Magnon-microwave backaction noise evasion in cavity magnomechanics

TL;DR

This work tackles measurement backaction in cavity magnomechanical systems by proposing a two-tone, backaction-evading (BAE) scheme that targets a quantum-nondemolition quadrature of the mechanical mode. By balancing two microwave tones separated by $2\omega_b$ and tuning drive amplitudes to satisfy a specific ratio, the authors engineer a QND-like Hamiltonian that makes the mechanical quadrature $x_{b,\psi}$ immune to backaction, with backaction noise redirected into an orthogonal quadrature. They provide a comprehensive frequency-domain treatment of both single-tone and two-tone driving, deriving explicit expressions for mechanical and microwave noise spectra, imprecision noise, and added quanta, and they quantify robustness to imperfections such as incomplete tone separation and drive imbalance. The results show that, under realistic magnomechanical parameters, the minimum added noise can drop below the standard quantum limit around the lower magnon-microwave polariton, enabling sub-SQL thermometry and precision sensing, while also outlining regimes where robustness is traded off against ultimate noise performance. The framework is presented as a flexible route that can extend to other multimode systems and potentially support quantum state tomography, entanglement, and squeezing in magnomechanical platforms.

Abstract

In cavity magnomechanical systems, magnetic excitations couple simultaneously with mechanical vibrations and microwaves, incorporating the tunability of magnetism and the long lifetimes of mechanical modes. Applications of such systems, such as thermometry and sensing, require precise measurement of the mechanical degree-of-freedom. In this paper, we propose a scheme for realizing backaction evading measurements of the mechanical vibrations in cavity magnomechanics. Our proposal involves driving the microwave cavity with two tones separated by twice the phonon frequency and with amplitudes satisfying a balance relation. We show that the minimum added imprecision noise is obtained for drives centered around the lower frequency magnon-microwave polaritons, which can beat the standard quantum limit at modest drive amplitudes. Our scheme is a simple and flexible way of engineering backaction evasion measurements that can be further generalized to other multimode systems.

Figures (10)

• Figure 1: Schematic depiction of a cavity magnomechanical system. (a) The magnetic excitations (blue) couple simultaneously to a microwave mode (red) and mechanical vibrations (black). The cavity can be driven, and the output is used to probe the mechanics. The system is described by a model of interacting bosonic modes subject to dissipation.
• Figure 1: Ratio between the integral of the noise spectrum of the BAE quadrature, including the counter-rotating terms and its value without counter-rotating terms, for both the triple resonance and the dynamical backaction evasion schemes. Parameters as in Table 1 of the main text.
• Figure 2: Different cavity magnomechanics schemes. The Lorentzians indicate the resonance frequency and linewidths of the hybrid modes as they would be measured, for example, via transmission. Relevant mechanical sidebands are also indicated. (a) Triple resonance scheme: the magnon-microwave coupling $g_{mc}$ is half of the phonon frequency. The blue (red) sideband of the lower (upper) hybrid mode coincides with the upper (lower) hybrid mode frequency. (b) Dynamical backaction evasion scheme: the magnon-microwave coupling is equal to one phonon frequency. In this scheme, the sidebands of the hybrid modes coincide.
• Figure 2: Ratio between the uncertainty in the non-QND quadrature $\hat{p}_{\psi}$ and the reference value for an uncoupled oscillator in thermal equilibrium (a) as a function of the detuning between the central frequency of the two-tones and the microwave frequency for the triple resonant scheme and the dynamical backaction evasion scheme, and (b) as a function of the magnon-microwave coupling for different values of $\Delta_c$. Plots for zero temperature and all parameters as in Table 1.
• Figure 3: Number of added quanta to the measurement. The number of added quanta is offset by the vacuum fluctuations in a single-tone cavity magnomechanical system at zero temperature and for a zero detuned drive as a function of the drive amplitude $\epsilon_d/\sqrt{\kappa_c}$. The curves shown are for magnon-microwave couplings varying from $\omega_b/2$ (red, continuous curve) to $\omega_b$ (blue dashed line), with the thin lines corresponding to intermediate values. The values of drive amplitude depicted here correspond to linear magnomechanical couplings $\vert g_{mb} \vert$ in the range $\approx 10^{-3} \kappa_c$ to $0.5 \kappa_c$. All other parameters as in Table \ref{['Table0']}.