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Coupled micro and nanomechanical resonators are of significant interest within a number of areas of research, ranging from synchronization, nonlinear dynamics and chaos, to quantum sensing and transduction. Building upon our work on soft-clamped membrane resonators, here we present a study on phononic dimers, consisting of two defects embedded in a phononic crystal membrane. These devices exhibit widely tunable (2--100 kHz) interdefect coupling strengths, leading to delocalized hybrid modes with mechanical Qf products >10^140. 2em{0ex}Hz at room temperature, ensuring low thermomechanical force noise. The mode splitting exhibits a strong dependence on the dimer orientation within the crystal lattice, as well as the spatial separation between the two defects. Given the importance of dynamic range for sensing applications, we characterize the relevant mechanical nonlinearities, specifically the self- and cross-Duffing parameters, as well as self- and cross-nonlinear dampings. This work establishes soft-clamped resonators with engineered spatial and spectral multimode structure as a versatile mechanical platform both in the classical and quantum regimes. Applications in microwave-to-optical transduction and magnetic resonance force microscopy are particularly attractive prospects.
Catalini et al. (Wed,) studied this question.