Quantum Geometric Tensor and Critical Metrology in the Anisotropic Dicke Model

TL;DR

This paper explores how the quantum geometric tensor reveals critical phenomena in the anisotropic Dicke model, highlighting anisotropic effects in classical limits and proposing a flexible approach for quantum precision measurement.

Contribution

It introduces a novel analysis of the quantum geometric tensor in the anisotropic Dicke model, uncovering anisotropic critical behaviors and their implications for quantum metrology.

Findings

Classical spin limit favors rotating-wave coupling.

Classical oscillator limit shows symmetry in bias coupling.

Interplay of anisotropic ratio, spin length, and frequency ratio enhances critical behavior.

Abstract

We investigate the quantum phase transition in the anisotropic Dicke model through an examination of the quantum geometric tensor of the ground state. In this analysis, two distinct classical limits exhibit their unique anisotropic characteristics. The classical spin limit demonstrates a preference for the rotating-wave coupling, whereas the classical oscillator limit exhibits symmetry in the coupling strength of the bias. The anisotropic features of the classical spin limit persist at finite scales. Furthermore, we observe that the interplay among the anisotropic ratio, spin length, and frequency ratio can collectively enhance the critical behaviors. This critical enhancement without trade-off between these factors provides a flexible method for quantum precision measurement.