  We use a Born-Markov approximated master equation approach to study the
symmetrized-in-frequency current noise spectrum and the oscillator steady state
of a nanoelectromechanical system where a nanoscale resonator is coupled
linearly via its momentum to a quantum point contact (QPC). Our current noise
spectra exhibit clear signatures of the quantum correlations between the QPC
current and the back-action force on the oscillator at a value of the relative
tunneling phase (\eta = -\pi/2) where such correlations are expected to be
maximized. We also show that the steady state of the oscillator obeys a
classical Fokker-Planck equation, but can experience thermomechanical noise
squeezing in the presence of a momentum-coupled detector bath and a
position-coupled environmental bath. Besides, the full master equation clearly
shows that half of the detector back-action is correlated with electron
tunneling, indicating a departure from the model of the detector as an
effective bath and suggesting that a future calculation valid at lower bias
voltage, stronger tunneling and/or stronger coupling might reveal interesting
quantum effects in the oscillator dynamics.
