一些简单的量子系统，例如量子光学、离子阱、冷原子系统，可以被非常好的操控，它们是实现量子调控的理想系统。就目前的技术水平而言，在可以预见的一段时间内，要实现有一定规模的普适量子计算还是一个非常有挑战的任务。然而，现有的技术已经可以用来实现一些特定的量子任务，特别是模拟一些基本物理原理，例如相变非平衡动力学中的Kibble-Zurek(K-Z)机制。K-Z机制是描述相变过程中拓扑缺陷密度与系统参数变化速率之间关系的理论,它直接和相变过程中的对称破缺相关联。在经典相变（由温度驱动）情况下，已有实验验证了K-Z机制的有效性。然而在量子相变（由量子起伏驱动）中，到现在为止，还未有可靠的实验来检验其正确与否。我们将在前期工作的基础上利用量子光学系统来模拟横场量子Ising 模型中的拓扑缺陷密度，进而检验量子相变中的K-Z机制。

Some well controllable systems, such as ultra-cold atoms,ion traps and quantum optical systems, are idea systems for quantum manipulation. Although it is a big challenge to implement a practical large-scale universal quantum computation with current technologies, these techonologies still can do some important quantum tasks, and particular simulation of some physical principles, such as Kibbel-Zurek Mechanism (KZM) in nonequilibrium dynamics in quantum phase transition. The KZM describes the relation between the density of topologic defects and the transite rate. This mechanism directly connectes with the symmetry broken during second order phase transitions. For the classical phase transition, the KZM has been experimentally confirmed in a lot of different systems. However, the experiments of the KZM in quantum phase transition are till missing. In this study, we will focus on the KZM in quantum phase transition based on our verification of adiabatic-impulse aproximation in Landau-Zener model. We will simulate the defect production in the transverse field quantum Ising model during the phase transition and try to confirm the KZM based on quantum optical systems.