| Summary: | To efficiently manipulate parametric mode mixing is an intriguing physical issue for phonon-cavity electromechanics, which is also crucial for various technological applications ranging from frequency synthesis to nonlinear spectroscopy. Here, we theoretically investigate the dependence of phononic high-order sidebands on intra- and inter-mode couplings in two interconnected electromechanical resonators. When the system operates in a strong inter-mode coupling regime, we report that two inter-mode phonon-scattering pathways allow us to selectively obtain either odd- or even-order sidebands at different output ports. The signal intensities of the separated sidebands can be independently modulated by introducing harmonic actuation forces acting on the interconnected resonators. Once the intra-mode coupling becomes totally dominant, the direct transition between intra-mode phonons only triggers the emergence of full-order sidebands in the nonlinear responses. In this case, increasing the quality factor of the resonators is beneficial for amplifying a few low order sidebands nearby the principal modes of the resonators but sacrificing the order of the sidebands.
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