Quantum Fisher Information Probing a Quantum-Gas Cavity QED

Motivated by recent efforts in simulating nonequilibrium scenarios of the Dicke model in quantum-gas cavity QED, we investigate direct probing of the normal-to-superradiant quantum phase transition via Quantum Fisher Information (QFI). This transition represents a paradigmatic example of spontaneous symmetry breaking in quantum optics, where the system’s $Z_2$ symmetry is broken in the superradiant phase. At zero temperature, we derive analytical expressions for the QFI in the limit where the atomic transition frequency—scaled by the cavity frequency—tends to infinity. Furthermore, we analyze the impact of finite temperature on the QFI in both the thermodynamic limit and the regime of a finite but large number of atoms. All results demonstrate that the QFI exhibits a singularity as the coupling crosses the critical point—a clear signature of quantum criticality associated with spontaneous symmetry breaking. The divergent behavior of the QFI across the quantum phase transition directly relates to measuring dynamic susceptibilities using experimentally accessible Bragg spectroscopy tools and resources.