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arXiv:1503.03953 · The European Physical Journal D

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

Yuyu Zhang, Xiang-You Chen

Published Oct 30, 2015• 5 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2015-60323-1

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arXiv:1312.1426•New Journal of Physics•Jun 17, 2014•134 citations
Quantum Fisher information to the X states of the collective atom ensemble and the scaled quantum fisher information of the atomic subsystem are evaluated analytically in the Dicke Hamiltonian. Critical behavior of the two kinds of Fisher information are in accordant with the analytical results in the thermodynamic limit. Finite-size scaling is analyzed with the large accessible system size due to the effective technique proposed previously. Scaling exponents of the quantum Fisher information are found.
We explore the steady-state critical behavior of the finite-size open Dicke model—a model that incorporates spontaneous emission decay of the collective atomic spin states and decay of the cavity field. From the perspective of quantum information theory, we can often better characterize the quantum phase transition. In this paper, we characterize the super-radiant phase transition of the steady state of the open Dicke model by numerically calculating the quantum Fisher information (QFI). We calculate the QFI for the atomic state and the cavity field state, as well as their derivatives. We find that the QFI of the cavity field state is more sensitive to atomic decay, and is suppressed more severely in the presence of atomic decay. In contrast, the QFI of the atomic state is less sensitive to the photon loss of the cavity field.
The single-mode Dicke model is well known to undergo a quantum phase transition from the so-called normal phase to the superradiant phase (hereinafter called the 'superradiant quantum phase transition'). Normally, quantum phase transitions can be identified by the critical behavior of quantities such as entanglement, quantum fluctuations, and fidelity. In this paper, we study the role of the quantum Fisher information (QFI) of both the field mode and the atoms in the ground state of the Dicke Hamiltonian. For a finite but large number of atoms, our numerical results show that near the critical atom-field coupling, the QFI of the atomic and the field subsystems can surpass their classical limits, due to the appearance of nonclassical quadrature squeezing. As the coupling increases far beyond the critical point, each subsystem becomes a highly mixed state, which degrades the QFI and hence the ultimate phase sensitivity. In the thermodynamic limit, we present the analytical results of the QFI and their relationship with the reduced variances of the field mode and the atoms. For each subsystem, we find that there is a singularity in the derivative of the QFI at the critical point, a clear signature of the quantum criticality in the Dicke model.