Phonon-cavity electromechanics allows the manipulation of mechanicaloscillations similar to photon-cavity systems. Many advances on this subjecthave been achieved in various materials. In addition, the coherent phonontransfer (phonon Rabi oscillations) between the phonon cavity mode and anotheroscillation mode has attracted many interest in nano-science. Here wedemonstrate coherent phonon transfer in a carbon nanotube phonon-cavity systemwith two mechanical modes exhibiting strong dynamical coupling. Thegate-tunable phonon oscillation modes are manipulated and detected by extendingthe red-detuned pump idea of photonic cavity electromechanics. The first- andsecond-order coherent phonon transfers are observed with Rabi frequencies 591kHz and 125 kHz, respectively. The frequency quality factor productfQ_m~2=10^12 Hz achieved here is larger thank k_B T_base/h, which may enablethe future realization of Rabi oscillations in the quantum regime.
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