腔光力系统基于辐射压实现腔模和力学振子模之间的耦合，它是研究光力 耦合量子现象的重要平台。近年来，随着半导体制造工艺的改进和纳米技术的 发展，各种具有实用价值的腔光力装置被制造出来，并从中观察到丰富的光力 耦合量子效应。例如，基于腔光力系统ᨀ出的量子态转移、量子纠缠态的制 备、量子相位门的构建和光子阻塞效应的实现等。这些研究成果在量子信息与 量子计算领域内具有重要的科学意义和应用价值。本论文主要研究基于腔光力 系统的量子态操控。论文的主要成果如下:

论文提出了一个基于腔光力系统、利用非绝热和乐量子计算的方法，构建 一组普适的单比特量子门的方案。所研究的系统包含两个光学腔以及与它们每 一个都耦合的机械振子，它利用系统的单激发态构成计算子空间，通过调节光 力耦合，在满足平行输运和循环演化的条件下，获得一组普适的单比特非绝热 和乐量子门。这组量子门包含Not门和Hadamard门，可分别用于实现双腔之间 的态转移和纠缠产生。我们还评估了环境噪声对量子态保真度的影响。本方案 实现的这组单比特量子门还具有内禀容错以及能被快速构造实现的优点。

论文提出了一个实现基于量子化机械振动的非局域声子的纠缠浓缩方案。 该方案需要两对具有相同部分纠缠形式的非局域声子对，其中一对为拟被浓缩 的目标纠缠声子对，另外一对是帮助实现目标声子对纠缠浓缩的辅助声子对。 仅需通过如下三个步骤便可以完成纠缠浓缩。第一，利用腔光力的交叉克尔相 互作用和Mach-Zehnder干涉仪的结合，经过成功后选择产生目标声子和辅助声 子之间的最大纠缠；第二，用红失谐的泵浦光驱动腔光力系统实现声子和光子 的态转移；第三，进行Bell态分析。我们的方案既可以完成对处于Bell态的非局 域部分纠缠声子对的浓缩，还可以拓展到多声子的情况。

论文提出了一个基于旋转腔光力系统制备非互易机械压缩的模型。在这个 模型中，一个回音壁腔模耦合到一个具有杜芬非线性的振子模，而后者同时与 另一光学模存在二次方耦合。杜芬非线性和二次方光力耦合的协同作用产生机 械压缩，旋转回音壁腔的光学Sagnac效应则引发压缩的非互易性。我们揭示了 非互易机械压缩对系统控制参数的依赖关系，发现由本模型实现的非互易机械 压缩对环境热噪声具有鲁棒性，具有实现经典态和量子态之间转换的声子开关 功能。

论文研究了基于周期调制光力耦合的腔光力系统的探测响应。在该模型 中，两束频率相近、相位差固定的相干光注入一个Fabry-Perot ´ 腔，其所形成的 拍频场与相应的腔光力系统的相互作用，使得频率与低频注入场相同的腔内场 的振幅按两注入场的拍频做周期变化，从而实现了对该系统光力耦合的周期调 制。光力耦合调制的引入，改变了光力系统原有的探测响应特性，例如，探测 谱中，探测场的透射在光力诱导透明点两边由没有调制时的探测吸收转变成现 在的探测放大；系统具有光学晶体管的功能，通过调节光力耦合参数的相位和 幅度来实现探测放大和探测吸收之间的切换，以及可控慢光效应等。

Cavity optomechanical system (COMS), where a cavity mode couples to mechanical oscillator mode via radiation-pressure force, is an important platform for investigating the quantum phenomena resulting from optomechanical coupling. Recently, with the improvement of semiconductor technology and the development of nanotechnology, various cavity optomechanical devices have been manufactured and the rich quantum effects based on the COMS, such as the quantum state transfer, the preparation of quantum entanglement, the construction of quantum phase gate, and the realization of photon blocking effect, have been observed. These achievements are of the significance of science and important application values in the quantum information and quantum computing. In this thesis, we focus on the manipulation of the quantum state of a COMS. The main achievements of this paper are as follows:

We propose a scheme to achieve a set of universal single-qubit quantum gates based on a COMS by using the nonadiabatic holonomic quantum computation. The system under consideraion consists of two optical cavities which both couple to a mechanical oscillator. A computing subspace is constructed with the single-excited states of the system and, by adjusting the optomechanical coupling, a set of universal single-qubit nonadiabatic holonomic quantum gates are obtained under the conditions of parallel-transport and cyclic evolution. This set of universal quantum gates includes NOT gate and Hadamard gate, which can be used to achieve the quantum state transfer and the entanglement generation between two optical cavities, respectively. We also evaluate the effect of environmental noise on the fidelity of quantum state. Our singlequbit gates have the advantages of inherent fault tolerance and can be implemented quickly.

We realize the entanglement concentration (EC) for nonlocal phonons from quantized mechanical vibration. Our scheme requires two pairs of nonlocal phonon pairs with the same partially entangled form. One is the target entangled phonon pair to be concentrated, and another is the auxiliary phonon pair for helping the EC operation. Only three steps are needed. First, the combination of the optomechanical cross-Kerr interaction and the Mach-Zehnder interferometer is used to generate the maximum entanglement between the target phonon and the auxiliary phonon after the successful selection. Second, a state transfer between phonons and photons is performed based on a COMS driven by a red-detuned pump laser. Third, the Bell-state analysis is made. Our scheme can realize the EC for the nonlocal partially entangled phonon pairs in the Bell state and also applies to the multi-phonon EC.

We purpose a scheme for generating the nonreciprocal mechanical squeezing (NMS) based on a spinning COMS. In this scheme, a whispering-gallery-cavity (WGC) mode couples to a mechanical mode of Duffing nonlinearity, while the latter also couples quadratically to an optical mode. The mechanical squeezing results from the joint effect of the Duffing nonlinearity and the quadratic optomechanical coupling, and the optical Sagnac effect of the spinning WGC induces the nonreciprocity of the mechanical squeezing. We reveal the dependence of the NMS on the control parameters, which shows the robustness of our NMS scheme to the thermal noise of the mechanical environment, and find its phonon-switch function for the transformation between classical state and quantum state. Our result has reference values for realizing in practice the phonon-based information processing and communication.

We investigate a probe response of a COMS with a periodically modulated optomechanical coupling. In this investigation, two coherent beams with their frequencies separated each other by a small distance and fixed phase difference are injected into a Fabry-Perot cavity, and the interaction between the beat-frequency field formed from ´ the input fields and the corresponding COMS makes the amplitude of their intracavity counterpart whose frequency is the same as that of the injected field with low frequency change periodically according to the beat frequency, which leads to the periodic modulation of the optomechanical coupling of the COMS. The introduction of the periodic modulation of the optomechanical coupling changes the probe response of our COMS. For instance, at both sides of the optomechanical induced transparency point on the probe spectrum, the transmission of the probe field is switched from the absorption in the absence of the modulation to the amplification in the presence of modulation. The system has the function of an optical transistor, that is, it can switch from the probe amplification to the probe absorption or vice versa, and realize controllable slow light effect by adjusting the optomechanical coupling.