  We derive a measurement operator corresponding to a quantum nondemolition
(QND) measurement of an atomic ensemble. The quantum measurement operator takes
the form of a positive operator valued measure (POVM) and is valid for
arbitrary interaction times, initial coherent state amplitudes, and final
photon measurement outcomes. We analyze the dependence on various parameters
and show that the effect of the QND measurement for short interaction times is
to apply a Gaussian modulation of the initial state wavefunction. We derive
approximate expressions for the POVM in various limits, such as the short
interaction time regime and projective measurement limit. Several examples are
shown which shows how spin squeezing and Schrodinger cat states can be
generated using the measurement.
