| Quantum control theory (QCT) is concerned with the active manipulation of phys- ical and chemical processes on the atomic and molecular scale. For a specified con- trol objective, and with restrictions imposed by many possible constraints, the time- dependent field required to manipulate the system in a desired way can be designed using quantum control theory. This dissertation proposes several novel applications of QCT to actively manipulate the dynamics of both quantum and classical systems with and without interactions with an external environment, in both relativistic and non-relativistic regimes. In Chapter 2, the paradigm of spectral dynamic mimicry (SDM) in which laser fields are shaped to make any atomic and molecular systems look identical spectrally is put forward. SDM successfully avoids optimization rou- tines, and provides a powerful tool to find a laser pulse that induces a desired optical response from an arbitrary dynamical system. As illustrations, driving fields are com- puted to induce the same optical response from a variety of distinct systems (open and closed, quantum and classical). The formulation may also be applied to design materials with specified optical characteristics. These findings reveal unexplored flex- ibilities of nonlinear optics. Little is known about the control of relativistic quantum systems. Therefore, an extension of QCT to the Dirac equation is proposed. The main contributions are: (i) Chapters 3 and 4 reach an unprecedented level of control while providing exciting new insights on the complex quantum dynamics of relativis- tic electrons. The method developed provides a very powerful tool to generate new analytical solutions to the Dirac equation, (ii) Chapters 5 and 6 present an open system interaction formalism for the Dirac equation. The presented framework en- ables efficient numerical simulations of relativistic dynamics within the von Neumann density matrix and Wigner phase space descriptions, an essential requirement for the application of QCT, (iii) Chapter 7 proposes a Lindblad model of quantum elec- trodynamics (QED). The presented formalism enables a very efficient and practical numerical method to simulate QED effects, such as the Lamb shift and the anomalous magnetic moment of the electron, for a broad variety of systems. |
