I will discuss theoretical work describing how optomechanical systems can be used to measure quantum energy fluctuations of a driven mechanical resonator, and how the higher moments of such fluctuations possess unusual properties.
We provide a full quantum mechanical analysis of a weak energy measurement of a driven mechanical resonator. We demonstrate that measurements too weak to resolve individual mechanical Fock states can nonetheless be used to detect the nonclassical energy fluctuations of the driven mechanical resonator, i.e., "phonon shot noise". We also show that the third moment of the oscillator's energy fluctuations provides a far more sensitive probe of quantum effects than the second moment, and that measuring the third moment via the phase shift of light in an optomechanical setup directly yields the type of operator ordering postulated in the theory of full-counting statistics.
In the field of optomechanics, one typically studies the interaction of a single mechanical resonator and a single optical cavity mode. In this thesis, we investigate collective quantum effects in optomechanical systems with two or more optical and mechanical modes. First, we study the generation and destruction of entanglement between two mechanical resonators effected by optical cavity fields. We also describe how the optomechanical interaction can be employed to mediate strong coherent coupling and entanglement between a micromechanical membrane and a single atom. Secondly, we show that a configuration with two optical and a single mechanical mode can lead to enhanced nonlinear interactions, which can be exploited for quantum non-demolition measurements of the phonon and photon numbers. Finally, we explore the quantum many-body dynamics of optomechanical arrays. In particular, we research into the transition from a disordered state due to quantum noise to a state with phasecoherent mechanical oscillations. As an intermediate step towards this study, we also investigate the nonlinear classical dynamics of single- and multi-mode optomechanical setups and compare theoretical predictions to experimental data.
In cavity optomechanics, the standard large-detuning regime is commonly described by retaining only the radiation-pressure interaction, while higher-order mirror--field interactions are assumed to be negligible. This approximation, however, fails to provide a microscopic explanation for the vacuum-mediated heat transfer observed between the mechanical membranes in the experiment of Fong, et.al.,[Nature \textbf{576}, 243 (2019)], whose physical origin has remained under active debate. Here, using a fully quantum model, we show that the neglected higher-order optomechanical interactions naturally generate phonon-phonon coupling and quantitatively account for the observed energy exchange within the standard optomechanical framework. Building on this microscopic description, we further propose a protocol in which phonon-phonon interaction drives a cyclic process enabling net work extraction. Our results establish the fundamental role of higher-order optomechanical interactions and provide a microscopic framework for describing next-generation optomechanical experiments beyond the linear approximation.