Quantum Limited Measurements In Gravitational Wave Detectors PDF Download

Einstein's General Theory of Relativity predicts the existence of gravitational waves, which are the ripples of spacetime. Recently, ground-based kilometer scale Fabry-Perot Michelson interferometers detected the gravitational waves radiated from a pair of black holes as they coalesced and merged. This event represented a gravitational explosion of 3 solar mass of gravitational wave energy. This was the most powerful transient astronomical event ever observed. However the gravitational wave detectors required to detect this event are the most sensitive instruments ever created, able to detect a mechanical energy of ~10-32 J. The operation of gravitational wave detectors is based on the optomechanical coupling that converts tiny differential mechanical motion of the test masses to measurable optical signals. These detectors are based on the concept of a simple Michelson interferometer. However, to turn this concept into a practical design requires the creation of the most beautiful and intricate optomechanical devices. Understanding the optomechanical physics of gravitational wave detectors, and using this understanding to design methods for improving sensitivity, is the main motivation of the research work presented in this thesis. After the background introduction in Chapter 1 and 2, Chapter 3 discusses the energy exchange between circulating optical fields and the test masses by analysing a simple optomechanical model of gravitational wave detector,. This chapter reveals the fact that the gravitational wave energy can be directly absorbed by gravitational wave detectors using a process of detuning. This draws the connection between interferometric detectors with bar detectors, and gives a better understanding of laser interferometer detectors as transducers of gravitational wave energy. In Chapter 4, a new classical noise source in gravitational wave detectors is introduced. It arises from the optomechanical coupling between thermal excitations of mirror acoustic modes and the intra-cavity optical fields. The results show that the new noise source will not significantly affect the sensitivity of the detectors within the current target frequency range of advanced detectors, but could set limits on future low frequency detectors that aim to exceed the quantum noise limit. Chapter 5 to 8 in this thesis are devoted to the study of quantum noise in gravitational wave detectors. This noise comes from optomechanical interactions at the quantum level. These chapters focus on two quantum limits that constrain the sensitivity of the detectors: (1) the Standard Quantum Limit due to the trade-o between the shot noise and radiation pressure noise; (2) the Mizuno Limit due to the trade-obetween the detector's detection bandwidth and its peak shot-noise-limited sensitivity. Both of these limits can be surpassed. To beat the Standard Quantum Limit over the detection band, it has been proposed to inject squeezed vacuum into the interferometer through a very narrowbandfilter cavity. Such narrowband cavities which ideally ought to be tunable, are difficult to realise. Chapter 5 shows that optomechanics can create an extremely narrowfilter cavity bandwidth comparable to the mechanical bandwidth, which can be realised by an optomechanical cavity pumped by red-detuned laser light. Optomechanical devices are very sensitive to the thermal noise. For solving this issue, optomechanics allows us to increase the resonance frequency and the Q-factor of the mechanical resonator thereby diluting the thermal noise. This is called optical dilution. Chapter 5 also presents a novel optical dilution method which suppresses both quantum noise and potential optomechanical instabilities associated with the optical spring.Optomechanics can also create negative dispersion. Negative dispersion allows the creation of a white light cavity, which can be used in the interferometer design to circumvent the Mizuno Limit. In Chapter 6, an interferometer con-figuration with an optomechanical filter cavity operating in the dynamcially unstable blue-detuned region is studied. It is shown that, using feedback control to stabilise the system ,this configuration can in-principle broaden detector bandwidth without sacrificing its peak sensivity, thereby surpassing the Mizuno limit.The optomechanical approach to white light cavity is very different from previously discussed methods, which proposed the use of stable atomic gaseous media as to create white light cavities. Quantum noise analysis had not been done before for such systems. Chapter 7 shows that the sensitivity of an interferometer configuration with a double-gain atomic filter is strongly constrained by stability requirements and an additional quantum noise. This noise is associated with the parametric amplification process arising in atomic media. Due to these constraints, some designs are not able to surpass the Mizuno limit.Optomechanical systems are concrete examples of general linear optical measurement devices. Chapter 8 discusses the quantum sensitivity limit of these general measurement devices. Using the Heisenberg uncertainty principle, this chapter presents anew derivation of the upper bound of the displacement sensitivity of these linear optical measurement devices. The result reveals that fact that the fundamental quantum limit of a linear optical measurement device is determined by the quantum fluctuation of optical power.