The performance of optical measurement systems is ultimately limited by the quantum nature of light. In this thesis, two techniques for circumventing the standard quantum measurement limits are modelled and tested experimentally. These techniques are electro-optic control and the use of squeezed light. An optical parametric amplifier is used to generate squeezing at 1064nm. The parametric amplifier is pumped by the output of a second harmonic generation cavity, which in turn is pumped by a Nd:YAG laser. By using various frequency locking techniques, the quadrature phase of the squeezing is stabilised, therefore making our squeezed source suitable for long term measurements. The best recorded squeezing is 5.5dB (or 70\%) below the standard quantum limit. The stability of our experiment makes it possible to perform a time domain measurement of photocurrent correlations due to squeezing. This technique allows direct visualisation of the quantum correlations caused by squeezed light. On the road to developing our squeezed source, methods of frequency locking optical cavities are investigated. In particular, the tilt locking method is tested on the second harmonic generation cavity used in the squeezing experiment. The standard method for locking this cavity involves the use of modulation sidebands, therefore leading to a noisy second harmonic wave. The modulation free tilt-locking method, which is based on spatial mode interference, is shown to be a reliable alternative. In some cases, electro-optic control may be used to suppress quantum measurement noise. Electro-optic feedback is investigated as a method for suppressing radiation pressure noise in an optical cavity. Modelling shows that the `squashed' light inside a feedback loop can reduce radiation pressure noise by a factor of two below the standard quantum limit. This result in then applied to a thermal noise detection system. The reduction in radiation pressure noise is shown to give improved thermal noise sensitivity, therefore proving that the modified noise properties of light inside a feedback loop can be used to reduce quantum measurement noise. Another method of electro-optic control is electro-optic feedforward. This is also investigated as a technique for manipulating quantum measurements. It is used to achieve noiseless amplification of a phase quadrature signal. The results clearly show that a feedforward loop is a phase sensitive amplifier that breaks the quantum limit for phase insensitive amplification. This experiment is the first demonstration of noiseless phase quadrature amplification. Finally, feedforward is explored as a tool for improving the performance of quantum nondemolition measurements. Modelling shows that feedforward is an effective method of increasing signal transfer efficiency. Feedforward is also shown to work well in conjunction with meter squeezing. Together, meter squeezing and feedforward provide a comprehensive quantum nondemolition enhancement package. Using the squeezed light from our optical parametric amplifier, an experimental demonstration of the enhancement scheme is shown to achieve record signal transfer efficiency of $T_{s}+T_{m}=1.81$.

Part I of this thesis is concerned with cavity optomechanical systems subject to periodic driving. We develop a Floquet approach to solve time-periodic quantum Langevin equations in the steady state, show that two-time correlation functions of system operators can be expanded in a Fourier series, and derive a generalized Wiener-Khinchin theorem that relates the Fourier transform of the autocorrelator to the noise spectrum. Weapply our framework to optomechanical systems driven with two tones. In a setting used to prepare mechanical resonators in quantum squeezed states, we nd and study the general solution in the rotating-wave approximation. In the following chapter, we show that our technique reveals an exact analytical solution of the explicitly time-periodic quantum Langevin equation describing the dual-tone backaction-evading measurement of a single mechanical oscillator quadrature due to Braginsky, Vorontsov, and Thorne [Science 209, 547 (1980)] beyond the commonly used rotating-wave approximation and show that our solution can be generalized to a wide class of systems, including to dissipatively or parametrically squeezed oscillators, as well as recent two-mode backaction-evading measurements. In Part II, we study nonreciprocal optomechanical systems with several optical and mechanical modes. We show that an optomechanical plaquette with two cavity modes coupled to two mechanical modes is a versatile system in which isolators, quantum-limited phase-preserving, and phase-sensitive directional ampliers for microwave signals can be realized. We discuss the noise added by such devices, and derive isolation bandwidth, gain bandwidth, and gain-bandwidth product, paving the way toward exible, integrated nonreciprocal microwave ampliers. Finally, we show that similar techniques can be exploited for current rectication in double quantum dots, thereby introducing fermionic reservoir engineering. We verify our prediction with a weak-coupling quantum master equation and the exact solution. Directionality is attained through the interference of coherent and dissipative coupling. The relative phase is tuned with an external magnetic eld, such that directionality can be reversed, as well as turned on and off dynamically.