1. Kavli Nanoscience Institute, Condensed Matter Physics, MS 114-36,


2. Applied Physics, California Institute of Technology, Pasadena, California 91125, USA


3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA

Correspondence to: M. L. Roukes¹ Correspondence and requests for materials should be addressed to M.L.R. (Email: roukes@caltech.edu).

The observation of the quantum states of motion of a macroscopic mechanical structure remains an open challenge in quantum-state preparation and measurement. One approach that has received extensive theoretical attention^{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13} is the integration of superconducting qubits as control and detection elements in nanoelectromechanical systems (NEMS). Here we report measurements of a NEMS resonator coupled to a superconducting qubit, a Cooper-pair box. We demonstrate that the coupling results in a dispersive shift of the nanomechanical frequency that is the mechanical analogue of the 'single-atom index effect'¹⁴ experienced by electromagnetic resonators in cavity quantum electrodynamics. The large magnitude of the dispersive interaction allows us to perform NEMS-based spectroscopy of the superconducting qubit, and enables observation of Landau–Zener interference effects—a demonstration of nanomechanical read-out of quantum interference.