Quantum Magnetometry with Orientation beyond Steady-State Limits in Cavity-Magnon Systems

We propose a transient vector quantum magnetometry protocol based on cavity-magnon systems. By exploiting finite-time dynamics initialized from a reservoir-engineered squeezed steady state, our scheme retains residual squeezing-induced quadrature noise reduction, which suppresses transient added noise and enhances the short-time signal-to-noise ratio beyond conventional unsqueezed steady-state limits. IQ demodulation of orthogonal cavity-output quadratures enables crosstalk-free reconstruction of all three components of a transient magnetic field, providing access to both its magnitude and orientation. This vector capability is relevant for short-lived magnetic phenomena such as pulsed spin excitations, magnetic textures, nanoscale current transients, and biomagnetic signals. In the long-time limit, we derive a closed-form stationary noise spectrum and identify the on-resonance noise-cancellation condition g_{am}=sqrt[κ_{a}κ_{m}]/2 at which the cavity-added noise vanishes without strong coherent coupling. Injected squeezing further suppresses the cavity-added noise away from resonance, while an array of N yttrium iron garnet spheres reduces the magnon-probe noise contribution by a factor of 1/N. Our results establish cavity-magnon systems as a scalable platform for transient, vector-resolved quantum magnetometry.