Large-N scaling behavior of the quantum fisher information in the Dicke model

TL;DR

This paper investigates how the quantum Fisher information (QFI) behaves near the superradiant phase transition in the Dicke model, providing analytical expressions and finite-size scaling analysis for large systems.

Contribution

It offers explicit analytical expressions for the QFI in the Dicke model and characterizes its large-size scaling behavior with accurate critical exponents.

Findings

QFI captures quantum criticality in the Dicke model

Explicit analytical expression for ground state QFI

Finite-size scaling with accurate critical exponents

Abstract

Quantum Fisher information (QFI) of the reduced two-atom state is employed to capture the quantum criticality of the superradiant phase transition in the Dicke model in the infinite size and finite-$N$ systems respectively. The analytical expression of the QFI of its ground state is evaluated explicitly. And finite-size scaling analysis is performed with the large accessible system size due to the effective bosonic coherent-state technique. We also investigate the large-size scaling behavior of the scaled QFI of the reduced $N$-atom state and show the accurate exponent.