Quantum manipulation of a two-level mechanical system

Salvatore Chiavazzo1, Anders Søndberg Sørensen2, Oleksandr Kyriienko1, and Luca Dellantonio1,3,4

1Department of Physics and Astronomy, University of Exeter, Exeter, Devon EX4 4QL, UK
2Center for Hybrid Quantum Networks (Hy-Q), Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
3Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
4Department of Physics & Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

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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.

In this work we show how to perform a two-phonon cooling with micro-mechanical membranes. This cooling is a second-order process acting on two excitation-quanta per time, ultimately leading to protected 2-level state. Finally, we introduce possible procedures to correctly manipulate the state, demonstrating its use as a 2-level system.

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