Formation of NOON states from Fock-state Bose-Einstein condensates

States of the form vertical bar N >(a) vertical bar 0 >(b) + vertical bar 0 >(a) vertical bar N >(b), where a and b are single-particle states-i.e., NOON 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 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 "feed-forward" correction circuit is shown to convert them into proper form so that 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.