On quantum effects in the dynamics of macroscopic test masses
On quantum effects in the dynamics of macroscopic test masses
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宏观测试质量动力学中的量子效应
DOI：
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发表时间：
2009
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通讯作者：
H. Müller
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作者：
H. Müller
在上个世纪，两个革命性的新概念丰富了理论物理领域：量子力学理论和广义相对论。后者预测了引力波的存在，引力波可以从大质量天体发出。利用大型激光干涉仪首次直接观测引力波，给出了最有希望的探测器设计。这些干涉仪在手臂的伸展以及镜面测试质量的大小和重量方面都很大。由于各种可能的技术改进，干涉仪的灵敏度将会越来越高。预计计划中的下一代激光干涉仪引力波探测器的灵敏度在测量过程中已经受到量子效应的限制。这无疑提出了一个问题，即探测器测试质量的动力学中是否存在量子效应。本论文将在理论上提供引力波探测器灵敏度的提高与在这种探测器中制备宏观量子态的可能性之间的联系。在本论文的第一部分，我们从理论上探讨了一种光学测速仪的量子测量噪声--Sagnac干涉仪，它在输出端口附加了一个失谐腔。这种失谐信号回收技术已经在迈克尔逊干涉仪上进行了研究，并被用于引力波探测器GEO600。结合简单Sagnac干涉仪的量子噪声分析，这是我们研究的基础：我们优化了Sagnac干涉仪对现实经典噪声环境附近的某个引力波源的探测灵敏度。由于迈克尔逊干涉仪作为一种位置计，具有失谐信号循环，可以将引力波应变转换为真实的镜面运动，因此我们比较了速度计和位置计中的换能器效应。此外，我们还从理论上研究了相对于其载波和子载波失谐的腔的条件输出压缩。在此基础上，对有质动力挤压机进行了理论分析。在第一部分关于激光干涉仪量子测量过程的知识的基础上，本文第二部分对干涉仪测试质量的位置和动量条件态进行了理论分析。我们的动机不是从随机主方程中获得条件状态，而是借助所谓的维纳滤波方法。利用这种方法，我们计算了在任何线性马尔可夫测量过程下，测试质量的高斯态的条件协方差矩阵的最一般表达式。然后我们具体到干涉计量学，并从理论上说明在什么情况下迈克尔逊干涉仪中测试质量的条件态变得接近于纯量子态，表现出压缩甚至纠缠的量子特征。这当然取决于经典噪音的水平。但我们通过给出经典噪声的频谱和干涉实验中的标准参考标准量子极限之间的必要关系来量化这一点。
In the last century two revolutionary new concepts have enriched the field of theoretical physics: the theory of quantum mechanics and the general theory of relativity. The latter one has predicted the existence of gravitational waves, which can be emitted from massive astrophysical objects. The most promising detector design for the first direct observation of gravitational waves is given by large-scale laser interferometers. These interferometers are large in terms of the extension of their arms as well as in terms of the size and the weight of their mirror-endowed test masses. Due to a vast choice of possible technological improvements the sensitivity of those interferometers will be increased more and more. It is expected that the sensitivity of the planned next generation of laser interferometer gravitational-wave detectors already becomes limited by quantum effects in the measurement process. This certainly raises the question about the existence of quantum effects in the dynamics of the test masses of the detector. This thesis will theoretically provide a link between the increase of the sensitivity of gravitational-wave detectors and the possibility of preparing macroscopic quantum states in such detectors. In the first part of this thesis, we theoretically explore the quantum measurement noise of an optical speed meter topology, the Sagnac interferometer, equipped with an additional detuned cavity at the output port. This detuned signal-recycling technique was already investigated when applying it to a Michelson interferometer and is used in the gravitationalwave detector GEO600. Together with the quantum noise analysis of the simple Sagnac interferometer, it is the basis of our study: we optimize the Sagnac interferometer’s sensitivity towards the detection of a certain gravitational-wave source in the vicinity of a realistic classical noise environment. Motivated by the fact that the Michelson interferometer, as a position meter, with detuned signal-recycling can transduce the gravitational-wave strain into real mirror motion, we compare the transducer effect in a speed and in a position meter. Furthermore, we theoretically investigate the conditional output squeezing of a cavity which is detuned with respect to its carrier and its subcarrier. Therewith we pursue the theoretical analysis of the ponderomotive squeezer. With the knowledge gained in the first part about the quantum measurement process in laser interferometers, the second part of this thesis comprises a theoretical analysis of the conditional state in position and momentum of the interferometer’s test masses. We motivate not to obtain the conditional states from a stochastic master equation but with the help of the so-called Wiener filtering method. Using this method, we calculate the most general expression for the conditional covariance matrix of the Gaussian state of a test mass under any linear Markovian measurement process. Then we specify to the interferometry and theoretically show under which circumstances the conditional states of the test masses in a Michelson interferometer become close to pure quantum states, showing quantum features as squeezing or even entanglement. This certainly depends on the level of the classical noise. But we quantify this by giving a necessary relation between the spectrum of the classical noise and a standard reference in interferometric experiments, the standard quantum limit.