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

We present a transient quantum sensing framework for cavity-magnon systems that circumvents the inevitable loss of initial-state quantum properties plaguing conventional steady-state protocols. Explicitly incorporating finite-time dynamics and adopting an engineered steady state as the initial condition, we derive the exact transient noise spectrum. We show that residual initial quantum correlations alone can drastically enhance the short-time signal-to-noise ratio (SNR) beyond that achievable with unsqueezed steady-state schemes. Through analysis of the transient spectral density and joint measurements of orthogonal cavity quadratures, we realize crosstalk-free reconstruction of all three magnetic field components, enabling orientation of magnetic signals. In the long-time limit, our theory yields a closed-form stationary noise spectrum and uncovers a resonance condition $g_{am}=\sqrt{\kappa_a\kappa_m}/2$, where cavity field quantum noise is fully canceled without requiring strong coherent coupling. Away from this resonance, injected squeezing further suppresses cavity induced noise and broadens the detection bandwidth. Extending the framework to an array of $N$ yttrium iron garnet (YIG) spheres generates a collective bright mode, with magnon-probe noise scaling as $1/N$. Our results establish a unified route to scalable, high precision, multidimensional quantum magnetometry using cavity-magnon platforms.