Optimal Multiparameter Quantum Estimation of Magnonic Couplings in a Magnomechanical Cavity

TL;DR

This work addresses the problem of jointly estimating the magnon–photon coupling $G_{mc}$ and the magnon–phonon coupling $G_{mb}$ in a cavity magnomechanical system. Using a linearized three-mode Gaussian-state model, the authors derive the SLD- and RLD-based quantum Fisher information matrices and compare simultaneous versus individual parameter estimation, also evaluating the heterodyne classical Fisher information. They show that the right logarithmic derivative (RLD) bound $oldsymbol{ m B}_R$ is consistently tighter than the symmetric logarithmic derivative (SLD) bound $oldsymbol{ m B}_S$, making the most informative bound $oldsymbol{ m B}_{MI}$ coincide with $oldsymbol{ m B}_R$ across a range of parameters; heterodyne detection yields a classical information flow that closely approaches the quantum limit in the Gaussian regime. Numerical results with realistic parameters reveal that increasing drive, optimizing detuning away from resonance, and reducing temperature and mechanical damping enhance the information content and improve joint estimation accuracy, supporting practical high-precision sensing in hybrid quantum devices.

Abstract

In this work, we introduce an experimentally viable scheme to enhance the simultaneous estimation precision of the couplings $G_{mc}$ and $G_{mb}$, with a particular focus on the performance of heterodyne detection. By comparing simultaneous and individual estimation strategies, we demonstrate that the simultaneous approach offers a notable advantage in our system. To support this, we compute the quantum Fisher information matrices (QFIMs) based on the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD). Our results show that the quantum Cramér Rao bound (QCRB) associated with the RLD is consistently lower than that of the SLD, indicating superior estimation precision. From a physical standpoint, this improvement reflects the system's enhanced capacity to encode, transfer, and extract quantum information while allowing optimal control of fundamental interactions. We show that increasing the Rabi frequency, cavity loss rate, and the average number of photons and phonons, combined with reduced mechanical damping and temperature, enhances the system's sensitivity to the coupling parameters. These mechanisms act on the available quantum resources, such as entanglement, squeezing, and state purity, leading to more precise estimations. Furthermore, our analysis reveals that under certain conditions, heterodyne detection can closely approach the ultimate precision set by the QFIM. This suggests that a measurement strategy based on heterodyne detection can offer an efficient and practical route for estimating the couplings $G_{mc}$ and $G_{mb}$, paving the way for high precision hybrid quantum sensors.

Figures (7)

• Figure 1: The schematic illustrates a hybrid magnomechanical system where a YIG sphere is placed inside a microwave cavity at the point of maximum magnetic field intensity of the cavity mode. A uniform static magnetic field is applied to establish magnon–photon interaction. To enhance the magnomechanical coupling, the magnon mode is externally driven by a microwave source (not depicted). At the sphere’s location, three mutually orthogonal magnetic fields are present: the static bias field (along the $z$-axis), the external drive field (along the $y$-axis), and the magnetic field of the cavity mode (along the $x$-axis).
• Figure 2: Ratio between the QCRB based on RLD and that based on SLD as a function of the cavity mode detuning $\Delta_c$, under varying dissipation rates $\kappa_m$ of the magnon mode.
• Figure 3: Dynamics of the performance ratio $\Gamma$ for the estimation of the constant couplings $G_{mc}$ and $G_{ms}$ as a function of the cavity detuning $\Delta_c$, for various values of magnon dissipation rate $\kappa_m$ in (a), and for different temperatures $T$ in (b). In panel (a), the temperature is fixed at $T=60 \,\text{mK}$, and all other parameters are identical to those used in Fig. \ref{['R']}.
• Figure 4: The most informative QCRB ($\mathcal{B}_{MI}$) as a function of the cavity mode detuning $\Delta_c$: (a) under various values of the Rabi frequency $\Omega$, (b) for different cavity mode dissipation rates $\kappa_c$, and (c) for different temperatures $T$. The parameters used are identical to those in Fig. \ref{['R']}.
• Figure 5: Behavior of the most informative QCRB ($\mathcal{B}_{MI}$) as a function of the Rabi frequency $\Omega$: (a) for various temperatures $T$, and (b) under various values of the mechanical damping rate $\gamma_s$. The cavity dissipation rate is fixed at $\kappa_c = 6 \;\text{MHz}$, with all remaining parameters matching those employed in Fig. \ref{['R']}.