Dynamics and current fluctuations in an ac-driven charge shuttle

The behaviour of a charge shuttle under a pure ac field has been recently considered theoretically and experimentally. If the system presents an asymmetry in the tunnelling amplitudes the device acts as a nanoelectromechanical rectifier, transforming a pure ac voltage field into a direct current. In this paper, we first review the model and the appearance of the rectifying effect for bias voltages below the threshold of self-oscillation. We discuss in some detail the dynamics of the central island that, like the current, presents a strong dependence on the forcing ac field frequency. In the presence of both a constant and a small oscillating bias voltage, we analyse the transition from the static to the self-oscillating solution. We then consider current fluctuations (full counting statistics) for periodic motion of the grain. We explicitly evaluate the current noise numerically and we find that it shows clear signatures of correlated transport at certain locking frequencies. In the adiabatic limit, we obtain a simple expression for the full counting statistics and calculate explicitly the first four moments.