Squeezed-Light-Enhanced Multiparameter Quantum Estimation in Cavity Magnonics

TL;DR

This work tackles simultaneous estimation of multiple parameters in a cavity magnomechanical system by introducing a degenerate optical parametric amplifier to suppress quantum noise and reduce the most informative quantum Cramér–Rao bound. It develops a Gaussian-state framework using SLD and RLD quantum Fisher information to quantify ultimate precision, and analyzes both steady-state and dynamical regimes. The authors compare SLD-based minimal bounds with classical Fisher information from homodyne and heterodyne measurements, showing that OPA-assisted setups can deliver substantial quantum-enhanced precision with practical Gaussian readouts. The results offer a robust, experimentally feasible path toward high-precision metrology in hybrid magnomechanical and optomechanical platforms.

Abstract

Improving multiparameter quantum estimation in magnonic systems via quantum noise suppression is a well-established and critical research objective. In this work, we propose an experimentally realistic scheme to improve the precision of simultaneously estimating different parameters in a cavity-magnon system by utilizing a degenerate optical parametric amplifier (OPA). The OPA enhances the estimation precision by decreasing the most informative quantum Cramér-Rao bound, calculated employing the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD). We show that when nonlinearity is introduced into the system, quantum noise is significantly suppressed. Our results show how different physical parameters influence multiparameter estimation precision and provide a detailed discussion of the associated physical mechanisms in the steady state. Our results focus on exploring practical Gaussian measurement schemes that can be realized experimentally. Besides, we further analyze the system's dynamics, comparing both the SLD quantum Fisher information (QFI) and the classical Fisher information (CFI) for both homodyne and heterodyne detection. This approach provides a robust foundation for multiparameter quantum estimation, offering significant potential for application in hybrid magnomechanical and optomechanical systems.

Figures (7)

• Figure 1: (a) Schematic representation of the cavity-magnon system, with a YIG sphere positioned at the magnetic field antinode of the microwave cavity mode to maximize coupling. A uniform magnetic field $\mathbf{B}$ is applied to bias the YIG sphere, with its orientation including at least one component parallel to the $z$-axis. Moreover, an external electromagnetic field drives the cavity mode. (b) The interaction between the photon mode and the magnon mode presents by cavity-magnon coupling $g_{\rm mc}$. (c) The system utilizes a degenerate optical parametric amplifier (OPA) process where, mediated by second-order nonlinearity, a single pump photon of frequency $\omega_{\rm d}$ is converted into two cavity photons of frequency $\omega_{\rm c}$ (signal and Idler with same frequency $\omega_c$). This process is governed by the resonance relation $\omega_{\rm d}=2\omega_{\rm c}$.
• Figure 2: Plot of the BMI as function of the temperature $\rm T$ for different values of the gain $\lambda$, with $\theta=1.65\pi$.
• Figure 3: Plot of the variation of the BMI versus (a) $\lambda/\gamma_{\rm c}$ with $\theta=1.65\pi$ and (b) $\theta/\pi$ with $\lambda=0.75\gamma_c$, for different values of ${\rm g_{mc}}$.
• Figure 4: Plot of the variation of the $BMI$ as function of (a) cavity detuning $\Delta_{\rm c}/\gamma_{\rm m}$ for different value of the cavity-magnon coupling ${\rm g}_{\rm mc}$ and (b) magonon detunig $\Delta_{\rm m}/\gamma_{\rm m}$ for different value of the power $P$. Using $\lambda = 0.67\gamma_c$ and $\theta=1.65\pi$.
• Figure 5: Plot of the dynamical evolution of the $\rm BIM$ for various value of (a) $\gamma_{\rm c}$ and (b) $\gamma_{\rm m}/{\rm g_{mc}}$ with $\lambda =0.65\gamma_{\rm c}$ and $\theta=1.65\pi$.