Magnetometry with Broadband Microwave Fields in Nitrogen-Vacancy Centers in Diamond

TL;DR

This work introduces a broadband microwave magnetometry approach for NV centers that encodes the full NV resonance spectrum into the time-domain transmission of a short MW pulse. Magnetic-field estimation is performed via either a maximum-likelihood KL-divergence minimization or neural-network regression, achieving sensitivities below $1~ ext{nT}/ oot{2} ext{Hz}$ and offering a path toward $pT/ oot{2} ext{Hz}$ with further optimization. Crucially, the method operates without a bias magnetic field and supports high update rates ($ ext{1–10 kHz}$), enabling vector magnetometry with practical robustness against noise and without relying on optical detection. Johnson–Nyquist noise is treated as the main practical limit, with results indicating strong potential for field sensing in realistic experimental settings.

Abstract

Nitrogen vacancy (NV) centers in diamond are optically addressable and versatile light-matter interfaces with practical application in magnetic field sensing, offering the ability to operate at room temperature and reach sensitivities below pT/$\sqrt{\mathrm{Hz}}.$ We propose an approach to simultaneously probe all of the magnetically sensitive states using a broadband microwave field and demonstrate that it can be used to measure the external DC magnetic field strength with sensitivities below 1~nT/$\sqrt{\mathrm{Hz}}.$ We develop tools for analyzing the temporal signatures in the transmitted broadband microwaves to estimate the magnetic field, comparing maximum likelihood estimation based on minimizing the Kullback-Leibler divergence to various neural network models, and both methods independently reach practical sensitivities. These results are achieved without optimizing parameters such as the bandwidth, power, and shape of the probing microwave field such that, with further improvements, sensitivities down to $\mathrm{pT/\sqrt{Hz}}$ can be envisioned. Our results motivate novel implementations of NV-based magnetic sensors with the potential for vectorial magnetic field detection at 1-10 kHz update rates and improved sensitivities without requiring a bias magnetic field.

Figures (7)

• Figure 1: In this scheme, the MW field generator sends a broadband pulse to the NV ensemble. This can be achieved with a stripline waveguide, allowing evanescent coupling of the MW field to the NV centers or NV ensemble embedded in a MW cavity. As the MW input propagates through the sample, the NV centers partially absorb the signal and consequently modify the signal's intensity. This alteration is depicted in the output signal (red curve). The external magnetic field influences the frequencies at which NV centers absorb the microwave field. This leads to changes in the partially transmitted MW signal, thereby providing information about the underlying magnetic field. Shown below are the atomic and quantum structures of the NV center.
• Figure 2: Top: Expected MW absorption in an ODMR measurement, due to spin transitions from $|m_{s} = 0\rangle$ to $|m_{s} = \pm 1\rangle$ in ensemble NV centers, are given by the ground-state-manifold Hamiltonian and combined with Lorentzian lines with 1 MHz linewidth. Magnetic field is oriented along angular coordinates $(\pi/6,\pi/3)$ relative to the diamond. Bottom: Fourier transform of a Gaussian pulse (85 MHz FWHM) transmitted through an ensemble of NV centers in different magnetic fields. In the frequency domain and within linear response theory, the absorption profile from the top graph is imprinted on the MW spectrum.
• Figure 3: The time-domain MW transmission through an NV ensemble, $P(t)$, calculated using the same parameters as Fig. \ref{['fig:ODMR_broadbandaddresing']} for applied magnetic fields ranging from 0 to 10 G. Each magnetic field strength corresponds to a distinct and unique signal behavior, illustrating the variation in the response function as the external magnetic field changes.
• Figure 4: The KL divergence ($D_{KL}$) is computed across a range of magnetic field values applied to the probability distribution $Q(t| B_{model})$ while keeping the probability distribution $P(t)$ constant. The resulting curve reaches its minimum at the magnetic field strength where $P(t)$ and $Q(t| B_{model})$ exhibit the highest similarity. It should be noted that the granularity of the magnetic field, $B_{model}$, in the analysis is set at 10$^{-5}$ G; all other parameters are the same as in Fig. \ref{['fig:ODMR_broadbandaddresing']}.
• Figure 5: Absolute magnetic field estimation error, $\delta B = |\tilde{B} - B_{\text{true}}|$ , as a function of the true magnetic field $B_{\text{true}}$ for various signal-to-noise ratios (SNR) in dB. The vertical axis is displayed on a logarithmic scale to highlight variations across several orders of magnitude. Scatter markers represent individual data points for each SNR, while the dashed horizontal lines indicate the mean $\delta$B for the corresponding SNR. The results show a strong decrease in $\delta$B with increasing SNR.