Local Magnetometry from Measurement-Induced Dissipation

Abstract

Magnetic phases are commonly identified through macroscopic magnetization, yet many ordered states, including antiferromagnets and altermagnets, possess a vanishing net moment despite distinct local spin structure. We show that such an order can be accessed through the measurement-induced steady state of a single primary qubit locally coupled to a spin lattice. Using a controlled primary-ancillary qubit protocol, we derive analytically that the steady state \emph{encodes} a locally weighted exchange field in a signed observable that is linear in the weak-coupling regime. Numerical simulations demonstrate lattice-scale resolution of antiferromagnetic and altermagnetic textures and robustness against short-correlated noise. Our results establish measurement-induced dissipation as a resource for detecting magnetic order through microscopic structure rather than through global moments.

Figures (2)

• Figure 1: Here a schematic of the setup is presented. The two-level dissipative system (the primary qubit, represented by the red dot) in proximity to a 2D magnetic lattice, coupled via a spin-spin interaction (shown as blue hue) that falls of fast, typical of assumed gaussian coupling. In the inset we show one plausible spin structure of the lattice.
• Figure 2: Spatial maps of the steady-state observable $s_y(\mathbf{r}_0)$ obtained by scanning the primary qubit across the lattice. Panels (a–c) show antiferromagnetic order and (d–f) altermagnetic order AltermagneticLattice. Columns correspond to the noiseless case, diagonal noise, and fully correlated noise. Although both phases satisfy $\sum_i \mathbf{S}_i = 0$ and therefore produce no response in probes sensitive only to net magnetization, their distinct local spin textures generate different effective fields $B_{\mathrm{eff}}(\mathbf{r}_0)=\sum_i J_i(\mathbf{r}_0)\mathbf{S}_i$, which are directly reflected in the steady-state response. Noise reduces contrast but preserves the characteristic spatial patterns, demonstrating the robustness of the protocol. Data are shown for $J_0=1$ and $\alpha=1$; noise amplitudes are sampled from $[-0.02,0.02]$.