Entanglement, Nonlinear Dynamics, and the Heisenberg Limit

Luca Pezzé (1) , A. Smerzi (2)

1 laboratoire Charles Fabry de l'Institut d'Optique / Optique atomique
2 UNITN - Università degli Studi di Trento = University of Trento

We show that the quantum Fisher information provides a sufficient condition to recognize multi-particle entanglement in a N qubit state. The same criterion gives a necessary and sufficient condition for sub shot-noise phase sensitivity in the estimation of a collective rotation angle θ . The analysis therefore singles out the class of entangled states which are {\it useful} to overcome classical phase sensitivity in metrology and sensors. We finally study the creation of useful entangled states by the non-linear dynamical evolution of two decoupled Bose-Einstein condensates or trapped ions.

Domains: Optics [physics.optics]

Luca Pezzé, A. Smerzi. Entanglement, Nonlinear Dynamics, and the Heisenberg Limit. Physical Review Letters, 2009, 102 (10), pp.100401. ⟨10.1103/PhysRevLett.102.100401⟩. ⟨hal-00626569⟩