Quantum manipulation of a two-level mechanical system

TL;DR

This paper develops a theoretical framework for two-phonon cooling in a nonlinear electromechanical system, enabling quantum control of mechanical states and the creation of nonclassical states with potential experimental implementation.

Contribution

It introduces a quantitative theory for two-phonon cooling and proposes a scheme for quantum operations on a two-level mechanical system.

Findings

Effective reduction of mechanical Hilbert space to ground and first excited states.

Ability to perform arbitrary Bloch sphere rotations on mechanical states.

Feasibility of implementing the scheme in current electromechanical devices.

Abstract

We consider a nonlinearly coupled electromechanical system, and develop a quantitative theory for two-phonon cooling. In the presence of two-phonon cooling, the mechanical Hilbert space is effectively reduced to its ground and first excited states, allowing for quantum operations at the level of individual phonons and preparing 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 $\pi$-pulse. We characterise detrimental processes that reduce the coherence in the system, and demonstrate that our scheme can be implemented in state-of-the-art electromechanical devices.