Optomechanical Simulations for Optimizing Spin-Phonon-Photon Coupling in a Silicon Nanobeam - Ahopelto, Simeoni (2024)
In optomechanical systems, the light is utilized to measure tiny mechanical displacements of matter. Creating a confined electric inside an optical cavity makes small fluctuations in a mechanical system visible. This property can be taken advantage of when measuring the state of a quantum system, such as an electron's spin. In this thesis, we investigated the geometric design of a photonic crystal silicon nanobeam working as a quantum transducer between donor spins, phonons, and photons. The photonic crystal nanobeam combines an optical cavity with a mechanical oscillator, so that their resonance frequencies can be coupled via strain to a spin state of a donor atom in a magnetic field. The nanobeam was optimized with simulations using electromagnetic and mechanical FEM eigenfrequency solvers in COMSOL Multiphysics software. We optimized the coupling using a width tapered nanobeam design. We reached an optomechanical coupling of a few MHz with optical frequencies around 200 THz, as well as a spin-strain coupling around 100 Hz for a phosphorus donor in a magnetic field of 1 T. The optimized coupling strengths suggest that coupling spins via mechanical strain of the nanobeam is not feasible for optical single spin measurements with the current fabrication limitations but can be used for bulk spin measurements. Furthermore, the designed nanobeam can be utilized for displacement measurements near the zero-point energy of the nanobeam.