Mass sensing by quantum criticality

Mass sensing connects 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 5 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 ω_b=11×2π  MHz. Namely, an ultrasensitive mechanical mass sensor of the resolution Δm/m∼2Δω_b/ω_b∼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.