Coherent control of a classical nanomechanical two-level system

The Bloch sphere is a generic picture describing the coherent dynamics of coupled classical or quantum-mechanical two-level systems under the control of electromagnetic fields1,2. It is commonly applied to systems such as spin ensembles3, atoms4, quantum dots5 and superconducting circuits6. The underlying Bloch equations7 describe the state evolution of the two-level system and allow the characterization of both energy and phase relaxation processes3,8,9. Here we realize a classical nanomechanical two-level system2 driven by radiofrequency signals. It is based on the two orthogonal fundamental flexural modes of a high-quality-factor nanostring resonator that are strongly coupled by dielectric gradient fields10. Full Bloch sphere control is demonstrated by means of Rabi11, Ramsey12 and Hahn echo13 experiments. Furthermore, we determine the energy relaxation time T1and phase relaxation times T2 and T2*, and find them all to be equal. Thus decoherence is dominated by energy relaxation, implying that not only T1 but also T2 can be increased by engineering larger mechanical quality factors.     «

The Bloch sphere is a generic picture describing the coherent dynamics of coupled classical or quantum-mechanical two-level systems under the control of electromagnetic fields1,2. It is commonly applied to systems such as spin ensembles3, atoms4, quantum dots5 and superconducting circuits6. The underlying Bloch equations7 describe the state evolution of the two-level system and allow the characterization of both energy and phase relaxation processes3,8,9. Here we realize a classical nanomechanic...     »