Observation of measurement-induced localization phenomena in a solid-state spin system

Abstract

Quantum measurement can profoundly impact the dynamics of many-body systems, for instance, inducing phase transitions from volume-law chaotic phases to area-law localized phases. While chaotic phases emerge naturally in generic many-body systems, the experimental realization of a fully localized phase driven by measurement remains challenging, primarily owing to the stringent requirement of near-perfect isolation of the system from environmental dissipation. Here we experimentally observe measurement-induced localization phenomena in an interacting $^{13}\mathrm{C}$ nuclear spin system in diamond. In contrast to previous circuit-model-based experiments, our well-isolated system evolves under a physical many-body Hamiltonian with measurements intervening at intervals. By implementing either projective measurements on a single spin or global weak measurements on the entire system, we observe substantially prolonged spin autocorrelation times as the measurement frequency increases. Our results, combined with numerical simulations, provide evidence that quantum measurement can drive a many-body system into a localized regime, and lay the groundwork for future experimental investigations into measurement-induced many-body dynamics and related entanglement phenomena.

The paper investigates whether repeated measurements suppress thermalization in an interacting solid-state spin network, and whether this suppression can indicate a measurement-induced localized regime. The platform is a $^{13}\mathrm{C}$ nuclear-spin network surrounding a diamond NV center, evolving under intrinsic dipolar interactions rather than a gate-based circuit. Single-spin autocorrelations are measured using NV-mediated initialization and readout. Without intermediate measurements, the target spin relaxes with a stretched-exponential timescale of $77.9(2.6)$ ms and exponent $0.539(16)$. Repeated projective measurements on that spin extend its autocorrelation time to $1.06$ s. Repeated laser pulses also implement weak measurements across an operationally defined network of approximately 100 spins, with effective measurement strength $\gamma_{\mathrm{global}}\approx0.1f$, where $f$ is the pulse repetition frequency. These likewise prolong autocorrelation times. At sufficiently high rates, transverse hyperfine coupling produces additional single-spin relaxation, identified as an anti-Zeno effect. Simulations of steady-state two-spin mutual information for 6–10 spins show a nonmonotonic dependence on measurement strength; its peak defines an estimated crossover that overlaps the experimental onset of autocorrelation enhancement. Lindblad simulations including the NV and eight nuclear spins qualitatively reproduce several observed trends without additional phenomenological nuclear dissipation. Entanglement entropy and mutual information are not measured experimentally, so the connection to an entanglement-transition localized regime is indirect. Computational limits restrict the dynamical simulations to eight spins, with a configuration selected to match the data; they do not reproduce the observed double-exponential relaxation. The origin of the unmonitored stretching exponent also remains unresolved.