  We investigate a non-destructive measurement technique to monitor
Josephson-like oscillations between two spatially separated neutral atom
Bose-Einstein condensates. One condensate is placed in an optical cavity, which
is strongly driven by a coherent optical field. The cavity output field is
monitored using a homodyne detection scheme. The cavity field is well detuned
from an atomic resonance, and experiences a dispersive phase shift proportional
to the number of atoms in the cavity. The detected current is modulated by the
coherent tunneling oscillations of the condensate. Even when there is an equal
number of atoms in each well initially, a phase is established by the
measurement process and Josephson-like oscillations develop due to measurement
back-action noise alone.
