, the HMX was found to exist in a highly reactive dense fluid. Important differences exist between the dense fluid (supercritical) phase and the solid phase, which is stable at standard conditions. One difference is that the dense fluid phase cannot accommodate long-lived voids, bubbles, or other static defects, whereas voids, bubbles, and defects are known to be important in initiating the chemistry of solid explosives.107 On the contrary, numerous fluctuations in the local environment occur within a time scale of tens of femtoseconds (fs) in the dense fluid phase. The fast reactivity of the dense fluid phase and the short spatial coherence length make it well suited for molecular dynamics study with a finite system for a limited period of time chemical reactions occurred within 50 fs under the simulation conditions. Stable molecular species such as H20, N2, C02, and CO were formed in less than 1 ps. 

An intense femtosecond laser spectroscopy-based research focusing on the fast relaxation processes of excited electrons in nanoparticles has started in the past decade. The electron dynamics and non-linear optical properties of nanoparticles in colloidal solutions [1], thin films [2] and glasses [3] have been studied in the femto- and picosecond time scales. Most work has been done with noble metal nanoparticles Au, Ag and Cu, providing information about the electron-electron and electron-phonon coupling [4] or coherent phenomenon [5], A large surface-to-volume ratio of the particle gives a possibility to investigate the surface/interface processes. 

Several recent reviews have presented broad overviews of ultrafast time-resolved spectroscopy [3-6], We shall concentrate instead on a selected, rather small subset of femtosecond time-resolved experiments carried out (and to a very limited extent, proposed) to date. In particular, we shall review experiments in which phase-coherent electronic or, more often, nuclear motion is induced and monitored with time resolution of less than 100 fs. The main reason for selectivity on this basis is the rather ubiquitous appearance of phase-coherent effects (especially vibrational phase coherence) in femtosecond spectroscopy. As will be discussed, nearly any spectroscopy experiment on molecular or condensed-phase systems is likely to involve phase-coherent vibrational motion if the time scale becomes short enough. Since the coherent spectral bandwidth of a femtosecond pulse often exceeds collective or molecular vibrational frequencies, such a pulse may perturb and be perturbed by a medium in a qualitatively different manner than a longer pulse of comparable peak power. The resulting spectroscopic possibilities are of special interest to these reviewers. 

The coherent motion initiated by an excitation pulse can be monitored by variably delayed, ultrashort probe pulses. Since these pulses may also be shorter in duration than the vibrational period, individual cycles of vibrational oscillation can be time resolved and spectroscopy of vibrationally distorted species (and other unstable species) can be carried out. In the first part of this section, the mechanisms through which femtosecond pulses may initiate and probe coherent lattice and molecular vibrational motion are discussed and illustrated with selected experimental results. Next, experiments in the areas of liquid state molecular dynamics and chemical reaction dynamics are reviewed. These important areas can be addressed incisively by coherent spectroscopy on the time scale of individual molecular collisions or half-collisions. 

The time-dependent oscillations in absorption or other observables can be thought of as quantum beats resulting from coherent excitation of several vibronic levels contained within the bandwidth of the ultrashort excitation pulse. In a formal sense, the experiment is the same as other quantum beat experiments carried out on femtosecond or longer time scales. However, in most such experiments different molecular vibrational degrees of freedom that... 

Coherent control has to be performed on a very short time scale in order to win over dephasing processes. Therefore femtosecond lasers are generally demanded [1399]. 

It is important to note at this point that, in the gas phase, the processes that destroy or scramble coherence, such as collisions or spontaneous emission, generally take place on a much longer time-scale than the process that is being coherently controlled by the shaped femtosecond laser field, and thus do not interfere. 

Coherent control is based on interference effects, which become essential when an excited state can be populated on two ore more excitation paths. The population rates then depend on the phase relations between the optical waves that are inducing these excitations. Coherent control has to be performed on a very short time scale in order to win over dephasing processes. Therefore femtosecond lasers are generally demanded [15.32]. 

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