Quantum Fisher Information of Driven Multi-particle Systems in Structured Bosonic Reservoirs

We investigate the dynamics of the precision of the parameter estimation in many driven atoms, each of which interacts with a local structured bosonic reservoir respectively. The evolution of quantum states for single driven atom is described by the time local quantum master equation. The dynamics of the quantum Fisher information for many entangled atoms is obtained by means of the supreoperator mapping. The estimation limit is superior to the standard quantum limit during a characteristic interval. At a given time, the precision of parameter estimation can be improved to a maximal value if the number of entangled atoms is chosen to be an optimal value. The optimal number of entangled atoms is determined by the dynamical property. The decay of quantum Fisher information is accelerated with the increase of the number of entangled atoms.