Three-dimensional optical characterization of magnetostrictive deformation in magnomechanical systems

TL;DR

This work introduces an optical method for real-time, three-dimensional characterization of magnetostrictive deformation in magnomechanical YIG-sphere systems. By detecting deformation-induced high-order Hermite-Gaussian modes in the scattered probe field through postselection and balanced homodyne detection, the approach achieves picometer-scale precision in x, y, and z directions. A Fisher-information analysis demonstrates that higher-order probe beams and balanced homodyne detection significantly enhance sensitivity, outperforming traditional array-detection methods for in-plane deformations. The scheme directly reads out magnomechanical backaction and 3D cooling dynamics, with potential applicability to nonmagnetic spherical objects as a versatile tool in magnomechanics and precision metrology.

Abstract

Magnomechanical systems with YIG spheres have been proven to be an ideal system for studying magnomechanically induced transparency, dynamical backaction, and rich nonlinear effects, such as the magnon-phonon cross-Kerr effect. Accurate characterization of the magnetostriction induced deformation displacement is important as it can be used for, e.g., estimating the magnon excitation number and the strength of the dynamical backaction. Here we propose an optical approach for detecting the magnetostrictive deformation of a YIG sphere in three dimensions (3Ds) with high precision. It is based on the deformation induced spatial high-order modes of the scattered field, postselection, and balanced homodyne detection. With feasible parameters, we show that the measurement precision of the deformation in $x$, $y$, and $z$ directions can reach the picometer level. We further reveal the advantages of our scheme using a higher-order probe beam and balanced homodyne detection by means of quantum and classical Fisher information. The real-time and high-precision measurement of the YIG sphere's deformation in 3Ds can be used to determinate specific mechanical modes, characterize the magnomechanical dynamical backaction and the 3D cooling of the mechanical vibration, and thus finds a wide range of applications in magnomechanics.

Figures (8)

• Figure 1: Schematic diagram of the magnetostrictive deformation of a YIG sphere. The YIG sphere is positioned in a uniform bias magnetic field $H$ and driven by a microwave field (not shown) whose magnetic component is perpendicular to the bias field. The magnetostrictive interaction leads to the geometric deformation of the YIG sphere, which, in each direction, can be decomposed into a small displacement fluctuation (orange ellipsoid) around an average displacement (purple ellipsoid). Here, the probe field is shown in pink and the scattered field corresponding to the deformed purple (orange) ellipsoid is shown in purple (orange). The small variation of the radial waist size and the shift of the axial waist position are denoted by $\delta r$ and $\delta z$, respectively.
• Figure 2: Weight coefficients $C_{nm}$ of $\text{HG}_{nm}$ modes in the scattered field as a function of the variation in the waist radius (a) and the waist position (b) for a $u_{00}$ probe beam. The black lines denote the first-order approximations derived from Eq. \ref{['eqqq2']}. The solid (dashed) curves in (a) denote $\delta\omega_{x(y)}<0$ ($\delta\omega_{x(y)}>0$).
• Figure 3: Measurement scheme based on high-order modes of the scattered field, postselection, and balanced homodyne detection.
• Figure 4: Schematic diagram of the weak measurement process used in our scheme.
• Figure 5: Minimum measurable deformations (MMDs) versus (a) the postselection probability, (b) the probe power, (c) and the mode order of the probe beam. The purple, magenta, and orange dots (c) correspond to $\delta\omega_x$ versus $n$; $\delta\omega_y$ versus $m$; and $\delta z$ versus $\nu=\text{max}[m,n]$, respectively. We use a YIG sphere with the diameter of 250 $\mu$m, the detector resolution bandwidth $\tau_r=1$ Hz, the probe beam wavelength $\lambda=125$$\mu$m, and the beam waist of the probe beam $\omega_0=150$$\mu$m.