Manipulation Of Quantum State In Cold Trapped Ion System

As a highly controllable system,trapped ion system is one of the most important platforms for quantum computing as well as quantum simulation and fundamental quan-tum mechanics.In this thesis,we first give a brief review of the principle of ion trap and the basic laser ion interaction,and then we describe the two trapped ion systems we used,which are the four rod linear ion trap for¹⁷¹Yb⁺?Simon Fraser University?and the blade-shaped Paul trap for⁴⁰Ca⁺?NUDT?.Meanwhile we introduce the optimization methods for micro-motion compensation and ion loading.Next we quantitatively sepa-rated the dephasing sources,which are mainly the laser and magnetic field noise,by using the 5 transition lines with different magnetic sensitivities of a single trapped⁴⁰Ca⁺and the conventional Ramsey experiment,and we proposed some methods for optimization of laser frequency noise and the coherence of qubit is improved.Then we introduced three experiments related to the manipulation of quantum states of trapped ions.Since the lin-ear ion string has a similar structure to crystals and the potential for trappping ions can be precisely controlled by tuning the external electric field,trapped ions are very suitable for simulating crystals.In the first work we investigated the structural quantum phase transition in the four rod ion trap.This work includes the optimization of trap frequency stability by precisely sampling and freedback control of the RF voltage,and the measured stability of trap frequency is better than 5 ppm in both radial and axial directions.Besides the spectroscopy of trap potential near the linear to zigzag phase transition of 4¹⁷¹Yb⁺ions is also measured.In the second work,we demonstrated the application of shortcuts to adiabaticity?STA?in quantum adiabatic research by realizing quantum adiabatic Grover's search algorithm with the help of STA.Lastly,we proposed and realized an experimental scheme for demonstration of the weak value amplification effect by using the pure atomic degrees of freedom?internal and motional state?of a single trapped⁴⁰Ca⁺ ion.In this work we verified that the tiny shift of the wavepacket of motional ground state can be am-plified by 25 when the weak value is real and the amplification effect is extremely sensitive to relative phase of internal state when the weak value is an imaginary number,this work paves the way for the quantum metrology.