Phonon-Electron-Nuclear Spin Hybrid Systems in an Electromechanical Resonator

Abstract

A recent progress on hybrid systems with a GaAs-based electromechanical resonator is reviewed. Fundamental experimental techniques including fabrication of an electromechanical resonator integrated with a GaAs heterostructure and transport measurements using a cryogenic amplifier are explained. The first topic is on a hybrid system composed of a gate-tunable quantum dot (QD) and quantum point contact (QPC) integrated into a piezoelectricity-based electromechanical resonator. The piezoelectric coupling between them enables us to detect milli-Kelvin phonon states via current flowing through the QD/QPC. Noise analysis based on an equivalent circuit elucidates that the displacement sensitivity is amplifier-limited and the estimated intrinsic sensitivity with a QD transducer potentially reaches the zero-point motion of the resonator. The second topic is on quadrupole-coupling between electrically tunable phonon states in an electromechanical resonator and a nuclear spin ensemble within it. As a consequence of a rapidly oscillating strain induced by a strongly driven mechanical resonator, nuclear magnetic resonance (NMR) frequency shifts which can be regarded as mechanical analogue of ac-Stark shift known in cavity quantum electrodynamics is observed. This prototype system potentially opens up quantum state engineering for electrons, phonons, and nuclear spins such as coherent coupling between them.