  We show that the nanoresonator position can be squeezed significantly below
the ground state level by measuring the nanoresonator with a quantum point
contact or a single-electron transistor and applying a periodic voltage across
the detector. The mechanism of squeezing is basically a generalization of
quantum nondemolition measurement of an oscillator to the case of continuous
measurement by a weakly coupled detector. The quantum feedback is necessary to
prevent the ``heating'' due to measurement back-action. We also discuss a
procedure of experimental verification of the squeezed state.
