Quantum capacitance mediated carbon nanotube optomechanics

Cavity optomechanics allows the characterization of a vibration mode, its cooling and quantum manipulation using electromagnetic fields. Regarding nanomechanical as well as electronic properties, single wall carbon nanotubes are a prototypical experimental system. At cryogenic temperatures, as high quality factor vibrational resonators, they display strong interaction between motion and single-electron tunneling. However, small vibrational deflection and length have made their optomechanical coupling to microwave fields, as used in solid state cavity quantum electrodynamics or quantum information experiments, so far impossible. Here, we demonstrate large optomechanical coupling of a suspended carbon nanotube quantum dot and a microwave cavity, amplified by several orders of magnitude via the inherent nonlinearity of Coulomb blockade. From an optomechanically induced transparency (OMIT) experiment, we obtain an outstanding single photon coupling of up to $g_0=2\pi\cdot 88\,\rm{Hz}$. This indicates that normal mode splitting and full optomechanical control of the carbon nanotube vibration in the quantum limit is reachable in the near future. A unique experimental system becomes accessible, where the nanomechanically active part directly incorporates a quantum-confined electron system. Mechanical manipulation and characterization via the microwave field is complemented by the manifold physics of single electron devices.