Two-parameter estimation with three-mode NOON state in a symmetric three-well system

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.