A correlation with phonons sustained by a pair of electromechanical resonators that differ both in size and frequency is demonstrated. In spite of the electromechanical resonators being spatially distinct, they can still be strongly dynamically coupled via a classical analogue of the beam splitter interaction with a cooperativity exceeding five, and parametric down-conversion which results in both resonators self-oscillating. This latter regime yields a classical variant of a two-mode squeezed state which is identified as perfectly correlated phase-locked vibrations between the two resonators. The creation of a correlation between two separate mechanical resonators suggests that extending this interaction to vacuum phonon states could enable a macroscopic two-mode squeezed state to be generated. Conversely, the ability to resolve the correlated state via the self-oscillations could be harnessed to build a new class of detector where an external stimulus neutralises the phase-locked vibrations.
Two modes of an electromechanical resonator are coupled through the strain inside the structure with a cooperativity as high as 107, a state-of-the-art value for purely mechanical systems, which enables the observation of normal-mode splitting. This coupling is exploited to transduce the resonator’s fundamental mode into the bandwidth of the second flexural mode, which is 1.4 MHz higher in frequency. Thus, an all-mechanical heterodyne detection scheme is implemented that can be developed into a high-precision displacement sensor.
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