Enhanced multiparameter quantum estimation in cavity magnomechanics via a coherent feedback loop

TL;DR

This paper presents a feasible scheme using coherent feedback and driving fields to enhance the simultaneous quantum estimation of coupling strengths in cavity magnon mechanics, achieving near-optimal precision.

Contribution

It introduces a novel feedback-assisted approach for multiparameter quantum estimation in cavity magnon systems, improving precision beyond traditional bounds.

Findings

Significant reduction in estimation errors for coupling strengths.

RLD-based quantum Cramer Rao bound outperforms SLD-based bound.

Heterodyne detection approaches the quantum limit in suitable regimes.

Abstract

Multiparameter quantum metrology plays a fundamental role in uncovering and exploiting the distinctive features of quantum systems. In this work, we propose an effective and experimentally feasible scheme to significantly enhance the simultaneous quantum estimation of the photon magnon and magnon mechanical coupling strengths in a hybrid cavity magnon mechanical platform. Our approach relies on the assistance of a coherent feedback loop combined with the injection of a coherent driving field. We show that an appropriate tuning of the system and feedback parameters leads to a substantial reduction of the estimation errors associated with both coupling strengths. To quantify the metrological performance of the proposed scheme, we employ the quantum Cramer Rao bound (QCRB) as a fundamental benchmark for multiparameter estimation. We explicitly compute and compare the QCRBs derived from the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD) formalisms. Our results demonstrate that the RLD based QCRB is systematically lower than the SLD based bound, indicating superior estimation precision in the considered noncommutative estimation scenario. We further analyze the performance of heterodyne detection and show that, in suitable parameter regimes, the corresponding classical estimation precision closely approaches the ultimate quantum limit predicted by our scheme. Finally, we discuss the experimental feasibility of the proposed setup within currently available cavity magnon mechanical platforms. Owing to its general character, the framework developed here can be readily extended to the high precision estimation of other physical parameters in hybrid quantum systems.