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Exact Quantum Motions of a Single Trapped Ion Interacting with Laser in Lamb-Dicke Regime

Author: YangMeiRong
Tutor: HaiWenHua
School: Hunan Normal University
Course: Atomic and Molecular Physics
Keywords: Trapped Ions Laser pulse Laser standing wave Lamb-Dicke approximation Exact solution
CLC: O413.1
Type: Master's thesis
Year: 2010
Downloads: 45
Quote: 0
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Abstract


Ion trap as a modern atomic and molecular physics research one of the most representative devices, has been widely used in various fields of science and technology research. Trapped ions and in particular the combination of laser cooling, the ion trap has broader application. It is not only used as a powerful tool to be used to test the basic principles of quantum mechanics, and in quantum logic operations, quantum computing, quantum information and quantum state preparation and other high-tech fields of study and more are being extensively used, makes people trapped ions in the ion trap kinetic characteristics of growing interest. However, due to external environmental parameters and initial conditions of its own has a great influence trapped ions, the two small changes may cause large ion trajectory shift occurs, the movement of ions occurs even cause chaos, so makes it difficult to control the motion of ions. Therefore, the dynamics of trapped ions depth study also very important. This paper is divided into four chapters, the main contents are as follows: The first chapter introduces the basic principles and Paul trap ions trapped less research the history and status quo. In the second chapter, the research standing wave laser pulses, imprisoned in a Paul trap single ions in the Lamb-Dicke area duration exercise. Only a limited form of the system obtained exact solutions of classical mechanics, but also through trial solution method to obtain exact solutions of the system of quantum mechanics and non-continuous time-varying spectrum. Based on the exact solution describes the probability wave packet string and energy expectation value, we find: a) the Lamb-Dicke region, the ion motion does not appear chaotic state; b) wave packet wave packet string string center and the height and width by laser pulses The strength and wave vector control, by adjusting the laser intensity and wave vector can control the deformation of the wave packet string and dissemination: c) laser pulses in an instant, the ion energy expectation value transitions, while in the laser off period, there is a narrow band form: d) there is a laser pulse intensity and the wave vector of the critical value near the critical point, system stability will change. In the third chapter, under the action of laser standing wave, imprisoned in a Paul trap single ions in the Lamb-Dicke area duration exercise. Obtained system of infinite series exact solution in the form of classical mechanics, the same way through the trial solution to obtain exact solutions of the system of quantum mechanics and the continuous time-varying spectra, it is with the classic Mathieu equation directly. Mathieu Equations by taking into exact solution of quantum mechanics, we analyzed the probability of laser standing wave packet on the specific impact of the string, the following conclusions: a) wave packet string height and width of the range of functions in a small time period oscillations by laser impact is very small, the wave packet string propagation in space, the approximation is not deformed. b) a first approximation, the center wave packet string periodic oscillation amplitude and frequency are controlled by the laser field, the greater the intensity of the laser, the smaller the frequency, the wave packet string smaller oscillation amplitude, oscillation frequency, the greater; When the intensity of the laser is smaller, the higher the frequency, the oscillation amplitude of the wave packet string greater the frequency of oscillation is smaller. The fourth chapter is a summary of the work of this thesis, and Paul Trapped Ion Dynamics made a prospect. In this article, the author's main work focuses on the second and third chapters.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Quantum theory > Quantum mechanics ( wave mechanics,matrix mechanics )
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