  We present a detailed study of an atom interferometer which can be realized
in a double-well potential. We assume that the interferometric phase is
imprinted in the presence of coherent tunneling between the wells. We calculate
the ultimate bounds for the estimation sensitivity and show how they relate to
the precision of the Mach-Zehnder interferometer. The interferometer presented
here allows for sub shot-noise sensitivity when fed with the spin-squeezed
states with reduced either the relative population imbalance or the relative
phase. We also calculate the precision of the estimation from the population
imbalance and show that it overcomes the shot-noise level when the entangled
squeezed-states are used at the input.
