On quantum effects in the dynamics of macroscopic test masses

Abstract

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.