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One of the noise sources that currently limits gravitational wave (GW) detectors comes from the quantum nature of the light causing uncertain amplitude and phase. Phase uncertainty limits the precision of an interferometric measurement. This measurement is also subject to quantum back-action, caused by the radiation pressure force fluctuations produced by the amplitude uncertainty (QRPN). In order to lower this quantum noise, GW detectors plan to use squeezed light injection. In this thesis, I focus on using radiation-pressure-mediated optomechanical (OM) interaction to generate squeezed light. Creating squeezed states by using OM interaction enables wavelength-independent squeezed light sources that may also be more compact and robust than traditionally used non-linear crystals. We analyze the system with realistic imperfections (losses & classical noise), and use the concepts to design an experiment to obtain the most possible squeezing in a broad audio-frequency band at room temperature. This involves an optimization for the optical properties of the cavity and the mechanical properties of the oscillator. We then show its experimental implementation, and subsequent observation of QRPN as well as OM squeezing. These are the first ever direct observations of a room temperature oscillator's motion being overwhelmed by vacuum fluctuations. This is shown in the low frequency band, which is relevant to GW detectors, but poses its own technical challenges, and hence has not been done before. Being in the back-action dominated regime along with optimized optical properties has also enabled us to observe OM squeezing. That is the first direct observation of quantum noise suppression in a room temperature OM system. It is also the first direct evidence of quantum correlations in the audio frequency band, in a broad band at non-resonant frequencies.