Cavity electromechanics using flipped silicon nitride membranes

Silicon nitride (SiN) membrane electromechanics have shown to serve as excellent systems for applied research on sensing and transduction applications. Nevertheless, their relatively large mass in combination with high-Q also makes them suitable formore fundamental research, where gravitational effects can be tested on large mass quantum states, an experiment which has been elusive till so far. However, creating long-lived mechanical quantum states can be challenging for numerous reasons. One difficulty arises when integrating these membranes into a microwave circuit. In particular, the degradation of the mechanical resonator quality factor in an unpredictable manner. Another complication is that we often have to deal with a low coupling between the devices, which makes the control aspect of the mechanical resonator tougher.
In this thesis, we present a robust SiN based electromechanical platform that uses a custom-built flipchip tool. It allows for achieving single photon-phonon coupling on the order of Hz and high-Q factors at cryogenic temperatures consistently. In chapter 1, we introduce the field of optomechanics and the motivations for extending this field to microwave frequencies. In chapter 2, we provide a detailed derivation of the electro mechanical hamiltonian and use the Heisenberg-Langevin equation of motion to derive an analytical expression for the classical cavity field and mechanical amplitudes. After introducing fluctuations operators in the field amplitudes, we are able to obtain an expression for the noise power spectral density using Wiener–Khinchin theorem. In chapter 3, we give an extensive overview of the design and fabrication methods that we followed to make the electromechanical devices used in our experiments. In chapter 4, we optimise the shape of a lumped-element resonator that is to be used in our electro mechanical system. By simulating with electromagnetic software Sonnet EM, we show that a large loop inductor can negatively impact the resonator quality factor in case a copper platform is located at the bottom of the device. The losses improve tremendously when replacing the loop with a meandered design of the inductor. In chapter 5, we combine a square SiN membrane with the optimised lumped-element resonator, using the flipchip tool. We show that the electromechanical system offers large enough sensitivity to quantify the vibrations originating fromthe cryocooler at the mixing chamber stage. This device shows promise to serve as a broadband cryogenic accelerometer. In chapter 6, we demonstrate that placing the square SiN membrane within a silicon phononic shield significantly enhances the mechanical quality factor and therefore the cooperativity. We also discuss the implications of mechanically induced cavity noise on the measurements. In chapter 7, we conclude the thesis and present the prospects of overcoming mechanical induced cavity noise that afflicts our measurements using 2 different methods i.e. a mechanical isolation system and microwave noise locking mechanism.