Triple-Tone Microwave Control for Sensitivity Optimization in Compact Ensemble Nitrogen-Vacancy Magnetometers

TL;DR

This paper addresses the sensitivity loss in NV ensemble magnetometry caused by the $^{14}$N hyperfine splitting, proposing triple-tone MW control to coherently address all hyperfine lines. It develops and validates a master-equation model of NV dynamics and uses it to compare single-tone and triple-tone driving for pulsed ODMR and Ramsey protocols across MW power and dephasing regimes. The main results show up to a threefold improvement in pulsed ODMR sensitivity in the low-dephasing regime, while Ramsey sensitivity gains occur only when MW power is limited and high-drive conditions reduce the advantage. The work provides practical operating guidelines for implementing multi-tone control in compact, power-limited NV sensors, and suggests future extensions (e.g., NSP, $^{15}$N) to further mitigate hyperfine-related contrast losses.

Abstract

Ensembles of nitrogen-vacancy (NV) centers in diamond are a well-established platform for quantum magnetometry under ambient conditions. One challenge arises from the hyperfine structure of the NV, which, for the common $^{14}$N isotope, results in a threefold reduction of contrast and thus sensitivity. By addressing each of the NV hyperfine transitions individually, triple-tone microwave (MW) control can mitigate this sensitivity loss. Here, we experimentally and theoretically investigate the regimes in which triple-tone excitation offers an advantage over standard single-tone MW control for two DC magnetometry protocols: pulsed optically detected magnetic resonance (ODMR) and Ramsey interferometry. We validate a master equation model of the NV dynamics against ensemble NV measurements, and use the model to explore triple-tone vs single-tone sensitivity for different MW powers and NV dephasing rates. For pulsed ODMR, triple-tone driving improves sensitivity by up to a factor of three in the low-dephasing regime, with diminishing gains when dephasing rates approach the hyperfine splitting. In contrast, for Ramsey interferometry, triple-tone excitation only improves sensitivity if MW power is limited. Our results delineate the operating regimes where triple-tone control provides a practical strategy for enhancing NV ensemble magnetometry in portable and power-limited sensors.

Figures (11)

• Figure 1: (a) Schematic of the experimental setup for implementing MW control: An AWG produces the signal, which is mixed with the local oscillator in the IQ mixer. The output is amplified and delivered to the NV ensemble inside the Quantum Demonstrator, which houses the magnetometer that integrates optical excitation and microwave delivery. Fluorescence is collected and digitized using a high-speed digitizer, enabling measurement of spin-state-dependent signals. (b) Ground-state energy level diagram of the negatively charged nitrogen-vacancy (NV) center in diamond, showing the spin-1 triplet sublevels and hyperfine splitting from the host $^{14}$N nuclear spin. The $m_s = 0 \leftrightarrow \pm1$ transitions each split into three lines spaced by 2.16 MHz. (c) Illustration of single-tone (bottom) and triple-tone (top) MW excitation, where the latter addresses all hyperfine transitions simultaneously, enhancing fluorescence contrast; the ODMR curves are real data where the measured signal is plotted as a function of the MW frequency, and the tones sent are a cartoon representation.
• Figure 2: Pulsed ODMR slope maps for single-tone (a-b) and triple-tone (c-d) driving. (a, c) Simulated slopes as functions of Rabi frequency and pulse duration. (b, d) Corresponding experimental data acquired on a 21×21 grid of pulse durations and MW amplitudes.
• Figure 3: Simulation of pulsed ODMR sensitivity versus dephasing rate $\gamma$. (a) Optimized slope and slope$/\sqrt{T}$ for single-tone and triple-tone. (b) Enhancement ratios (triple/single tone curves in (a)), showing a threefold improvement at low $\gamma$ with diminishing gains at higher $\gamma$. (c)Slope ratio across for fixed Rabi frequency at three dephasing rates ($\gamma = 0.1, 0.5, 1~\mu\text{s}^{-1}$)
• Figure 4: Single-tone Ramsey simulations (top) and corresponding experimental measurements (bottom) as a function of detuning for two Rabi frequencies. The color scales are proportional to the population in $m_s = 0$ after the pulse sequence. (a)-(b) At 0.34 MHz, well-defined Ramsey fringes are observed, with close agreement between theory and experiment. (c)-(d) At 3.14 MHz, hyperfine beating distorts the fringes, accompanied by revival features from constructive interference of the $^{14}$N hyperfine components.
• Figure 5: Triple-tone Ramsey simulations (top) and experiments (bottom) over a detuning range of –1.1 to +3.9 MHz. In each case, the signal is proportional to the population in $m_s = 0$. (a,b) Low Rabi frequency (0.37 MHz) (c,d) Intermediate Rabi frequency (0.75 MHz) (e,f) Higher Rabi frequency (1.04 MHz).