Approaching broadband quantum-limited displacement noise in a deformable optical cavity

An outstanding goal of the optomechanics community, particularly in the field of gravitational wave detection, is to demonstrate a system with a broadband displacement sensitivity limited by quantum fluctuations of the probe field. This thesis presents significant progress in this direction, namely a means of achieving a sufficiently small off-resonant thermal noise of a deformable optomechanical cavity through the incorporation of a low mass, highly compliant, cryogenically cooled mirror structure with a sensitive motional readout. We conclusively demonstrate the mitigation of Brownian fluctuations in this system by the reduction of the thermal bath temperature, and our measurements are shown to be in close agreement with a finite element analysis of the device. This analysis has been utilized in devising improved oscillator geometries. This work provides a clear path towards the observation of quantum fluctuations in our system and demonstrates the Brownian properties of the crystalline multilayers which make them a promising technology for the realization of low-thermal-noise reflectors in the quantum regime