Quantum manipulation of a two-level mechanical system

We consider a nonlinearly coupled elec-tromechanical system, and develop a quan-titative theory for two-phonon cooling. In the presence of two-phonon cooling, the mechanical Hilbert space is effectively re-duced to its ground and first excited states, allowing for quantum operations at the level of individual phonons and prepar-ing nonclassical mechanical states with negative Wigner functions. We propose a scheme for performing arbitrary Bloch sphere rotations, and derive the fidelity in the specific case of a ir-pulse. We characterise detrimental processes that re-duce the coherence in the system, and demonstrate that our scheme can be im-plemented in state-of-the-art electrome-chanical devices.

Automated summary

We study a nonlinearly coupled electromechanical system and establish a quantitative theory for two-phonon cooling. Two-phonon cooling reduces the mechanical Hilbert space to its ground and first excited states, enabling quantum operations on individual phonons and the preparation of nonclassical mechanical states. We propose a scheme for implementing arbitrary Bloch sphere rotations and derive the fidelity for a specific case. We also analyze detrimental processes that degrade coherence and demonstrate the feasibility of our scheme in state-of-the-art electromechanical devices.