  We analyze squeezing of the nanoresonator state produced by periodic
measurement of position by a quantum point contact or a single-electron
transistor. The mechanism of squeezing is the stroboscopic quantum
nondemolition measurement generalized to the case of continuous measurement by
a weakly coupled detector. The magnitude of squeezing is calculated for the
harmonic and stroboscopic modulations of measurement, taking into account
detector efficiency and nanoresonator quality factor. We also analyze the
operation of the quantum feedback, which prevents fluctuations of the
wavepacket center due to measurement back-action. Verification of the squeezed
state can be performed in almost the same way as its preparation; similar
procedure can also be used for the force detection with sensitivity beyond the
standard quantum limit.
