Coherent control experiments

Coherent control experiments were also performed under intense photoexcitation near the Lindemann stability limit [38-41], above which the long-range order of the crystal would be lost. 

The value of coherent control experiments lies not only in their ability to alter the outcome of a reaction but also in the fundamental information that they provide about molecular properties. In the example of phase-sensitive control, the channel phase reveals information about couplings between continuum states that is not readily obtained by other methods. Examination of Eq. (15) reveals two possible sources of the channel phase—namely, the phase of the three-photon dipole operator and that of the continuum function, ESk). The former is complex if there exists a metastable state at an energy of (D or 2 >i, which contributes a phase to only one of the paths, as illustrated in Fig. 3b. In this case the channel phase equals the Breit-Wigner phase of the intermediate resonance (modulo n),... 

The systematically performed pump-probe spectroscopy on alkali clusters provided a good indication about suited candidates for a coherent control experiment. Among these, the fragmentation dynamics of the heteronu-clear trimer Na2K appeared to us the best. The corresponding pump-probe spectrum is shown in Fig. 14(a). It clearly exhibits — superimposed on an exponential decay with a time constant of 3.28 ps — an oscillatory behaviour with a period of roughly 500 fs. The Fourier-transform of this... 

Many of the initial theoretical models used to vahdate the concept of coherent control and optimal control have been based on the interaction of the electric field of the laser light with a molecular dipole moment [43, 60, 105]. This represents just the first, or lowest, term in the expression for the interaction of an electric field with a molecule. Many of the successful optimal control experiments have used electric fields that are capable of ionizing the molecules and involve the use of electric field strengths that lead to major distortions of the molecular electronic structure. With this in mind, there has been discussion in the... 

In order to know the true nature of active catalytic species, several control experiments must be carried out to get coherent data. In this way, some authors have proposed strategies, each of them involving various tests. 

The previous sections focused on the case of isolated atoms or molecules, where coherence is fully maintained on relevant time scales, corresponding to molecular beam experiments. Here we proceed to extend the discussion to dense environments, where both population decay and pure dephasing [77] arise from interaction of a subsystem with a dissipative environment. Our interest is in the information content of the channel phase. It is relevant to note, however, that whereas the controllability of isolated molecules is both remarkable [24, 25, 27] and well understood [26], much less is known about the controllability of systems where dissipation is significant [78]. Although this question is not the thrust of the present chapter, this section bears implications to the problem of coherent control in the presence of dissipation, inasmuch as the channel phase serves as a sensitive measure of the extent of decoherence. 

Although coherent control is now a mature field, much remains to be accomplished in the study of the channel phase. There is no doubt that coherence plays an important role in large polyatomic molecules as well as in dissipative systems. To date, however, most of the published research on the channel phase has focused on isolated atoms and diatomic molecules, with very few studies addressing the problems of polyatomic and solvated molecules. The work to date on polyatomic molecules has been entirely experimental, whereas the research on solvated molecules has been entirely theoretical. It is important to extend the experimental methods from the gas to the condensed phase and hence explore the theoretical predictions of Section VC. Likewise interesting would be theoretical and numerical investigations of isolated large polyatomics. A challenge to future research would be to make quantitative comparison of experimental and numerical results for the channel phase. This would require that we address a sufficiently simple system, where both the experiment and the numerical calculation could be carried out accurately. 

The earliest control experiments were performed in double- (or multiple-) pump and probe scheme on optical phonons generated via ISRS in transparent materials by Nelson and coworkers [24,25], Shortly later, similar experiments were carried out on coherent phonons generated in semiconductors via TDFS by Dekorsy and coworkers [26], and on those generated in semimetals via DECP by Hase and coworkers [27] (Fig. 2.1 in the previous chapter). These experiments demonstrated that the amplitude of the coherent oscillation can be controlled by varying the temporal separation At between the two pump pulses. At = nT leads to the maximum enhancement of the amplitude with an integer n and the phonon period T, while At = (n + 1/2)T results in complete cancelation. 

Double pump experiments on an organic charge transfer complex TTF-CA by Iwai and coworkers demonstrated a new class of coherent control on a strongly correlated electron-lattice system [44]. While the amplitude of the coherent oscillation increased linearly with pump fluence for single pump experiments, the amplitude in the double pump experiments with a fixed pulse interval At = T exhibited a strongly super-linear fluence dependence (Fig. 3.16). The striking difference between the single- and double-pulse results indicated a cooperative nature of the photo-induced neutral-ionic transition. 

In the following, we describe two prominent types of spectral phase modulation, each of which plays an important role in coherent control. Both types, namely sinusoidal (Section 6.2.1) and quadratic (Section 6.2.2) spectral phase modulation, are relevant for the experiments and simulations presented in this contribution. We provide analytic expressions for the modulated laser fields in the time domain and briefly discuss the main characteristics of both classes of pulse shapes. 

Periodic spectral phase-modulation functions have been used in numerous experiments and theoretical studies on coherent control of atoms [75-79] and molecules [24, 25, 42, 68, 73, 80-85]. Applying a sinusoidal phase-modulation function of the form... 

A negative chirped pulse is shown in Figure 6.4c. Experiments and theoretical studies on coherent control of ultrafast electron dynamics by intense chirped laser pulses will be discussed in Sections 6.3.2.3 and 633.2. 

Here we describe the development of the coherent-control toolbox with gas-phase iodine molecules [37 1, 48]. The gas-phase molecules are isolated from each other, so that they have long coherence lifetime, serving as an ideal platform to observe and control quantum coherence. First, we describe our experiments to observe and control the temporal evolution of the WP interference. Second, the eigenstate picture of the WP interference is presented. Finally, we demonstrate the application of WPI to ultrafast molecular computing. 

In order to achieve coherent control in a laboratory experiment, three major requirements are to be met. Well-defined final states cannot be reached without the preparation of a well-defined initial state. Ultrashort, spectrally wide and intense laser pulses at different wavelengths must be produced for excitation and a good characterization of the final product states must be achieved. 

A beautiful experiment demonstrating coherent control in the sense of the Tannor-Kosloff-Rice scheme was carried out by Baumert et al. [17] using resonant three-photon ionization and fragmentation of Na2. 

Despite these notable successes, much remains to be done before coherent control can become a practical tool. Virtually all the successes to date have involved very simple molecules. Although learning algorithms may prove to be useful for controlling complex molecules, they have so far shed little light on the dynamics involved. Two very important problems where experiments lag far behind theory are the selective control of molecules with different chirality and the control of bimolecular reactions. A major... 

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