Globalized critical quantum metrology in dynamics of quantum Rabi model by auxiliary nonlinear term

TL;DR

The paper tackles the limitation of local critical quantum metrology in the quantum Rabi model by introducing an auxiliary neutral quadratic term, making the critical point a continuous regime with a globally accessible QFI $F_g$ that can be tuned via $\lambda$ and observed through quadrature readouts. By deriving an effective low-energy description and the QFI dynamics, the authors show that the divergence in metrological precision extends across the entire coupling range, not just near $g_c^{(0)}=1$, with $g_c^{(\lambda)}=\sqrt{1+4\lambda/\omega}$ setting the globalized thresholds. They present a concrete measurement scheme based on $\langle X\rangle_t$, derive the inverted variance $I_g(t)$, and establish scaling relations linking $I_g(t)$ and $F_g$, while analyzing finite-frequency and decoherence effects that still preserve the globalized enhancement. The work suggests a feasible protocol for broadening the applicability of CQM in light-matter systems, with potential realization in hybrid platforms employing optomechanical or Kerr-magnon elements, enabling robust, globally enhanced metrological performance.

Abstract

Quantum Rabi model (QRM) is a fundamental model for light-matter interactions, the finite-component quantum phase transition (QPT) in the QRM has established a paradigmatic application for critical quantum metrology (CQM). However, such a paradigmatic application is restricted to a local regime of the QPT which has only a single critical point. In this work we propose a globalized CQM in the QRM by introducing an auxiliary nonlinear term which is realizable and can extend the critical point to a continuous critical regime. As a consequence, a high measurement precision is globally available over the entire coupling regime from the original critical point of the QRM down to the weak-coupling limit, as demonstrated by the globally accessible diverging quantum Fisher information in dynamics. We illustrate a measurement scheme by quadrature dynamics, with globally criticality-enhanced inverted variance as well as the scaling relation with respect to finite frequencies. In particular, we find that the globally high measurement precisions still survive in the presence of decoherence. Our proposal paves a way to break the local limitation of QPT of the QRM in CQM and enables a broader application, with implications of applicability in realistic situation.

Figures (7)

• Figure 1: Globalized critical quantum metrology. (a) Time evolution of the quantum Fisher information (QFI) $F_g(t)$ for $g = 0.097$ (lower line), $g = 0.098$ (middle line), $g = 0.099$ (upper line) in the vicinity of critical coupling point $g = 0.1$ at $\lambda =-0.2475 \omega$. (b) Logarithm of $F_g$ as a function of $g$ at time moment $t=1000\omega$ at $\lambda=0.0,-0.05,-0.10,-0.15,-0.20$ (from right to left). The vertical dashed lines mark the critical points $g_c^{(\lambda)}$ at the corresponding values of $\lambda$. (c) Density plot of Logarithm of $F_g$ in the $\lambda$-$g$ plane at $t=1000/\omega$.
• Figure 2: Measurement scheme: Sensitivity resource of $\left\langle X\right\rangle _t$ extended from $g=1$ to weak couplings. (a) Variations of $\left\langle X\right\rangle _t$ with respect to $g$ for $\lambda=0$ (rightmost), $\lambda=-0.2\omega$ (middle) and $\lambda=-0.247\omega$ (lefttmost). (b) A close-up view of $\left\langle X\right\rangle _t$ around $g=0.1$ for $\lambda=-0.247\omega$ (peaked line) $\lambda=0$ (flat line). Here $t=75 /\omega$.
• Figure 3: Globally available high measurement precision available from dynamics of $\left\langle X\right\rangle _t$. Time evolution of the inverted variance $I_g$ at $g=0.9$ (a) and at $g=0.1$ (b). Red (blue) lines represent the $\lambda=0$ ($\lambda=-0.247\omega$) case [blue lines are higher in (a) and lower in (b)]. The dashed lines mark the peak values.
• Figure 4: Scaling relation of the inverted variance ($I_g$) and the QFI ($F_g$). The numerical data are represented by the diamonds ($\lambda=0$, $g=0.9$) and dots ($\lambda=-0.247\omega$, $g=0.1$), while the analytical results are denoted by the dash-dotted line ($\lambda=0$, $g=0.9$) and dashed line ($\lambda=-0.247\omega$, $g=0.1$). Te integer number $n$ labels the peaks of $I_g$ in time evolution.
• Figure 5: Surviving precision resources at finite frequencies. (a) Inverted variance $I_g(t)$ at $\lambda =0, g=0.9$ for different frequency ration $\eta$. (b) Inverted variance $I_g(t)$ at $\lambda =-0.247\omega, g=0.1$ for different frequency ration $\eta$.