  Nanomechanical resonators having small mass, high resonance frequency and low
damping rate are widely employed as mass detectors. We study the performances
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.
