Creation of NOON States from Double Fock-State/Bose-Einstein Condensates

NOON states (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) have been used for predicting violations of hidden-variable theories (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 Zender interferometer can lead to the creation of the NOON state in which a and b refer to arms of the interferometer and N is the total number of particles in the two condensates. The modification of the interferometer involves making conditional "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. The result is equivalent to the quantum experiment in which a large molecule passes through two slits. The NOON states are combined in a final beam splitter and show interference. Attempts to detect through which "slit" the condensates passed destroys the interference.