Coherent Manipulating And Controlling Of Trapped Ions

In the past few years, the field of trapped-ion quantum computation and quantum information processing, whether theoretical studying or experimental exploring, have achieved tremendous progress. Many important results have been gained. We can now manipulate and control coherently not only the internal electronic states, but also the external motional states with very high precision by coupling the trapped ions to laser fields. This makes trapped-ion system ideally suited for quantum computation and quantum information processing, as well as quantum-optical and quantum-dynamical studies under well-controlled conditions. This paper reports the following research works, besides the introduction of the basic principles for ion trapping and cooling, and trapped-ion quantum computation.For N trapped ions in a linear trap, we have proposed a method to engineer the center-of-mass or collective modes to be in an equidistant superposition of coherent states on a line of phase space with random superposition coefficients. For two trapped-ion system, we have proposed a method to produce one- and two-mode squeezed states and their superposition for center-of-mass and breathing modes, and to realize a two-vibration-mode beam-splitter transformation similar to that in quantum optics for two beams.In Lamb-Dicke limit, we have obtained the exact analytic solution of the Jaynes-Cummings-like model for two trapped ions interacting with a laser beam, and invested the collapses and revivals in the occupation of the internal electronic states, as well as the coherent and squeezing properties of the phonon field. It has been shown that when the initial internal states of both ions being in the ground and the center-of-mass mode in a coherent state, there are visible collapses and revivals in the occupation of all internal electronic states, which become more and more clear as the number of the initial phonons increases. The coherence of the phonon field decreases rapidly with the increasing of number of the initial phonons, and oscillates in some way with time. For'weak'field with small phonons, there exists squeezing in the component of coordinate or momentum. The maximum squeezing in momentum component for...