弗兰克-康登效应在离子阱量子信息处理中的应用研究

The purpose of this project is to study Franck-Condon effect and its application in linear trapped-ion quantum information processing. Based on Franck-Condon principle, ionic Franck-Condon physics is explored with the superposition of vibrational wave functions generated by spin-dependent potential induced and controlled by a magnetic field gradient. Experimental schemes will be designed based on realistic magnetic field gradient and other parameters in the devices. The main contents are as follows: On the one hand, by numerically solving the master equation of the system and using the evolution of the superposition of vibrational wave functions, we explore 3D sideband cooling of the trapped ions via adiabatic fast passage microwave pulses and Franck-Condon blockade; On the other hand, the applications in quantum state engineering are discussed, including how to control the ion by manipulating the vibrational states with the evolution of the system; focusing on the impact of the experimental error on Franck-Condon physics by analyzing different parameters; investigating how to manipulate the quantum states by mean of the superposition of the vibrational wave functions. The project focuses on the combination of the theory and the experiment, which not only helps to deepen our understanding of Franck-Condon principle, but also provides a theoretical reference to the physical study of complex systems.

本课题旨在研究线性离子阱中离子的弗兰克-康登效应及其在量子信息处理中的应用。基于弗兰克-康登原理，在梯度磁场作用下利用自旋相关势引起的离子振动跃迁波函数的叠加来探求囚禁离子的弗兰克-康登物理。将结合实验装置中梯度磁场等参数的数值，设计实验方案。具体研究内容如下：通过数值求解系统的主方程，利用离子振动跃迁波函数的叠加演化，一方面引入绝热通道微波脉冲借助弗兰克-康登阻塞开展对囚禁离子的3D边带冷却工作；另一方面讨论弗兰克-康登效应在量子态操控方面的应用，包括：考虑系统的演化如何通过控制振动态来操控离子；讨论不同实验参数下实验误差对弗兰克-康登效应的影响；研究如何利用振动波函数的叠加进行量子态操控。本课题着眼于理论结合实验进行，将不仅有助于深化我们对弗兰克-康登原理本身的认识，而且也为研究复杂体系的弗兰克-康登物理提供理论参考。

鉴于真空的超洁净环境和内外态的高可控性，离子阱系统成为实现量子信息处理的重要物理体系之一。本课题从理论上研究了线性离子阱中离子的弗兰克-康登效应及其在量子信息处理中的应用。基于离子激发态和基态之间弗兰克-康登阻塞，我们得出一定的阱频和磁场梯度可以延长离子激发态的寿命，从而在一定程度上压制离子激发态的自发辐射；并利用主方程方法中的Lindblad方程来求解体系的弗兰克-康登因子随时间的变化，进而探求体系中弗兰克-康登效应的动力学特性。在此基础上，开展了弗兰克-康登效应在量子态操控方面的应用研究，比如弗兰克-康登效应对两比特CNOT门的影响以及运动态Fock态的制备等。这些研究成果结合实验进行，不仅有利于深化我们对弗兰克-康登原理的认识，而且也有助于复杂体系的弗兰克-康登物理在量子信息方面的研究。