Quantum Fisher information, which plays a central role in parameter estimation theory, is a useful quantity for metrological applications. We use quantum Fisher information to distinguish and characterize behaviors of the evolved state for Bose-Einstein condensates in a symmetric double well, which display a classical bifurcation and a transition from Josephson oscillation to self-trapping. We find that the precision of the parameter estimation on the evolved state in the unstable regime is much higher than that in the stable regime, which lies at the shot-noise level. We also show that the parameter sensitivity of the evolved state approaches the Heisenberg limit in the Josephson oscillation regime, while it is just scaled as the shot-noise limit in the self-trapping regime. Finally, we discuss the relation between the parameter sensitivity of the evolved state and the entanglement entropy.

• Received 17 April 2012

DOI:https://doi.org/10.1103/PhysRevA.86.012320