Robust GHz-range AC Magnetometry with an ensemble of NV Centers in Diamond using Concatenated Continuous Dynamical Decoupling

TL;DR

The paper addresses the challenge of achieving high-sensitivity GHz-range AC magnetometry with dense NV ensembles, where inhomogeneities in detuning and drive amplitudes degrade performance. It demonstrates concatenated continuous dynamical decoupling (CCDD) as a robust approach to dress ensemble spins and detect GHz signals, outperforming conventional direct Rabi sensing in the presence of inhomogeneities. The authors experimentally realize GHz-range sensing with a large NV ensemble, observe extended coherence and the ability to detect weak signals (down to tens of kHz), and quantify a practical sensitivity of around 956 pT/√Hz under their conditions. This work advances practical, broadband GHz magnetometry in solid-state spin ensembles and suggests broad applicability to microwave sensing, device characterization, and other defect-qubit platforms where drive inhomogeneity limits conventional Rabi-based methods.

Abstract

Sub-picotesla level magnetometry has been demonstrated using negatively-charged nitrogen-vacancy (NV) centers in diamond by increasing the number of spins simultaneously used for sensing in an NV ensemble. However, such scale-up often introduces spatial inhomogeneities in detuning and control field amplitudes, which degrade sensitivity. Although several techniques have been utilized to overcome these challenges, including pulsed dynamical decoupling or shaped pulses, these are not generally compatible with the current state-of-the-art techniques for GHz-range AC magnetometry with NV ensembles, which are typically based on Rabi oscillations. In this work we experimentally demonstrate GHz-range AC magnetometry using a large ensemble of NV centers under spatially inhomogeneous drive fields by employing concatenated continuous dynamical decoupling, which is designed for robustness against such imperfections. We compare its performance with the conventional direct Rabi method and show that the robust dressed states in our method extend significantly the measuring range to weaker signals in GHz-range AC magnetometry.

Figures (4)

• Figure 1: (a) Energy diagram of the doubly dressed states with a target signal. A two level system (TLS) with energy splitting of $\omega_0$ is driven resonantly by a first drive at Rabi frequency $\Omega_1$ to be robust against detuning $\delta$. A second drive is further applied to mitigate the noise of the first drive $\Omega_1\epsilon_1$. The target signal can be detected when it is on resonance. (b) GHz-range AC magnetometry scheme using transverse CCDD. $\pi_y/2$ pulses are applied to prepare $x$ states, phase-locked to the first drive along $y$. (c) Schematic of the experimental setup around our ensemble system. An ensemble of NV centers inside a pink diamond is initialized by a green laser. Its spin state is controlled with a planar microwave (MW) antenna and readout through red-shifted photoluminescence (PL) collected by a compound parablocic concentrator (CPC).
• Figure 2: (a) Rabi oscillations under the single drive. A microwave field is applied resonantly with the central line $\omega_0 = (2\pi)\,$2.7081 GHz of the hyperfine sublevels from the $^{14}$N. The rapid decay of the Rabi oscillations reflects the inhomogeneity in the drive amplitude across the ensemble. The Rabi frequency of the first drive $\Omega_1$ is kept $(2\pi)\,$11.3 MHz throughout this article. (b) Rabi oscillations at angular frequency $\Omega_2\approx \Omega_1 / 10$ under the transverse CCDD sequence. They are sampled at time steps of $\tau_{\Omega_1} = 2\pi/ \Omega_1$ when the first dressed basis corresponds to the bare basis in the absence of noise. (c) Dynamics of the system under CCDD with a test MW signal. $\Omega_1=(2\pi)\,$11.3 MHz and $\Omega_2=(2\pi)\,$1.13 MHz are used for the CCDD, and the frequency of the target signal is set to $\omega_{\rm t} = \omega_0 - \Omega_2=(2\pi)\,$2.7070 GHz. The time increment is set to $\tau_{\Omega_2} = 2\pi/\Omega_2$. The background curve is fitted with a single-exponential function, which also appears in CCDD without the target signal SM. (d) Initial oscillations from the same measurement after background subtraction. The data is well fitted with an exponentially decaying sinusoidal function, yielding $\Omega_{\rm t}^{\prime}$ = $(2\pi)\,63.2$ kHz.
• Figure 3: Dynamics of the system under direct Rabi (top) and CCDD (botttom) with varying amplitudes of the target MW signal, shown in comparison to the system linewidth $\Delta\nu$ = 415 kHz. When the amplitude of the target MW signal is strong, such that its Rabi frequency exceeds the linewidth, the signal drives the system effectively, allowing for robust measurement (top right). See SM for details on the amplitude dependence. In contrast, when the signal amplitude is smaller than the linewidth, the Rabi oscillations suffer from the detuning, leading to rapid decrease in the measurement contrast (top left). This behavior determines a lower bound of the measurable amplitude of target MW signal. The top axis converts the Rabi frequency into the corresponding magnetic field amplitude (in tesla). In the CCDD case (bottom), the dressed state created by the CCDD enables robust detection of weaker signals (bottom right). As a result, CCDD extends the minimum detectable amplitude (bottom left). The bottom axis converts the oscillation frequency into the corresponding magnetic field amplitude (in tesla).
• Figure 4: Uncertainty evaluation. The amplitude of the target micrwave (MW) $B_{\rm t}$ are repeatedly measured under CCDD with the test MW signal. The amplitude is the same as in Fig. \ref{['fig_characterization']} and the interaction time is kept constant at $\tau$ = 67 $\mu$s. The Allan deviation (ADEV) and the standard error of the mean (SEM) for the measured magnetic field amplitude $B_{\rm t}$ are shown in red squares and blue circles, respectively. The sensitivity of this amplitude measurement is calculated to be 956 pT/$\sqrt{\rm Hz}$, based on the slope of the SEM (See SM for details).