  We examine how non-destructive measurements generate spin squeezing in an
atomic Bose-Einstein condensate confined in a double-well trap. The condensate
in each well is monitored using coherent light beams in a Mach-Zehnder
configuration that interacts with the atoms through a quantum nondemolition
Hamiltonian. We solve the dynamics of the light-atom system using an exact
wavefunction approach, in the presence of dephasing noise, which allows us to
examine arbitrary interaction times and a general initial state. We find that
monitoring the condensate at zero detection current and with identical coherent
light beams minimizes the backaction of the measurement on the atoms. In the
weak atom-light interaction regime, we find the mean spin direction is
relatively unaffected, while the variance of the spins is squeezed along the
axis coupled to the light. Additionally, squeezing persists in the presence of
tunneling and dephasing noise.
