Critical behavior of quantum Fisher information in finite-size open Dicke model

We explore the steady-state critical behavior of the finite-size open Dicke model—a model that incorporates spontaneous emission decay of the collective atomic spin states and decay of the cavity field. From the perspective of quantum information theory, we can often better characterize the quantum phase transition. In this paper, we characterize the super-radiant phase transition of the steady state of the open Dicke model by numerically calculating the quantum Fisher information (QFI). We calculate the QFI for the atomic state and the cavity field state, as well as their derivatives. We find that the QFI of the cavity field state is more sensitive to atomic decay, and is suppressed more severely in the presence of atomic decay. In contrast, the QFI of the atomic state is less sensitive to the photon loss of the cavity field.