Fast Non-adiabatic Control And Optimal Design In Quantum Systems

Quantum adiabatic theory is one of the most important conclusions in quantum mechanics, which has wide applications in quantum theory and quantum information science and techniques. However, quantum adiabatic process is a slow process in real-istic quantum control and quantum computation, so that the results might be affected by decoherence or environmental noise. To accelerate such slow adiabatic processes with the same results is quite demanding. The thesis is devoted to realizing fast non-adiabatic quantum control, for example, the atom cooling and transport, population transfer by invariant-based inverse engineering method. Additionally, the optimal protocols are further designed to minimize the effects of various noise and systematic errors. The main results are as follows:Firstly, we investigate fast and robust population transfer in two-level atomic sys-tems. Combing invariant-based inverse engineering and time-dependent perturbation theory, optimal protocols are found to optimize phase noise and frequency error. For a given constrain on frequency, a flat π pulse is the least sensitive protocol to phase noise. Three-level systems are generalized, and different optimal protocols are achieved with respect to detuning error or Rabi frequency error.Secondly, we investigate the effect of anharmonicity on fast and transitionless ex-pansions of cold atoms or ions in Gaussion trap. By using similar technique mentioned above, an optimal protocol is found to realize fast, transitionless expansions of cold atoms or ions in Gaussian trap. "Bang-Singular-Bang" optimal control is achieved, which also minimize the average energy of anharmonic perturbation.Thirdly, we investigate the transport of trapped ion in harmonic trap taking into account the effects of noise and error. For one single ion transport, the analytical optimal solution is found for white noise, which provides an useful reference for color noise. For two different-mass ions transport, a different method, namely, harmonic dynamical normal-mode approximation, is utilized to study the effect of spring constant error. An explicit trigonometric protocol is finally obtained as the optimal one.