A scheme for creating NOON-states of the quasi-momentum of ultra-cold atoms
has recently been proposed [New J. Phys. 8, 180 (2006)]. This was achieved by
trapping the atoms in an optical lattice in a ring configuration and rotating
the potential at a rate equal to half a quantum of angular momentum . In this
paper we present a scheme for confirming that a NOON-state has indeed been
created. This is achieved by spectroscopically mapping out the anti-crossing
between the ground and first excited levels by modulating the rate at which the
potential is rotated. Finally we show how the NOON-state can be used to make
precision measurements of rotation.Comment: 14 preprint pages, 7 figure