Optimal control and detection of chemical dynamics
by Zhenwen Shen
THESIS
1999
Ph.D. Chemistry
xx, 238 leaves : ill. ; 30 cm
Abstract
This dissertation focuses on the quantum mechanical study on the optimal control and detection of chemical dynamics, based on both the Liouville space density matrix and the Hilhert space wave function formalisms. Laser control of a chemical event, both theoretically and experimentally, remains to be active in the modern chemica1 dynamics and challenges the future dream of "molecular tailoring" . The aims of the dissertation are (1) to provide a complete formulation of the optimal control theory (OCT) for controlling the chemical dynamics with tailored light fields; (2) to demonstrate the feasibility of implementing the OCT in experimental realization. The subject material of this dissertation is as follows....[ Read more ]
This dissertation focuses on the quantum mechanical study on the optimal control and detection of chemical dynamics, based on both the Liouville space density matrix and the Hilhert space wave function formalisms. Laser control of a chemical event, both theoretically and experimentally, remains to be active in the modern chemica1 dynamics and challenges the future dream of "molecular tailoring" . The aims of the dissertation are (1) to provide a complete formulation of the optimal control theory (OCT) for controlling the chemical dynamics with tailored light fields; (2) to demonstrate the feasibility of implementing the OCT in experimental realization. The subject material of this dissertation is as follows.
Chapter 1 presents an overview on both the theoretical and experimental progresses on the control of chemical dynamics by light. It also summarizes some mathematical tools in quantum dynamics in both the Hilbert and the Liouville spaces.
Chapter 2 presents a general OCT via a single coherent optimal field in terms of the Liouville space density matrix dynamics. The theory is applicable to any molecular or atomic system, and allows the inclusion of mixed states and the reduced description for complex systems. Thus it can be used for quantum, classical, or semiclassical implementations of molecular dynamics. The conventional Hilbert space OCT in Chapter 3 can then be deduced clirectly from the generalized Liouville space formalism to the pure state case. In both Chapter 2 and Chapter 3, we also consider the weak control response regime in which the generalized OCT can be reduced to a linear eigen-equation problem. We further identify globally optima1 fields in both one- and two-photon control processes.
In Chapter 4, we implement the OCT to molecular systems involving two electronic surfaces. In order to increase the numerical efficiency, we introduce the rotating wave approximation (RWA) to eliminate the high oscillatory terms in the previous control formalism. Numerical demonstrations are carried out for the control of molecular dynamics in both the excited (single pump excitation) and the ground (phase-locked pump-dump excitation) electronic states.
Chapter 5 considers the general theory of pump-dump control via a pair of phase-unlocked coherent fields. This theory is a generalization of the previous chapters and can be readily extended to the control via multiple phase-unlocked fields. The control scheme considered here is motivated by experimental reality in which the pump-dump control fields carrying different frequencies may be impossible to be phase-locked. A comparison between phase-locked and phase-unlocked control schemes is made both theoretically and numerically.
In Chapter 6, we develop both the density matrix and wave function formulations for calculating the transient probe absorption signals to monitor the chemical dynanlics controlled by the optimal fields from the OCT and the parameterized fitted ones for experimental realization. The results show not only the controlled chemical dynamics, but also the experimental feasibility of those optimal fields.
In Chapter 7, we extend the pump-dump phase-unlocked control of two-surface molecular systems discussed in Chapter 5 to the control of multi-surface molecular systems. Numerical demonstrations are made for the pump-pump control of a three-surface molecular model system.
In Chapter 8, we incorporate the idea of the OCT with the coherent control scheme based on the direct interference among two or more independent photo-excitation paths. The resulting formulation determines not only the optimal relative amplitude and phases between two control fields of the paths, but also their optima1 temporal-spectra1 profiles.
Finally in Chapter 9, we draw the conclusion for the optimal control and detection of chemical dynamics in this dissertation and propose some future directions in this field.
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