Enhanced Optomechanical Levitation of Minimally Supported Dielectrics

Abstract: Optically levitated mechanical sensors promise isolation from thermal noise far beyond what is possible using flexible materials alone. One way to access this potential is to apply a strong optical trap to a minimally supported mechanical element, thereby increasing its quality factor $Q_m$. Current schemes, however, require prohibitively high laser power ($\sim10$ W), and the $Q_m$ enhancement is ultimately limited to a factor of $\sim$ 50 by hybridization between the trapped mode and the dissipative modes of the supporting structure. Here we propose a levitation scheme taking full advantage of an optical resonator to reduce the circulating power requirements by many orders of magnitude. Applying this scheme to the case of a dielectric disk in a Fabry-Perot cavity, we find a tilt-based tuning mechanism for optimizing both center-of-mass and torsional mode traps. Notably, the two modes are trapped with comparable efficiency, and we estimate that a 10-micron-diameter, 100-nm-thick Si disc could be trapped to a frequency of $\sim$ 10 MHz with only $30$ mW circulating in a cavity of (modest) finesse 1500. Finally, we simulate the effect such a strong trap would have on a realistic doubly-tethered disc. Of central importance, we find torsional motion is comparatively immune to $Q_m$-limiting hybridization, allowing a $Q_m$ enhancement factor of $\sim$ 1500. This opens the possibility of realizing a laser-tuned 10 MHz mechanical system with a quality factor of order a billion.