# Quantum capacitance mediated carbon nanotube optomechanics. (arXiv:1904.12188v3 [cond-mat.mes-hall] UPDATED)

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.