Strong anharmonicity in a carbon nanotube electromechanical oscillator populated with a few tens of quanta

It has been a long-sought goal to prepare nonlinear quantum states in a mechanical oscillator. However, intrinsic anharmonicity due to geometric nonlinearity in conventional micro and nano-electromechanical oscillators is extremely small at the level of zero-point motion. Here we demonstrate the ultra-strong coupling of the vibrations of a carbon nanotube resonator to single electron tunnelling.  The results in the suppression of the mechanical resonance frequency by up to 30%, which is one order higher than previous reported results.  Our device is in the so-called ultrastrong coupling regime, where the electromechanical coupling per phonon is one order of magnitude larger than the resonance frequency. This coupling results in a strong anharmonicity in the mechanical oscillator. More than 20% of the thermal energy is stored in the quartic potential when the number of quanta is about 80.  The strong electromechanical coupling in nanotube resonators opens up the possibility to realize a mechanical qubit.