Coherent phonon manipulation in coupled mechanical resonators
  Coupled mechanical oscillations were first observed in paired pendulum clocks in the mid-seventeenth century and were extensively studied for their novel sympathetic oscillation dynamics. In this era of nanotechnologies, coupled oscillations have again emerged as subjects of interest when realized in nanomechanical resonators for both practical applications and fundamental studies. However, a key obstacle to the further development of this architecture is the ability to coherently manipulate the coupled oscillations. This limitation arises as a consequence of the usually weak coupling between the constituent nanomechanical elements. Here, we report parametrically coupled mechanical resonators in which the coupling strength can be dynamically adjusted by modulating (pumping) the stress in the mechanical elements via a piezoelectric transducer. The parametric control enables the coupling rate between the two resonators to be made so strong that it exceeds their intrinsic energy dissipation rate by more than a factor of four. This ultra-strong coupling can be exploited to coherently transfer phonon populations, namely phonon Rabi oscillations, between the resonators via two coupled vibration modes, realizing superposition states of the two modes and their time-domain control. More unexpectedly, the nature of the parametric coupling can also be tuned from a linear first-order interaction to a non-linear higher-order process in which more than one pump phonon mediates the coherent oscillations. This demonstration of multi-pump phonon mixing echoes multi-wave photon mixing and suggests that concepts from non-linear optics can also be applied to mechanical systems. Ultimately, the parametric pumping is not only useful for controlling classical oscillations but can also be extended to the quantum regime, opening up the prospect of entangling two distinct macroscopic mechanical objects. 
Hajime Okamoto, Adrien Gourgout, Chia-Yuan Chang, Koji Onomitsu, Imran   Mahboob, Edward Yi Chang and Hiroshi Yamaguchi
cond-mat.mes-hall