Cavity Optomechanics with Membranes in Optical Resonators

In this thesis we study (theoretically and experimentally) various aspects of the classical and quantum dynamics of the non-isolated cavity-optomechanical system formed by a high-finesse Fabry-Pa'©rot (FP) cavity with a thin semitransparent highmechanical-quality vibrating membrane at its center. This optomechanical setup is called the Membrane-In-the-Middle (MIM) setup. In particular we show the subsequent five main results. 1. We determine to what extent optical absorption by the membrane hinders reaching a quantum regime for the cavity-membrane system. We show that even though membrane absorption may significantly lower the cavity finesse and also heat the membrane, one can still simultaneously achieve ground state cooling of a vibrational mode of the membrane and stationary optomechanical entanglement with state-of-the-art apparatuses. 2. We show that the coupling between the optical cavity modes and the vibrational modes of the membrane can be tuned by varying the membrane position and orientation. In particular, we demonstrate a large quadratic dispersive optomechanical coupling in correspondence with avoided crossings between optical cavity modes weakly coupled by scattering at the membrane surface. The experimental results are well explained by a first order perturbation treatment of the cavity eigenmodes. 3. We present an experimental study of dynamical back-action cooling of the fundamental vibrational mode of the membrane. We study how the radiation-pressure interaction modifies the mechanical response of the vibrational mode, and the experimental results are in agreement with a Langevin equation description of the coupled dynamics. The experiments are carried out in the resolved sideband regime, and we have observed cooling by a factor of 350. We have also observed the mechanical frequency shift associated with the quadratic term in the expansion of the cavity mode frequency versus the effective membrane position, which is typically negligible in other cavity optomechanical devices. 4. We demonstrate the analog of electromagnetically induced transparency in our setup at room temperature. Due to destructive interference, a weak probe field is completely reflected by the cavity when the pump beam is resonant with the motional red sideband of the cavity. Under this condition we infer a significant slowing down of light of hundreds of microseconds, which is easily tuned by shifting the membrane along the cavity axis. We also observe the associated phenomenon of electromagnetically induced amplification which occurs due to constructive interference when the pump is resonant with the blue sideband. 5. We show a phase/frequency noise cancellation mechanism due to destructive interference which can facilitate the production of ponderomotive squeezing in the kHz range and we demonstrate it experimentally, in collaboration with the University of Florence and the University of Trento, in an optomechanical system formed by a Fabry-Pa'©rot cavity with a micro-mechanical mirror.