Coherent control of a nanomechanical two-level system

The Bloch sphere is a generic picture describing a coupled two-level system and the coherent dynamics of its superposition states under control of electromagnetic fields 1. It is commonly employed to visualise a broad variety of phenomena ranging from spin ensembles 2 and atoms 3 to quantum dots 4 and superconducting circuits 5. The underlying Bloch equations 6 describe the state evolution of the two-level system and allow character-ising both energy and phase relaxation processes in a simple yet powerful manner 2,7,8. Here we demonstrate the realisation of a nanomechanical two-level system which is driven by radio frequency signals. It allows to extend the above Bloch sphere formalism to nanoelectrome-chanical systems. Our realisation is based on the two orthogonal fundamental flexural modes of a high quality factor nanostring resonator which are strongly coupled by a dielectric gradient field 9. Full Bloch sphere control is demonstrated via Rabi 10 , Ramsey 11 and Hahn echo 12 experiments. This allows manipulating the classical superpo-sition state of the coupled modes in amplitude and phase and enables deep insight into the deco-herence mechanisms of nanomechanical systems. We have determined the energy relaxation time T 1 and phase relaxation times T 2 and T * 2 , and find them all to be equal. This not only indicates that energy relaxation is the dominating source of decoherence, but also demonstrates that reversible dephasing processes are negligible in such collective mechanical modes. We thus conclude that not only T 1 but also T 2 can be increased by engineering larger mechanical quality factors. After a series of groundbreaking experiments on ground state cooling and non-classical signatures of nanomechanical resonators in recent years 13–17 , this is of particular interest in the context of quantum information processing 1,18 employing nanomechanical resonators 19,20. While the dynamics of a two-level system under the influence of a pulsed external electromagnetic field was observed in atomic and nuclear spin physics decades ago, a mechanical analogon to such a system remained elusive for a long time. Only recently, coherent exchange of energy quanta between a mechanical and an electrical mode was achieved: In 2010, O'Connell et al. 13 managed to control the swapping of a single quantum of energy between a qubit and a mechanical resonator, while Palomaki et al. 17 demonstrated the temporary storage of itinerant microwave photons in a mechanical resonator in 2012. At the same time, several approaches were …