The Research Of Properties Of Squeezing In Phonon Fields Of Trapped Ions

Ion trap is a typical and important system in physics, which has attracted more attentions for a long time and gained many important implications including the test of physics law, measurement of basic physics constant, measurement of precise spectroscopy and design of high-precise frequency standard. The system h'as made a rapid progress in quantum information processing, which is regarded as one of the prominent selective delegates in constructing quantum computer. In this system quantum bit is represented by two internal states of a trapped ion can be controlled by the interaction with lasers. It is important to study in detail the dynamical properties of trapped ions driven by laser. In this thesis, we mainly discuss the squeezed property of the phonon influenced by internal coherence of trapped-ion.In the first chapter, for the requirement of completeness of the content, we introduce the coherence of light field and its implications in Young's double-slit experiment and single-particle interference experiment based on the principle of state superposition of quantum mechanics. We also introduce the definition of squeezing and squeezed state, which provides theoretical foundation for the research of coherence of internal states and squeezing of vibratile phonon field.In the second chapter, we introduce briefly the structure of ion trap, the basic principle of trapping ion, the method of laser cooling, including Doppler cooling and side band cooling.In the third chapter, we discuss the interaction of two two-level trapped ions with classical laser field without Lamb-Dicke approximation. We find that the dynamics of the internal states of two trapped ions coupled to their phonon field can be described by a nonlinear Jaynes-Cummings model when the frequency of classical driving filed is resonant to the red-side band of center-of-mass mode. The coherence of internal states can induce squeezing of vibratile phonon field. When the internal state of trapped ions is initially in a non-coherent mixed state and the phonon field in a vacuum state, the evolved state of the phonon field does not appear squeezing; However, when the internal state is initially in a coherent superposition of pure states and the phonon field in a vacuum state, the evolved state of the phonon field shows squeezing. Under proper initial conditions, the squeezing is persistent and periodic in time, in particular, squeezed vacuum state can be obtained.