Design Methods Of Control Fields For Quantum Systems

The studies of control fields design methods for quantum systems is a critical issue in quantum control theory and practice, it can greatly promotes many developing domains such as quantum information, quantum physics, bond selective chemistry, nanometer and microbial techniques. However, due to the properties of quantum systems themselves, it is difficult to design control fields for generic high-dimension and complex quantum systems. By now, there is no universal control fields design method for quantum systems, so an untiring endeavor of the scholars in various domains is still needed. Under such a background, this thesis studies the control fields design methods for quantum systems including the open loop control design, quantum Lyapunov methods for closed quantum systems with generic mixed states, the control design for open quantum systems and so on. The main contents are as follows:1. The Lyapunov based methods for quantum systems are researched. At first, the dynamical equation of the quantum system is transferred into a homogeneous bilinear one in the interaction picture, so it becomes a homogeneous bilinear equation. Based on this, the Lyapunov control law is designed to achieve the generic mixed states control for closed quantum systems described in the interaction picture. The next, aiming at the convergence problem universally exists in the quantum Lyapunov methods at present, the sufficient and necessary conditions are proved under certain assumptions. The observable operator in the Lyapunov function is constructed using the coherent vector presentation of quantum states to guarantee the stability the control law. Based on this, the largest invariant set of the controlled system is deduced utilizing the Barblat lemma. The sufficient and necessary conditions are proved through the analyzing of the dynamical stabilities of the states in the largest invariant set. Then, for the situation that the system can't converge to the given target state, the Lie group decomposition technology is utilized to improve the quantum Lyapunov methods, and a strategy called transition path programming is proposed to accomplish the control task, the convergence of the proposed strategy is also proved; at last, system numerical simulation experiments are done to verify the validity of the analysis and the strategy proposed.2. Control fields for cubit systems are designed. Firstly, based on the Bloch sphere presentation of a single qubit state, control fields are designed from the viewpoint of the geometry to achieve an arbitrary pure state of a single qubit. Secondly, adiabatic passage technology is used to design control fields for two-qubit systems, the coherence phase between control pulses is utilized to prepare different quantum states, the relationship between the coherence phase and the states prepared are analyzed and an approximate equation is summarized. Thirdly, utilizing the physical meanings of the basic control pulses and the relation between the system control Hamiltonians and the energy level structure, control pulse sequences are designed to accomplish the population transfer of multi-qubit systems. And fourthly, system numerical simulations are done to verify the validity of the control pulses.3. Control fields design methods for open quantum systems are studied. For the simplest case, the impact of external control fields on the purity and coherence variety due to the interaction between particles is studied, and control fields are designed to preserve the particle purity and eliminate the purity fluctuations. A new control method is proposed, in which local non-unitary operations are induced by an assistant system and its interactions with the priori system. By controlling the interactions between the two systems, the purity and coherence of the priori system are compensated, and the decoherence effect is counteracted. All the designs are verified by numerical simulation experiments.4. A kind of weak measurement operators is defined. A sufficient condition of the parameters is given. The impact of weak measurements on different quantum systems are analyzed, and the applications of such measurements in dissipation and decoherence control for open quantum systems are also discussed.