  We analyze a scheme that uses quantum nondemolition measurements to induce
squeezing of a spinor Bose-Einstein condensate in a double well trap. In a
previous paper [Ilo-Okeke et al. Phys. Rev. A \textbf{104}, 053324 (2021)], we
introduced a model to solve exactly the wavefunction for all atom-light
interaction times. Here, we perform approximations for the short interaction
time regime, which is relevant for producing squeezing. Our approach uses a
Holstein-Primakoff approximation for the atoms while we treat the light
variables exactly. It allows us to show that the measurement induces
correlations within the condensate, which manifest in the state of the
condensate as a superposition of even parity states. In the long interaction
time regime, our methods allow us to identify the mechanism for loss of
correlation. We derive simple expressions for the variances of atomic spin
variables conditioned on the measurement outcome. We find that the results
agree with the exact solution in the short interaction time regime.
Additionally, we show that the expressions are the sum of the variances of the
atoms and the measurement. Beyond the short interaction time regime, our scheme
agrees qualitatively with the exact solution for the spin variable that couples
to light.
