Enhanced Optomechanical Levitation of Minimally Supported Dielectrics

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.