Driven Dissipation and Stabilization of a Levitated Rotor with Multi-Day Coherence

We report the experimental observation of nonlinear mode-crossing dissipation and injection-locking-like stabilization in a milligram-scale diamagnetically levitated quartz cube. By optically driving the cube to rotation rate near 360 RPM, we observe that its angular velocity does not decay smoothly but instead decreases in discrete steps whenever the instantaneous rotation frequency crosses one of several higher-order mechanical modes. We observe rotational dissipation times on the order of a few days. When a weak counteracting radiation-pressure torque is applied, the system unexpectedly stabilizes at a constant rotation rate that persists for about two days, constituting the mechanical analogue of injection locking. Our results reveal a new regime of multimode nonlinear dynamics in low-dissipation levitated solids and establish diamagnetic levitation as a platform for exploring non-Hamiltonian many-mode interactions and mechanically engineered nonlinear attractors and sensors.