Ultrasensitive Displacement Noise Measurement of Carbon Nanotube Mechanical Resonators

Mechanical resonators based on a single carbon nanotube are exceptional sensors of mass and force. The force sensitivity in these ultra-light resonators is often limited by the noise in the detection of the vibrations. Here, we report on an ultra-sensitive scheme based on a RLC resonator and a low-temperature amplifier to detect nanotube vibrations. We also show a new fabrication process of electromechanical nanotube resonators to reduce the separation between the suspended nanotube and the gate electrode down to $\sim 150$~nm. These advances in detection and fabrication allow us to reach $0.5~\mathrm{pm}/\sqrt{\mathrm{Hz}}$ displacement sensitivity. Thermal vibrations cooled cryogenically at 300~mK are detected with a signal-to-noise ratio as high as 17~dB. We demonstrate $4.3~\mathrm{zN}/\sqrt{\mathrm{Hz}}$ force sensitivity, which is the best force sensitivity achieved thus far with a mechanical resonator. Our work is an important step towards imaging individual nuclear spins and studying the coupling between mechanical vibrations and electrons in different quantum electron transport regimes.