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We report fast readout of the motion of a carbon nanotube mechanical resonator. A close-proximity high electron mobility transistor amplifier is used to increase the bandwidth of the measurement of nanotube displacements from the kHz to the MHz regime. Using an electrical detection scheme with the nanotube acting as a mixer, we detect the amplitude of its mechanical motion at room temperature with an intermediate frequency of 6 MHz and a timeconstant of 780 ns, both up to five orders of magnitude faster than achieved before. The transient response of the mechanical motion indicates a ring-down time faster than our enhanced time resolution, placing an upper bound on the contribution of energy relaxation processes to the room temperature mechanical quality factor. [ABSTRACT FROM AUTHOR]

We have fabricated suspended metal paddle resonators with carbon nanotubes functioning as self-detecting torsional springs. We observe gate-tunable resonances that either tune to higher or to lower frequencies when increasing the dc voltage on the back gate. We attribute the former modes to flexural vibrations of the paddle resonator, while the latter ones are identified as torsional vibrations. Compared to top-down silicon fabricated paddle resonators, nanotube springs have smaller torsional spring constants and provide a larger frequency tunability. [ABSTRACT FROM AUTHOR]

We have used the mechanical motion of a carbon nanotube (CNT) as a probe of the average charge on a quantum dot. Variations of the resonance frequency and the quality factor are determined by the change in average charge on the quantum dot during a mechanical oscillation. The average charge, in turn, is influenced by the gate voltage, the bias voltage, and the tunnel rates of the barriers to the leads. At bias voltages that exceed the broadening due to tunnel coupling, the resonance frequency and quality factor show a double dip as a function of gate voltage. We find that increasing the current flowing through the CNT at the Coulomb peak does not increase the damping, but in fact decreases damping. Using a model with energy-dependent tunnel rates, we obtain quantitative agreement between the experimental observations and the model. We theoretically compare different contributions to the single-electron induced nonlinearity, and show that only one term is significant for both the Duffing parameter and the mode coupling parameter. We also present additional measurements which support the model we develop: Tuning the tunnel barriers of the quantum dot to the leads gives a 200-fold decrease of the quality factor. Single-electron tunneling through an excited state of the CNT quantum dot also changes the average charge on the quantum dot, bringing about a decrease in the resonance frequency. In the Fabry-Pérot regime, the absence of charge quantization results in a spring behavior without resonance frequency dips, which could be used, for example, to probe the transition from quantized to continuous charge with a nanomechanical resonator. [ABSTRACT FROM AUTHOR]

Nanoscale resonators that oscillate at high frequencies are-useful in many measurement applications. We studied a high-quality mechanical resonator made from a suspended carbon nanotube driven into motion by applying a periodic radio frequency potential using a nearby antenna. Single-electron charge fluctuations created periodic modulations of the mechanical resonance frequency. A quality factor exceeding 105 allows the detection of a shift in resonance frequency caused by the addition of a single-electron charge on the nanotube. Additional evidence for the strong coupling of mechanical motion and electron tunneling is provided by an energy transfer to the electrons causing mechanical damping and unusual nonlinear behavior. We also discovered that a direct current through the nanotube spontaneously drives the mechanical resonator, exerting a force that is coherent with the high-frequency resonant mechanical motion. [ABSTRACT FROM AUTHOR]