Shot noise of a quantum shuttle

We formulate a theory for shot noise in quantum nanoelectromechanical systems. As a specific example, the theory is applied to a quantum shuttle, and the zero-frequency noise, measured by the Fano factor F, is computed. F reaches very low values (F approximately 10(-2)) in the shuttling regime even in the quantum limit, confirming that shuttling is universally a low noise phenomenon. In approaching the semiclassical limit, the Fano factor shows a giant enhancement (F approximately 10(2)) at the shuttling threshold, consistent with predictions based on phase-space representations of the density matrix.