Strong-field control

In Section 6.3.2, we presented experimental data from strong-field excitation and ionization of K atoms with shaped femtosecond laser pulses. Here we give a description of the apparatus and strategy used in the experiments presented in this contribution. Figure 6.12 gives an overview over the complete experimental two-color setup. For the experiments on strong-field control of K atoms (cf Sections 6.3.2.2, 6.3.2.3, and 6.5) only the one-color beamline was used. An... 

Bulation transfer between bound states and, especially, how to achieve complete nlatidn transfer between such states. In doing so we describe realistic methods for control, introduce a number of useful methods in strong-field control, and pave... 

To summarize, the optical paralysis scheme can be viewed as local control with complex fields. If the processes are sufficiently well described within the rotating wave approximation—that is, counter-rotating terms do not play a crucial role—the real fields that can be produced in the laboratory can be successful in locking populations in selected electronic states while other strong field control objectives can be achieved, which might be much more complex than the heating considered in this section. 

Bayer T, WoUenhaupt M, Baumert T (2008) Strong-field control Itmdscapes of coherent electronic excitation. J Phys B 41 074007... 

The preceding equation shows that the transit time dispersion under weak field conditions is controlled by conventional diffusion, whereas at strong fields, the main contribution to Ate arises from the field-assisted diffusion term. A crossover from Atj to Atj occurs in the field dependence of the transit time dispersion that corresponds to the crossover from Atj E to Atj E in the dependence of the transit time dispersion on the transit time. It is worth noting that all parameters describing the contribution of the preceding equation are defined by independent measurements, while the contribution of the field-induced diffusion depends on the value of the effective release time, which is poorly known and can be very different in different disordered materials. 

M. N. Kobrak and S. A. Rice. Equivalence of the Kobrak-Rice photoselective adiabatic passage and the Brumer-Shapiro strong field methods for control of product formation in a reaction. J. Chem. Phys., 109(1) 1-10(1998). 

In the following, we will discuss two basic - and in a sense complementary [44] - physical mechanisms to exert efficient control on the strong-field-induced coherent electron dynamics. In the first scenario, SPODS is implemented by a sequence of ultrashort laser pulses (discrete temporal phase jumps), whereas the second scenario utilizes a single chirped pulse (continuous phase variations) to exert control on the dressed state populations. Both mechanisms have distinct properties with respect to multistate excitations such as those discussed in Section 6.3.3. 

The use of strong fields to drive the dynamics leads to somehow similar effects than those of ultrafast pulses. If the Rabi frequency or energy of the interaction is much larger than the energy spacing between adjacent vibrational states, a wave packet is formed during the laser action. The same laser can prepare and control the dynamics of the wave packet [2]. Both short time widths and large amplitudes can concur in the experiment. However, the precise manipulation of dynamic observables usually becomes more difficult as the duration of the pulses decreases. 

We demonstrate coherent control in strong fields beyond (i) population control and (ii) spectral interference, since (i) control is achieved without altering the population during the second intense laser pulse, i.e., the population during the second laser pulse is frozen, and (ii) the quantum mechanical phase is controlled without changing the spectrum of the pulse sequence. The control mechanism relies on the interplay of the quantum mechanical phase set by the intensity of the first pulse and the phase of the second pulse determined by the time delay. 

Wilson and co-workers have also considered optimal control of molecular dynamics in the strong-field regime using the density matrix representation of the state of the system [32]. This formulation is also substantially the same as that of Kosloff et al. [6] and that of Pierce et al. [8, 9]. Kim and Girardeau [33] have treated the optimization of the target functional, subject to the constraint specified by (4.8), using the Balian-Veneroni [34] variational method. The overall structure of the formal results is similar to that we have already described. 

We consider, first, whether it is in principle possible to control the quantum dynamics of a many-body system. The goal of such a study is the establishment of an existence theorem, for which purpose it is necessary to distinguish between complete controllability and optimal control of a system. A system is completely controllable if an arbitrary initial state can be transformed, without loss to other states, into an arbitrary final state at some time T. A system is strongly completely controllable if an arbitrary initial state can be transformed, without loss to other states, into an arbitrary final state at a specified time T. Optimal control theory designs a field, subject to specified constraints, that guides the evolution of an initial state of the system to be as close as possible to the desired final state at time T. 

Probably one of the commonest reactions encountered in the template synthesis of macrocycles is the formation of imine C=N bonds from amines and carbonyl compounds. We have seen in the preceding chapters that co-ordination to a metal ion may be used to control the reactivity of the amine, the carbonyl or the imine. If we now consider that the metal ion may also play a conformational role in arranging the reactants in the correct orientation for cyclisation, it is clear that a limitless range of ligands can be prepared by metal-directed reactions of dicarbonyls with diamines. The Tt-acceptor imine functionality is also attractive to the co-ordination chemist as it gives rise to strong-field ligands which may have novel properties. All of the above renders imine formation a particularly useful tool in the arsenal of preparative co-ordination chemists. Some typical examples of the templated formation of imine macrocycles are presented in Fig. 6-12. 

Consider the problem of wave packet control in a weak laser field. Here wave packet control refers to the creation of a wave packet at a given target position on a specific electronic potential energy surface at a selected time tf. For this purpose, a variational treatment is introduced. In the weak field limit, the wave packet can be calculated by first-order perturbation theory without the need to solve explicitly the time-dependent Schrodinger equation. In strong fields, where the perturbative treatment breaks down, the time-dependent Schrodinger equation must be explicitly taken into account, as will be discussed in later sections. 

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