Mass detection with a nonlinear nanomechanical resonator

Nanomechanical resonators having small mass, high resonance frequency, and low damping rate are widely employed as mass detectors. We study the performance of such a detector when the resonator is driven into a region of nonlinear oscillations. We predict theoretically that in this region the system acts as a phase-sensitive mechanical amplifier. This behavior can be exploited to achieve noise squeezing in the output signal when homodyne detection is employed for readout. We show that mass sensitivity of the device in this region may exceed the upper bound imposed by thermomechanical noise upon the sensitivity when operating in the linear region. On the other hand, we show that the high mass sensitivity is accompanied by a slowing down of the response of the system to a change in the mass.

Figure 1

(Color online) Response of a driven Duffing resonator. Panel (a) shows the bistable region in the $({\omega }_p,p)$ plane. The response vs frequency is shown in panels (b), (c), and (d) for subcritical, critical, and overcritical driving force, respectively.

Figure 2

(Color online) Flow lines obtained by integrating Eq. (19) for the noiseless case $F=0$. The points $C_1$ and $C_3$ are attractors, and $C_2$ is a saddle point. The green (light gray) line is the sepatrix, namely, the boundary between the basins of attraction of both attractors. Panel (a) shows a wide view, whereas panel (b) shows a closer view of the region near $C_1$ and $C_2$. The cyan (light gray) line near the attractor $C_1$ in panel (b) demonstrates random motion in the presence of noise.

Figure 3

The function $g$. Panel (a) shows $g({\varphi }_{\mathrm{LO}}-{\varphi }_0)$ for the case $\zeta =0.1$ and ${\varphi }_C=0.5\pi$, and panel (b) for the case $\zeta =0.99$ and ${\varphi }_C=0.5\pi$. Panel (c) shows the minimum value of the function $g({\varphi }_{\mathrm{LO}}-{\varphi }_0)$ vs ${\varphi }_C$ for different values of $\zeta$.