QDsiM: A Noise-Aware Simulation Toolkit for Quantum Diamond Microscope

TL;DR

The paper addresses the challenge of bridging ideal NV-center ODMR theory and real-world noisy measurements by introducing QDsiM, a digital twin that combines a seven-level NV model with modular, experimentally-accessible noise modules. It presents a comprehensive theoretical framework—spanning ground-state spin Hamiltonians, a seven-level rate model, and ensemble averaging across four NV orientations—together with a detailed numerical workflow to generate realistic CW-ODMR spectra and reconstruct magnetic fields. The toolkit facilitates exploration of power broadening, contrast losses, and noise propagation, enabling parameter optimization via a contrast-to-linewidth figure of merit and offering denoising strategies for robust field inference. The framework is designed to be extensible to electric-field and strain effects, pulsed protocols, and machine-learning approaches, with clear practical relevance for field-deployable NV-based magnetometers. Overall, QDsiM provides a physically-grounded, flexible platform to design, test, and optimize NV quantum sensors under realistic operating conditions.

Abstract

The nitrogen-vacancy (NV) center in diamond is a leading solid-state platform for room-temperature quantum magnetometry owing to its long spin coherence times, optical spin initialization and readout, and high sensitivity to magnetic, electric, and thermal perturbations. As NV-based optically detected magnetic resonance (ODMR) systems transition from controlled laboratory environments toward portable and field-deployable sensors, a detailed understanding of realistic noise sources and experimental imperfections becomes essential for optimizing performance and sensitivity. In this work, we present a comprehensive simulation framework, i.e., a digital twin, for continuous-wave wide-field ODMR in NV-center ensembles. The model is built upon a physically consistent seven-level description of the NV center and incorporates a broad range of experimentally relevant noise and imperfection mechanisms as modular, parameterized components. These include laser and microwave amplitude fluctuations, microwave phase noise, uncertainty in the NV gyromagnetic ratio, spin dephasing, temperature-induced shifts of the ground-state zero-field splitting, surface-induced magnetic field perturbations, and photon shot noise. Power broadening and contrast degradation arising from optical and microwave driving are captured self-consistently through linewidth calculations. Also, the spatial inhomogeneity is modeled via a Gaussian laser intensity profile across the sensing region...

Figures (22)

• Figure 1: Energy level diagram of the negatively charged NV center in diamond, showing the exact processes that happen when NV is optically pumped along with MW application. It shows the optical and microwave transitions along the ISC through a non-radiative pathway.
• Figure 2: ODMR spectra of a single NV center orientation with and without an external magnetic field. The normalized fluorescence intensity is plotted as a function of microwave frequency. The red curve shows the ODMR spectrum in the absence of a magnetic field, exhibiting a single dip centered around 2.87GHz, corresponding to the zero-field splitting between the $m_s = 0$ and $m_s = \pm 1$ ground-state levels. The blue curve shows the spectrum when a static magnetic field is applied along the NV axis. The degeneracy of the $m_s = \pm1$ levels is lifted by the Zeeman effect, resulting in two distinct resonances symmetrically split about the zero-field resonance. This spectral splitting is a key feature used in NV-based magnetometry to infer magnetic field strength and orientation.
• Figure 3: Optically detected magnetic resonance (ODMR) spectrum of an NV ensemble in diamond. Top: The ODMR spectrum displays fluorescence contrast as a function of microwave frequency. Multiple dips are observed due to the Zeeman splitting of the $m_s = \pm 1$ sublevels under an applied magnetic field. NV centers are oriented along four distinct crystallographic axes; the projection of the magnetic field onto each orientation leads to different resonance frequencies, resulting in up to eight distinguishable dips (two per axis, corresponding to transitions $m_s = 0 \rightarrow \pm 1$). Bottom: The differential ODMR spectrum, computed as the numerical derivative of contrast with respect to frequency ($\mathrm{d}C/\mathrm{d}f$), highlights regions of rapid contrast change, improving dip visibility in noisy data.
• Figure 4: Comparison of optically detected magnetic resonance (ODMR) spectra in the presence and absence of noise and imperfections in an ensemble of nitrogen-vacancy (NV) centers. The black curve represents the ideal ODMR spectrum, free from noise sources, and displays well-resolved resonance dips resulting from the magnetic field-induced splitting of the NV spin sublevels. The red curve illustrates the spectrum with realistic imperfections, including laser and microwave power fluctuations, temperature variations, and uncertainty in the NV gyromagnetic ratio. These effects distort the resonance dips, reduce contrast, and introduce asymmetries, making interpretation more challenging. The comparison highlights the importance of incorporating noise sources into simulations to accurately replicate experimental observations and understand the performance limits of NV-based sensing systems.
• Figure 5: (a) Seven-level model of the NV center at zero magnetic field. (b) Magnetic-field-perturbed seven-level system showing Zeeman-induced level mixing and modified transition pathways.