Stress-Controlled Frequency Tuning and Parametric Amplification of the Vibrations of Coupled Nanomembranes

Abstract

Noninvasive tuning of the mechanical resonance frequencies of suspended parallel nanomembranes in various monolithic arrays is achieved by piezoelectric control of their tensile stress. Parametric amplification of their thermal fluctuations is shown to be enhanced by the piezoelectric actuation and amplification factors of up to 20 dB in the sub-parametric oscillation threshold regime are observed. I. INTRODUCTIONSuspended nano-and microresonators are ubiquitous in a wide range of sensing, photonics and telecommunication applications, for many of which a certain degree of tunability of their mechanical properties may be desirable [1,2]. Dynamical tuning of the mechanics can be achieved by modifying the stress of the resonant structures, e.g. capacitively [1, 3], electro-[4-6] or photothermally [7,8], by bending [9] or by heating [10]. In general, such a stress control may allow for modifying not only the mechanical resonance frequencies and quality factors, but also the nonlinear response of the resonators [1,[11][12][13]. Such a tunability is particularly interesting for arrays consisting of multiple resonators, for instance to match or enhance their collective response and sensing capabilities [14,15], to engineer and investigate complex collective dynamics [16][17][18], or to coherently manipulate phonons between them [19][20][21][22][23][24][25].Suspended drum-shaped resonators, made of low loss material such as silicon nitride and possessing high mechanical quality factors, can be efficiently coupled to electromagnetic fields, whether in the optical or microwave/radiofrequency domains [26][27][28][29][30][31][32][33]. Having multiple such membrane resonators [34-37] simultaneously interacting with cavity fields opens for a number of exciting applications, e.g., collectively enhanced optomechanics [38][39][40][41], optomechanical synchronization [42], phonon transport [43,44] or entanglement and multimode squeezing generation [45][46][47][48][49].We investigate here the tuning of the linear and nonlinear mechanical properties of suspended silicon nitride square drums by the application of a piezoelectrically controlled force to the chip supporting the drums. In this scheme, recently implemented with a single [50] and pairs of membranes [37,51], the compression of the frame caused by the piezoelectric force modifies the tensile stress of the silicon nitride films, thereby allowing for reversibly tuning the mechanical resonance frequencies without deteriorating their quality factors. We report here on the simultaneous tuning of the mechanical resonance frequencies of the membranes of various monolithic double-membrane arrays, and show for instance that the modes of membranes with close resonance frequencies can be tuned to degeneracy by the application of a bias voltage to the piezoelectric element. This tunability would be essential in the abovementioned applications involving optomechanical arrays. In addition to radiation pressure, such drum resonators naturally lend themselves to fluid pressure measurement...