Simulation of Millimeter-Wave Optomechanical Torque Sensors and RF Resonators

Abstract

Superconducting resonators provide a promising platform for sensing because of their low microwave dissipation and ability to support high quality factor electromagnetic resonances. This thesis investigates the design and characterization of superconducting resonator systems for sensitive microwave measurements, with particular emphasis on a millimeter-wave optomechanical torque sensor and superconducting spiral resonators coupled to coplanar waveguides. The first part of this thesis begins with examples of quantum-enabled and optomechanical torque sensors, followed by the theory of optomechanical torque sensing and the design and finite element analysis of a superconducting optomechanical torque sensor operating at an electromagnetic resonant frequency of 40 GHz. The device couples a torsional mechanical resonator to a superconducting electromagnetic resonator through an electric-field interaction confined within mechanically compliant capacitors. The mechanical resonator operates at frequencies ranging from the sub-MHz regime to a few MHz. The effects of device geometry on the optomechanical coupling strength, standard quantum limit photon number, and torque sensitivity are systematically investigated using the finite element method. These three quantities are critical figures of merit for evaluating the performance of the sensor and are explained in detail in this thesis. Based on this numerical analysis, the sensor geometry was optimized with respect to the minimum torque sensitivity, or more intuitively, the smallest detectable torque, and the standard quantum limit photon number, which depends on the coupling strength. The minimum torque sensitivity was determined to be 2.587 yNm/√Hz, while the minimum standard quantum limit photon number was found to be 9.206 × 10^−3. Not only were the optimized numerical figures of merit revealed by this analysis, but a suite of sensor designs with optimized figures of merit was also developed based on the geometric analysis. The second part of this thesis investigates superconducting spiral resonators inductively coupled to a coplanar waveguide as a simplified platform for studying microwave loss mechanisms relevant to superconducting circuits. Electromagnetic finite element method simulations were used to examine how the spiral geometry and resonator–waveguide separation determine the resonant frequency and external coupling rate within the 4–8 GHz band. The number of turns of the spiral resonator was varied to determine the designs corresponding to EM resonant frequencies of 4, 6, and 8 GHz, which were found to require 24.9, 18.8, and 16.24 turns, respectively. Additionally, the separation distances required to achieve external coupling rates of 1, 10, and 100 kHz were determined from the simulations for each of the three resonant frequencies. These coupling rates were selected because they correspond to desired external quality factors, which are discussed in greater detail in this thesis. Together, these studies demonstrate how geometric design can be used to engineer the coupling and performance of superconducting resonator systems. The results provide practical design guidelines for future quantum sensing applications and for studying microwave loss mechanisms in superconducting circuits.