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

We propose a theoretical scheme to realize two-parameter estimation via a Bose-Einstein condensates confined in a symmetric triple-well. The three-mode NOON state is prepared adiabatically as the initial state. Two phase differences between the wells are two parameters to be estimated. With the help of classical and quantum Fisher information, we study the sensitivity of the triple-well on estimating two phase parameters simultaneously. The result shows that the precision of simultaneous estimation of two parameters in a triple-well system can reach the Heisenberg scaling.