Experimental Realization Of Nonlinear Dynamics With A Single Trapped Ion In Surface-Electrode Ion Trap

The Duffing oscillator is widely used to describe nonlinear dynamics in oscillating systems. The corresponding Duffing equation models a damping and driven oscillator with more complicated behavior, which can be used to exhibit chaos in dynamics and hysteresis in resonance. The ion motion in a quadruple electromagnetic trap can be effectively approximated to be harmonic, the motion will exhibit nonlinearity when the ion is driven far away from the equilibrium point. Generally, this nonlinear oscillation can be used in resonance rejection and parameter detection in mass spectrometry; on the other hand, the motion which will produce the heating effection should be avoided because it can prevent the ion to be cooled down to ground state in quantum information processing. Therefore, it is important for us to do a study on the nonlinear oscillation with trapped ion.In this thesis we focus on the work about a complicated nonlinear oscillation of trapped ion in the surface-electrode ion trap system. Our main achievements are listed as follows:Firstly, we have a deep understanding of the trap potential. To obtain a general solution to Laplace’s equation, we have expanded the potential in terms of spherical harmonics. Considering the different layouts and the fabrication asymmetry of the surface-electrode ion trap, the total potential must be added the high order multipole potentials rather than the quadruple potential.Secondly, we describe the development of a surface-electrode ion trap system for scalable quantum computation and the creation and operation of a string of crystallized ions in one dimension and two dimensions. The surface-electrode ion trap system includes the home-built fine wire trap, the ultra high vacuum system, the laser system, the fluorescence detection system and the computer control system, which the technology is involved in the different fields such as the vaccum, optics, electronics, mechanics and the computer programing. We have successfully confined40Ca+ion crystals in both one dimension and two-dimensions by elaborately controlling the voltages on the electrodes and compensating the micromotion of the ions, and also cooled the ions down to the temperature23.3mK.Thirdly, the oscillation coupling and different nonlinear effects are observed in a single trapped40Ca+ion confined in our home-built surface-electrode ion trap. The coupling and the nonlinearity result from the high order multipole potentials, such as hexapole and octopole potentials, due to different layouts and the fabrication asymmetry of the surface-electrode ion trap. We solve a complicated Duffing equation with coupled oscillation terms in the multiplescale method, which fits the experimental values very well. Our investigation in the surface-electrode ion trap contributes to exploring multidimensional nonlinearity through current techniques and suppressing instability of qubits in quantum information processing with trapped ions.In addition, we describe the development of an optica system in the linear ion trap system, which is timing controling the AOM (Acousto-optical Modulators) switches output by the computer, and optimize the optica system and the computer programing. Meantime, we finish the experiment on the time evolution of a thermal distibution on the carrier transion, and by using the Wolfram Mathematica8, we get the average occupation number in the Rabi oscillation by a fit.