Spinning a levitated mechanical oscillator far into the deep-strong coupling regime

Abstract: The field of levitodynamics has made substantial advancements in manipulating the translational and rotational degrees of freedom of levitated nanoparticles. Notably, rotational degrees of freedom can now be cooled to millikelvin temperatures and driven into GHz rotational speeds. However, in the case of cylindrically symmetric nanorotors, only the rotations around their short axes have been effectively manipulated, while the possibility to control rotation around the longer axis has remained a notable gap in the field. Here, we extend the rotational control toolbox by engineering an optically levitated nanodumbbell in vacuum into controlled spinning around its long axis with spinning rates exceeding 1 GHz. This fast spinning introduces deep-strong coupling between the nanodumbell's libration modes, such that the coupling rate $g$ exceeds the bare libration frequencies $\Omega_0$ by two orders of magnitude with $g/\Omega_0=724\pm 33$. Our control over the long-axis rotation opens the door to study the physics of deep-strong coupled mechanical oscillators and to observe macroscopic rotational quantum interference effects, thus laying a solid foundation for future applications in quantum technologies. Additionally, we find that our system offers great potential as a nanoscopic gyroscope with competitive sensitivity.