  We propose a scheme to realize high-precision quantum interferometry with
entangled non-Gaussian states by driving the system through quantum phase
transitions. The beam splitting, in which an initial non-degenerate groundstate
evolves into a highly entangled state, is achieved by adiabatically driving the
system from a non-degenerate regime to a degenerate one. Inversely, the beam
recombination, in which the output state after interrogation becomes gradually
disentangled, is accomplished by adiabatically driving the system from the
degenerate regime to the non-degenerate one. The phase shift, which is
accumulated in the interrogation process, can then be easily inferred via
population measurement. We apply our scheme to Bose condensed atoms and trapped
ions, and find that Heisenberg-limited precision scalings can be approached.
Our proposed scheme does not require single-particle resolved detection and is
within the reach of current experiment techniques.
