Protection of quantum Fisher information for multiple phases in open quantum systems

We study the protection of quantum Fisher information (QFI) of two phases encoded in an open V-type three-level atom embedded in a zero-temperature bosonic reservoir and driven by a classical field. By transforming the problem into the model of an open driving-free V-type atom, we can then solve the dynamics analytically and study the evolution of QFI numerically. It is found that the QFI of both of the two phases can be protected effectively when the strength of the driving field is adequate. The protective effect enhances with the decrease in detuning between the frequency of the classical driving field and the frequency of the atomic transitions. Narrow width of the environmental spectrum is also beneficial for the protection of QFI of the phases.