Mass sensing by quantum criticality

Mass sensing connects the mass variation to a frequency shift of a mechanical oscillator, whose limitation is determined by its mechanical frequency resolution. Here we propose a method to enlarge a minute mechanical frequency shift, which is smaller than the linewidth of the mechanical oscillator, into a huge frequency shift of the normal mode. Explicitly, a frequency shift of about 20 Hz of the mechanical oscillator would be magnified to be a 1 MHz frequency shift in the normal mode, which increases it by five orders of magnitude. This enhancement relies on the sensitivity appearing near the quantum critical point of the electromechanical system. We show that a mechanical frequency shift of 1 Hz could be resolved with a mechanical resonance frequency $\omega_b = 11\times 2\pi$ MHz. Namely, an ultrasensitive mechanical mass sensor of the resolution $\Delta m /m \sim2\Delta \omega_b/\omega_b\sim 10^{-8}$ could be achieved. Our method has potential application in mass sensing and other techniques based on the frequency shift of a mechanical oscillator.