  We propose a scheme to realize two-parameter estimation via a Bose-Einstein
condensates confined in a symmetric triple-well potential. The three-mode NOON
state is prepared adiabatically as the initial state. The two parameters to be
estimated are the phase differences between the wells. The sensitivity of this
estimation scheme is studied by comparing quantum and classical Fisher
information matrices. As a result, we find an optimal particle number
measurement method. Moreover, the precision of this estimation scheme behaves
the Heisenberg scaling under the optimal measurement.
