High-throughput spin-bath characterization of spin-defects in semiconductors

TL;DR

The paper tackles the ill-posed problem of characterizing the local nuclear spin environment of a single spin-defect by introducing a trans-dimensional Bayesian framework that jointly infers the number, positions, and hyperfine couplings of surrounding nuclei from sparse coherence data. It integrates ab initio priors and a hybrid RJMCMC-based inference approach to deliver posterior distributions and to guide dynamical decoupling experiment design, laying groundwork for high-throughput screening and digital-twin studies of spin defects. The authors analyze fundamental detection limits under sparse and noisy data, demonstrate how to optimize experimental parameters, and validate the method on ten NV centers, showing reliable recovery of hyperfine couplings above $25\ \text{kHz}$ and a detectable threshold near $7.8125\ \text{kHz}$ under their conditions. Overall, this work provides uncertainty-quantified tools for scalable, resource-aware spin-bath characterization with potential applications across NV centers, SiC divacancies, and phosphorus donors in semiconductor quantum technologies.

Abstract

Detailed knowledge of the local environments of spin-defects in semiconductors, such as nitrogen vacancy (NV) centers in diamond or divacancies in silicon carbide, is crucial for optimizing control and entanglement protocols in quantum sensing and information applications. However, a direct experimental characterization of individual defect environments is not scalable, as spin bath measurements are extremely time consuming. In this work, we address the ill-posed inverse problem of recovering the atomic positions and hyperfine couplings of random nuclei surrounding spin-defects from sparse experimental coherence signals, which can be obtained in hours. To address the challenge to determine the number of isotopic nuclear spins along with their hyperfine couplings, we employ a trans-dimensional Bayesian approach that incorporates ab initio data. This approach provides posterior distributions of the numbers, hyperfine couplings, and locations of nuclear spins present in the sample. In addition to enabling high-throughput screening of spin-defects, we demonstrate how this trans-dimensional Bayesian approach can guide experimental design for dynamical decoupling experiments to detect nuclear spins within targeted hyperfine coupling regimes. While the primary focus is on accelerating spin-defect characterization, this Bayesian approach also lays the foundation for digital twin studies of spin-defects, where a virtual model of the spin-defect system evolves in real time with ongoing experimental measurements. Together, the set of tools we designed and applied paves the way for scalable deployment of spin-defects in semiconductors for quantum sensing and information applications.

Figures (5)

• Figure 1: Schematic of inverse problem. (Left) Representation of a single NV center in diamond with an external magnetic field ($B_Z$) applied along the axis of the NV center, and there are $k$ isotopic $^{13}$C randomly distributed at lattice sites, interacting with the central electronic spin (red) via the hyperfine interaction ($\mathbf{A}$) (see text for the definition of Hamiltonian terms). (Center) Experimental probing by applying $N$ dynamical decoupling $\pi$ pulses with varying inter-pulse spacings ($\tau$) to obtain (Right) a coherence signal. The inverse problem of interest is recovering the number of nuclear spins ($k$) and their hyperfine couplings ($\mathbf{A}$) from a sparse, noisy experimental coherence signal.
• Figure 2: Hyperfine coupling frequency detection limits from frequency sampling limits and simulations(a) Maximum detectable frequencies as a function of the number of interpulse spacings ($\tau$) sampled, shown for various maximum interpulse spacings ($\tau_{\text{max}}$). (b) Minimum detectable frequencies as a function of $\tau_{\text{max}}$ for different Carr-Purcell (CP) pulse numbers ($N$). (c) Schematic of average shot noise ($\varepsilon$) per data point for varying numbers of CP-pulses ($N$) with an arbitrary initial signal-to-noise ratio. (d) Minimum detectable hyperfine frequency, calculated as a function of the average $\varepsilon$ per data point, for joint fits of an N=8 and N=16 CP pulse experiment with $\tau_{\text{max}} = 8 \mu$s, $B_{\text{ext}} = 311$G, and 250 $\tau$ sampled at the natural concentration (1.1%) of $^{13}$C. The bootstrapped limit is shown for 0.95 confidence of detectability. The minimum frequency limit imposed by the experimental settings (7.8125 kHz).
• Figure 3: Accuracy of hybrid MCMC algorithm for recovering hyperfine couplings from simulated data. We applied our hybrid recovery method (see text) to simulations with 0.001 shot noise per data point, 250 $\tau$ sampled, a 0.008 ms longest $\tau$, 16 CP pulses, and 311 G magnetic field, and varied each one of the parameters independently for (a) maximum interpulse length $\tau_{\text{max}}$, (b) the number of CP pulses, and (c) magnetic field. For each of the parameters varied, we plot examples of simulated and recovered signals based on the data and detection rates, discrepancies in the number of recovered versus simulated spins, and false positive rates for the hybrid MCMC method averaged over random nuclear spin configurations consisting of 5 to 20 nuclear spins (for a total of 16 simulated nuclear spin configurations). Results are plotted by groupings of nuclear spins based on hyperfine magnitudes ($\sqrt{A_{\parallel}^2 + A_{\perp}^2}$) (see bottom colorbar).
• Figure 4: Experimental coherence signal data for 10 different nitrogen-vacancy (NV) centers under CP8 (left column) and CP16 (middle column) pulse sequences, overlaid with simulated coherence signals (green) generated from the modal spin configuration of the posterior distribution of nuclear spin configurations generated by our hybrid method to extract nuclear spin environments from experimental data. Each row corresponds to a distinct NV center. The right column shows the spatial distribution of nuclear spins in the modal configuration for each NV, plotted relative to the NV center (at the (0, 0, 0) position). Only lattice positions of nuclear spins with hyperfine magnitudes $> 25$ kHz are plotted. The hybrid method jointly analyzes CP8 and CP16 datasets to infer spin environments that best match the experimental data.
• Figure 5: Posterior distributions of the number and hyperfine couplings of spins from the hybrid algorithm applied to ten NV centers in diamond, plotted by magnitude ($\sqrt{A_{\perp}^2 + A_{\parallel}^2}$) of hyperfine coupling.