Quantum Geometric Tensor and Critical Metrology in the Anisotropic Dicke Model

We investigate the quantum phase transition in the anisotropic Dicke modelthrough an examination of the quantum geometric tensor of the ground state. Inthis analysis, two distinct classical limits exhibit their unique anisotropiccharacteristics. The classical spin limit demonstrates a preference for therotating-wave coupling, whereas the classical oscillator limit exhibitssymmetry in the coupling strength of the bias. The anisotropic features of theclassical spin limit persist at finite scales. Furthermore, we observe that theinterplay among the anisotropic ratio, spin length, and frequency ratio cancollectively enhance the critical behaviors. This critical enhancement withouttrade-off between these factors provides a flexible method for quantumprecision measurement.