  NOON states (states of the form $|N>_{a}|0>_{b}+|0>_{a}|N>_{b}$ where $a$ and
$b$ are single particle states) have been used for predicting violations of
local realism (Greenberger-Horne-Zeilinger violations) and are valuable in
metrology for precision measurements of phase at the Heisenberg limit. We show
theoretically how the use of two Fock state Bose-Einstein condensates as
sources in a modified Mach-Zehnder interferometer can lead to the creation of
the NOON state in which $a$ and $b$ refer to arms of the interferometer and $N$
is a subset of the total number of particles in the two condensates. The
modification of the interferometer involves making {}"side" measurements of a
few particles near the sources. These measurements put the remaining particles
in a superposition of two phase states, which are converted into NOON states by
a beam splitter if the phase states are orthogonal. When they are not
orthogonal, a {}"feedforward" correction circuit is shown to convert them into
proper form so a NOON results. We apply the NOON to the measurement of phase.
Here the NOON experiment is equivalent to one in which a large molecule passes
through two slits. The NOON components can be recombined in a final beam
splitter to show interference.
