光腔-机械振子-原子三元杂化腔光机械系统中光学性质的理论研究

Cavity optomechanical systems，developed in recent years, have become a new field in quantum optics and nonlinear optics. Due to the coupling between the optical degree of freedom (optical cavities) and the mechanical one (mechanical resonators) by the radiation pressure of light, it is easy to achieve quantum control over mechanical motion or, conversely, mechanical control over optical fields in such a coupled system. These properties make the cavity optomechnaical system have potential applications in quantum control, all optical communication, and optical information processing. . This project proposes to discuss the nonlinear dynamics and the propagation properties of light in a hybrid cavity optomechanical system with three coupling elements as the cavity, atoms and the resonator. By adding dissipation and fluctuation terms to the Heisenberg equations of motion derived from the Hamiltonian of the system, a set of nonlinear Heisenberg-Langevin equations, describing the dynamics of the hybrid system, is obtained. With Fourier transform method, the equations can be solved in frequency domain. The electromagnetically induced transparency phenomenon, slow light effect, and the amplification effect of the signal light will be discussed detailedly in this hybrid system, and the influence on the light propagation in this hybrid system will be exploited due to the change of the couplings between the cavity with the atoms as well as with the mechanical resonator. Schemes for realizing an all optical memory and transistor based on this hybrid system will be proposed. This project provides the theoretical basis for the possible applications of the hybrid cavity optomechanical system on all optical communication and optical information processing.

腔光机械系统是近年来在量子光学和非线性光学领域发展起来的一个新的研究领域。在腔光机械系统中，由于光学自由度（光腔）和力学自由度（机械振子）在光辐射压作用下相互耦合，因而利用该系统可以实现对力学元的量子操控及对光传播的有效调制。这使得腔光机械系统在量子调控及全光通讯和光信息处理方面有着潜在的应用价值。. 本项目拟以光腔-原子-机械振子三元杂化腔光机械系统为研究对象，讨论三元杂化系统中的非线性动力学行为和光传播特性。根据体系的哈密顿量，考虑系统的耗散及涨落项，推导出海森堡-朗之万方程组；利用傅里叶展开法在频域求解此方程组。讨论系统中光腔与原子及光腔与机械振子双耦合机制对电磁诱导透明、慢光及光信号放大效应的调制作用，提出基于该杂化系统实现理论可行的全光存储器及全光晶体管的理论方案，为三元杂化腔光机械系统在全光通讯及光信息处理领域的应用提供理论依据。

经过一年的努力，本项目按计划研究了光腔-机械振子-原子系综三元杂化系统中的光学效应，得到了一系列新的结论。1.研究了系统中的类电磁诱导透明现象，发现在该三元杂化系统中存在双窗口类电磁诱导透明现象。2. 研究了该三元杂化系统中的慢光和快光效应。3. 研究了系统中的光信号放大效应，发现了双窗口放大效应。4. 进一步研究了该三元杂化系统中的光学双稳行为。基于这些研究结果，后期我们将继续探讨系统中的其他非线性光学效应，如高阶边带效应等。在本项目资助下，我们在国际核心刊物发表论文一篇（Physical Review A，已接收），在全国百佳图书出版社出版专著一部，此外，有两篇文章在投稿，还有一些结果正在整理成文。