Coherent optimal control

Coherent optimal control by tailored strong-field laser pulses... 

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... 

This chapter has provided a brief overview of the application of optimal control theory to the control of molecular processes. It has addressed only the theoretical aspects and approaches to the topic and has not covered the many successful experimental applications [33, 37, 164-183], arising especially from the closed-loop approach of Rabitz [32]. The basic formulae have been presented and carefully derived in Section II and Appendix A, respectively. The theory required for application to photodissociation and unimolecular dissociation processes is also discussed in Section II, while the new equations needed in this connection are derived in Appendix B. An exciting related area of coherent control which has not been treated in this review is that of the control of bimolecular chemical reactions, in which both initial and final states are continuum scattering states [7, 14, 27-29, 184-188]. 

As discussed by M. Shapiro and R Brumer in the book Quantum Control of Molecular Processes, there are two general control strategies that can be applied to harness and direct molecular dynamics optimal control and coherent control. The optimal control schemes aim to find a sef of external field parameters that conspire - through quantum interferences or by incoherent addition - to yield the best possible outcome for a specific, desired evolution of a quantum system. Coherent control relies on interferences, constructive or destructive, that prohibit or enhance certain reaction pathways. Both of these control strategies meet with challenges when applied to molecular collisions. 

Since the classical treatment has its restrictions and the applicability of the quantum OCT is limited to low-dimensional systems due to its formidable computational cost, it would be very desirable to incorporate the semiclassical method of wavepacket propagation like the Herman-Kluk method [20,21] into the OCT. Recently, semiclassical bichromatic coherent control has been demonstrated for a large molecule [22] by directly calculating the percent reactant as a function of laser parameters. This approach, however, is not an optimal control. 

As this book has emphasized, there are two distinct paradigms for. the control of molecular processes coherent control and optimal control.. 

All of the quantum control scenarios involve a host of laser and system parameters. To obtain maximal control in any scenario necessitates a means of tuning the system and laser parameters to optimally achieve the desired objective. This topic, optimal control, is introduced and discussed in Chapters 4 and 13. The role of quantum interference effects in optimal control are discussed as well, providing a uniform picture of control via optimal pulse shaping and coherent control. 

With reference to the description of dipolar recoupling in the previous sections and our first presentation of these data in Ref. 70, we here demonstrate the applicability of optimal control theory for the design of dipolar recoupling experiments for transfer of coherence from N to which could involve typical and spin... 

Numerical optimisation approaches have been traditionally used in design of selective excitation and inversion pulses. This usually involved a variation of a small number of parameters that describe a subset of pulse shapes. Kobzar et al proposed to apply the optimal control theory to remove the restriction of the predetermined pulse shape and to obtain a general solution that meets the criteria of maximum rf-amplitude, maximum pulse duration, temporal digitisation of the pulse and compensations for Bi-field inhomogeneity. The application of the method allowed to improve most of the published selective pulses. The method was extended further to optimise coherence transfer steps in coupled spin systems.The reported optimised propagators maximised the... 

Although the demonstration of this technique was a success, its efficiency is limited because CW lasers interact only with a small part of the thermal distribution of the molecules. The decay of the coherence of the molecules and radiation limits the amount of energy that can be used effectively for control pm poses, because such coherence is a must for stable quantmn wave interference. In this regard, the two-femtosecond-pulse approach (Section 12.2) seems to be more effective, especially when used in combination with optimally shaped electromagnetic fields. Optimal control of the shape of the laser pulses used can provide effective excitation of the desired final quantum mechanical state. 

The composition of the electrolyte is quite important in controlling the electrolytic deposition of the pertinent metal, the chemical interaction of the deposit with the electrolyte, and the electrical conductivity of the electrolyte. In the case of molten salts, the solvent cations and the solvent anions influence the electrodeposition process through the formation of complexes. The stability of these complexes determines the extent of the reversibility of the overall electroreduction process and, hence, the type of the deposit formed. By selecting a suitable mixture of solvent cations to produce a chemically stable solution with strong solute cation-anion interactions, it is possible to optimize the stability of the complexes so as to obtain the best deposition kinetics. In the case of refractory and reactive metals, the presence of a reasonably stable complex is necessary in order to yield a coherent deposition rather than a dendritic type of deposition. 

The outputs of the sensors were used in two closed-loop control strategies developed for combustor performance optimization [7]. The objective of the first strategy, based on an adaptive least-mean squares (LMS) algorithm, was to maximize the magnitude and coherence of temperature oscillations at the forcing frequency /o in the measured region. The LMS algorithm was used to determine... 

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