Marzioni, Francesco (2025) Membrane-in-the-middle as paradigm for multi-oscillator optomechanics and rf electro-optomechanical transducer. [Tesi di dottorato]

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Abstract

This thesis has been written at the end of a three-year PhD program in Quantum Technologies offered jointly by University of Napoli “Federico II”, University of Camerino and CNR Firenze. My research activities have been carried out in the Optomechanics Laboratory at the University of Camerino, and the main works that I faced in this period are collected in this manuscript. Most generally, the treated topics belong to the investigation of systems based on the coupling between electromagnetic modes and mechanical modes. The contents are divided in two Parts to distinguish two different models and implementations. The first one reports about the advances in two-membrane cavity optomechanical systems, in particular we are interested in the so called sandwich-in-the-middle implementation, where two parallel membranes are placed inside a Fabry–Pérot optical cavity. The focus is on the analytical description of the two-membrane etalon dynamics, on the analysis of the effect of laser noise on the optomechanical system, and, finally, on a full dynamics model for the optomechanical system. The results presented in Part I constitute a significant contribution to the field because they lead to a more general description and understanding of the sandwich-in-the-middle system. Part II presents the research on electro-optomechanics. In this case the system is based on the membrane-in-the-middle scheme involving a single membrane in a Fabry–Pérot cavity. This solution allows to couple, at the same time, the mechanical mode to the electromagnetic mode of an LC-circuit in the radio-frequency domain via capacitive coupling, provided that the membrane is partially covered with a metal layer. The great interest on this kind of devices is justified by its possible application in signal transduction between the optical and the radio-frequency ranges of the electromagnetic spectrum, exploiting the common coupling to the same mechanical mode. We provide a theoretical model to cool down the radio-frequency circuit to the quantum ground state by means of optical sympathetic cooling assisted by optical in-loop feedback. Moreover, this thesis reports about the characterization of a membrane with an on-chip loss shield, in a cryogenic environment, designed for the purpose of implementing the electro-optomechanical device. The contributions are useful for the experimental realization of the transducer, and for reaching the quantum regime of operation in the radio-frequency range of energy, where the circuit is not in the ground state even at millikelvin temperature.

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