复合腔光力系统中算符法结合条件测量制备量子态及其量子Tomography研究

腔光力系统中的非经典量子态是研究宏观量子物理、量子精密测量和量子信息处理等方面宝贵的量子资源。针对当前主方程法在制备腔光力系统量子态上存在的不足，本项目提出构造复合腔光力系统，利用复合系统的时间演化算符与条件测量相结合的方法制备量子态，进而研究它们的非经典性质。通过分束器和参量放大器引入非高斯操作，研究这种直接执行于腔场的非高斯操作对所制备的光-机械量子态、机械量子态非经典性质的影响。另一方面，当前机械量子态、光-机械量子态量子Tomography重构的理论研究还十分滞后，为此，通过建立机械振动模坐标-动量中介表象、腔模与机械振动模中介纠缠态表象，发展腔光力学中的量子Tomography理论，并计算含机械振动模量子态的Tomogram。本项目的研究将为腔光力学进一步应用提供新的信息载体，并为腔光力学中的Tomography实验设计研究提供有益的理论参考。

Non-classical quantum state in cavity optomechanical system is precious quantum resource in the fields of macroscopic quantum physics, quantum precision measurement and quantum information processing. Aiming at the defect of the master equation approach in the aspect of producing quantum state, our project proposes to construct composite cavity optomechanical systems and prepares optical and mechanical quantum states by virtue of the combination of time evolution operator and conditional measurement, and then researches their non-classical properties. We introduce the non-Gaussian operation on optical field by means of beam splitter and parametric amplifier and study how the presence of this non-Gaussian operation affects the non-classical properties of the optomechanical quantum states and mechanical quantum states. On the other hand, in view of the fact that the study of quantum Tomography theory is still lagging behind at present, we develop the quantum Tomography theory within cavity optomechanics and calculate the Tomogram of the quantum states with mechanical mode by establishing position–momentum-intermediate representation of the mechanical mode and optomechanics-intermediate entangled state representation. The research of this project will provide new information carriers for the further application of cavity optomechanics and useful references for the experimental designs of Tomography in cavity optomechanics.