与超冷原子一样，超冷分子在精密测量、量子信息处理等方面有重要应用。如何得到超冷分子是人们首先要解决的问题，利用超冷原子来制备超冷分子是一种非常有效的方法，这使得超冷原子-分子耦合系统成为人们的研究对象。一般情况下，系统由大量微观粒子组成，应用量子光学和量子统计理论能够揭示系统所满足的宏观统计规律，并提供相应的微观解释。论文沿着这一思路，详细研究如何利用超冷原子来制备超冷分子，分析超冷原子-分子耦合系统的类光学特性。首先，论文研究了费米原子-分子耦合系统。该系统中自旋相反的费米原子通过Feshbach 共振方法形成基态分子。论文分析了背景粒子s-波散射对系统工作的影响，通过忽略各费米原子参与分子形成过程的概率差异，对多粒子系统进行简化，结合数值模拟，发现背景s-波散射在系统以分子形式存在为主的演化阶段有明显影响，其中排斥势散射有利于分子的形成。分子场在系统演化过程中会出现sub-Poisson统计分布。其次，论文对玻色原子-分子系统进行了分析，讨论了分子转化率随时间的变化关系，同时，为了更好的分析系统的纠缠特性，我们计算了系统的熵。在此基础上，我们研究了原子相干效应对超冷两态原子经光缔合形成分子的影响，发现光缔合形成的分子数随时间作近周期减幅振荡。其中原子相干效应对光缔合过程的暂态阶段影响强烈，而分子场始终保持sub-Poisson统计分布。最后，论文讨论了基于受激拉曼绝热通道(STIRAP)的原子-分子耦合系统的相干布居俘获。我们先对玻色原子-分子耦合系统的Λ型三能级模型进行研究，超冷原子在泵浦脉冲和斯托克斯脉冲作用下形成分子，计算了系统内各个态上的分子数分布，并利用平均场理论分析了分子在低能态上的相干布居俘获，以及绝热参数随脉冲变化情况。接着将上述研究推广到原子-分子耦合系统的双Λ型五能级模型，讨论分子在各能级状态上的分布。给出以粒子数态表示的相干俘获态，分析一般态与俘获态的交叠。我们发现利用STIRAP技术，双Λ型五能级原子-分子模型能够将两种分子相干俘获到相应的基态，通过改变作用脉冲，可以改变这两种分子的数量。

Ultracold atoms and molecules play an important role in quantum information and the manipulation of quantum states. In recent years it’s found that it is a useful way to prepare ultracold molecules with ultracold atoms, and it makes the ultracold atom–molecules coupled system become the focus of recent research. Quantum optics provided useful theories on studying ultracold atoms and molecules. Under normal circumstances, the system is composed of a large number of particles. Quantum statistical methods can give a microscopical explanation of such system and reveal the inherent laws. This paper will study the optical-like properties of ultracold atom-molecule coupled systems by these methods.Firstly，coupled Fermi atom-molecule system will be studied. The influence of the s-wave scattering of background particles on the association or disassociation of molecules in a system composing of two species of Fermi atoms with opposite spins and molecules is studied. Assuming that all Fermi atoms have the same probability in the formation of molecules, the system is simplified. The influence of the s-wave scattering becomes obvious in the period of evolution when most of the particles in the system are molecules, where the scattering with repulsive potential is propitious to the formation of molecules. Sub-Poisson statistical distribution of the molecular field is observed.Secondly, we discuss the coupled Bose atom-molecule system. Molecule conversion rate and entropy of system can be calculated according to the dual-mode Bose atom-molecule system by two methods: quantum statistics and Heisenberg equation. Based on the study, considering tri-mode atom-molecule model, the influence of atomic coherence on the formation of a molecular BEC from ultracold two-state atoms via photoassociation is discussed. The results show that, under the action of atomic coherence, the molecule number vibrates with an approximate period and the damped amplitude. We find that though atomic coherence has a strong influence in the transition of the whole photoassociation process, the molecules are always subjected to sub-Poisson statistical distribution.Finally, we want to study the coherent population trapping of the system based on the stimulated-Raman-adiabatic-passage (STIRAP). For Λ-type three-level atom-molecule model, molecules are formed from Bose atoms under the effect of pump pulse and Stokes pulse. The population distribution of molecules in different states is calculated via statistical methods. We find that the majority of atoms are converted to ground state molecules rather than those in excited state. The trapping state of the system is analyzed by the mean-field approach, and the adiabatic parameters of system change with the adjusted Rabi frequency of two pulse beams. Then the model is extended to the double Λ-type five-level atom-molecule system which is controlled by two groups of pulses. The trapping state is given in the form of the superposition of three low-energy states. We focus on the analysis of the population in these low-energy states, as well as the overlaps between the trapping state and the general state of the system. The number of molecules on the various states can be changed by adjusting the Rabi frequency of the coupling pulses.