  The single-mode Dicke model is well-known to undergo a quantum phase
transition from the so-called normal phase to the supperradiant phase
(hereinafter called the "superradiant quantum phase transition"). Normally,
quantum phase transitions are closely related to the critical behavior of
quantities such as entanglement, quantum fluctuations, and fidelity. In this
paper, we study quantum Fisher information (QFI) of the field mode and that of
the atoms in the ground state of the Dicke Hamiltonian. For finite and large
enough number of atoms, our numerical results show that near the critical
atom-field coupling, the QFIs of the atomic and the field subsystems can
surpass the classical limits, due to the appearance of nonclassical squeezed
states. As the coupling increases far beyond the critical point, the two
subsystems are in highly mixed states, which degrade the QFI and hence the
ultimate phase sensitivity. In the thermodynamic limit, we present analytical
results of the QFIs and their relationships with the reduced variances. For
each subsystem, we find that there is a singularity in the derivative of the
QFI at the critical point, a clear signature of quantum criticality in the
Dicke model.
