Quantum aspects of cavity optomechanics with atomic ensembles and ensemble arrays

While the motion of a many-atom ensemble of atoms interacting strongly with a single mode of an optical resonator can be devilishly complicated, under favorable conditions, the cavity can be made to interact with and to sense just one, or just a few, normal modes of the gaseous system. This leads to an atoms-based realization of cavity optomechanics, directly analogous to experiments in which one seeks to observe the motion of suspended mirrors, cantilevers, and membranes at the quantum limits of precision. I will discuss our progress toward demonstrating and understanding the distinctively quantum mechanical aspects of both the ``opto'' and ``mechanical'' portions of cavity optomechanical systems. Specifically, I will report on the observation of the ponderomotive squeezing of light by a mechanical oscillator, and of strong motional sideband asymmetry that demonstrates the quantization of collective atomic motion and quantifies the energy flux into the mechanical system due to quantum measurement backaction. I will conclude by describing our approach to realizing strong cavity coupling to a multi-mode mechanical system, specifically to an array of distinguishable mechanical oscillators. \\[4pt] The work reported in this talk was performed in collaboration with members of my research group, including Thierry Botter, Nathaniel Brahms, Daniel Brooks, Thomas Purdy and Sydney Schreppler, and was supported by the AFOSR and NSF.