Dispersive and Dissipative Coupling in a Micromechanical Resonator Embedded with a Nanomechanical Resonator

Abstract

A micromechanical resonator embedded with a nanomechanical resonator is developed whose dynamics can be captured by the coupled-Van der Pol-Duffing equations. Activating the nanomechanical resonator can dispersively shift the micromechanical resonance by more than 100 times its bandwidth and concurrently increase its energy dissipation rate to the point where it can even be deactivated. The coupled-Van der Pol-Duffing equations also suggest the possibility of self-oscillations. In the limit of strong excitation for the nanomechanical resonator, the dissipation in the micromechanical resonator can not only be reduced, resulting in a quality factor of >3× 10(6), it can even be eliminated entirely resulting in the micromechanical resonator spontaneously vibrating.

A correlated electromechanical system

“…To address this, the coupled electromechanical system detailed in figure 1(a) is developed, which consists of two radically different mechanical elements with a nanoresonator (n) placed into the clamping point of a micro-resonator (μ). This geometry is identified from a finite element method (FEM) simulation in order to maximise their inherent elastic coupling G, where the motion of one resonator generates strain which modifies the natural frequency of its counterpart and vice versa [24]. If the coupling between the micro-resonator and the nano-resonator can be modulated via strain then it can be parametrically enhanced, leading to a system Hamiltonian given by…”

“…In addition to generating strain, the piezoelectric transducers also enabled the motion of the mechanical elements to be both activated, with application of voltage, and measured from the resultant motion-induced piezovoltage [23,24]. This permitted the fundamental flexural modes of both resonators, whose motional profiles extracted from FEM simulations are shown in the insets to figure 1(a), to be identified, yielding a natural frequency 2 394.001 kHz w p = m with dissipation 2 2.8Hz g p = m for the micro-resonator and 2 2.557611 MHz w p = with 2 11Hz g p = for the nano-resonator, as shown in figure 1(b).…”

Nonlinear damping and dephasing in nanomechanical systems

“…It plays an important role in the dynamics of mesoscopic modes [2], even though typically |V | ω 0 . The energy decay rate is not affected by this term, except where a mode is very strongly driven [28,61]; such driving is not considered here.…”

“…The relaxation mechanisms include radiation into the bulk modes of the medium surrounding the nanosystem [19][20][21][22][23], nonlinear coupling between the modes localized inside the system [10,[24][25][26][27][28], and coupling with electronic excitations [29][30][31][32] and two-level defects [33][34][35].…”

“…Such friction is called linear. Recent experiments have shown that, already for moderate vibration amplitudes, in various nanomechanical and micromechanical systems the amplitude decay is nonexponential in time and/or the maximal amplitude of forced vibrations nonlinearly depends on the force amplitude [28,[36][37][38][39]; respectively, the friction force is a nonlinear function of the mode coordinate and velocity. Nonlinear friction (nonlinear damping) has recently attracted considerable attention also in the context of quantum information processing with microwave cavity modes, where it was engineered to be strong [40,41].…”