  We develop a Gaussian state treatment that allows a transparent quantum
description of the continuous, nondestructive imaging of and feedback on a
Bose-Einstein condensate. We have previously demonstrated [Phys. Rev. Lett.
\textbf{115}, 060401 (2015)] that the measurement back action of stroboscopic
imaging leads to selective squeezing and entanglement of quantized density
oscillations. Here, we investigate how the squeezing and entanglement are
affected by the finite spatial resolution and geometry of the probe laser beam
and of the detector and how they can be optimized.
