Narrow-bandwidth sensing of high-frequency fields with continuous dynamical decoupling

A special issue preface: diamond for quantum applications

This special issue discusses current progress in the utilization of defect centres in diamond as spin-photon interfaces for quantum applications. This issue is based on the discussions of the Theo Murphy meeting 'Diamond for quantum applications' which covered the recent progress of diamond growth and engineering for the creation and optimization of colour centres, toward the integration of diamond-based qubits in quantum systems. This article is part of the Theo Murphy meeting issue 'Diamond for quantum applications'.

Charge Stability and Charge-State-Based Spin Readout of Shallow Nitrogen-Vacancy Centers in Diamond

Spin-based applications of the negatively charged nitrogen-vacancy (NV) center in diamonds require an efficient spin readout. One approach is the spin-to-charge conversion (SCC), relying on mapping the spin states onto the neutral (NV0) and negative (NV-) charge states followed by a subsequent charge readout. With high charge-state stability, SCC enables extended measurement times, increasing precision and minimizing noise in the readout compared to the commonly used fluorescence detection. Nanoscale sensing applications, however, require shallow NV centers within a few nanometers distance from the surface where surface related effects might degrade the NV charge state. In this article, we investigate the charge state initialization and stability of single NV centers implanted ≈5 nm below the surface of a flat diamond plate. We demonstrate the SCC protocol on four shallow NV centers suitable for nanoscale sensing, obtaining a reduced readout noise of 5-6 times the spin-projection noise limit. We investigate the general applicability of the SCC for shallow NV centers and observe a correlation between the NV charge-state stability and readout noise. Coating the diamond with glycerol improves both the charge initialization and stability. Our results reveal the influence of the surface-related charge environment on the NV charge properties and motivate further investigations to functionalize the diamond surface with glycerol or other materials for charge-state stabilization and efficient spin-state readout of shallow NV centers suitable for nanoscale sensing.

Extending the coherence of spin defects in hBN enables advanced qubit control and quantum sensing

Negatively-charged boron vacancy centers ([Formula: see text]) in hexagonal Boron Nitride (hBN) are attracting increasing interest since they represent optically-addressable qubits in a van der Waals material. In particular, these spin defects have shown promise as sensors for temperature, pressure, and static magnetic fields. However, their short spin coherence time limits their scope for quantum technology. Here, we apply dynamical decoupling techniques to suppress magnetic noise and extend the spin coherence time by two orders of magnitude, approaching the fundamental T1 relaxation limit. Based on this improvement, we demonstrate advanced spin control and a set of quantum sensing protocols to detect radiofrequency signals with sub-Hz resolution. The corresponding sensitivity is benchmarked against that of state-of-the-art NV-diamond quantum sensors. This work lays the foundation for nanoscale sensing using spin defects in an exfoliable material and opens a promising path to quantum sensors and quantum networks integrated into ultra-thin structures.

Broadband microwave detection using electron spins in a hybrid diamond-magnet sensor chip

Quantum sensing has developed into a main branch of quantum science and technology. It aims at measuring physical quantities with high resolution, sensitivity, and dynamic range. Electron spins in diamond are powerful magnetic field sensors, but their sensitivity in the microwave regime is limited to a narrow band around their resonance frequency. Here, we realize broadband microwave detection using spins in diamond interfaced with a thin-film magnet. A pump field locally converts target microwave signals to the sensor-spin frequency via the non-linear spin-wave dynamics of the magnet. Two complementary conversion protocols enable sensing and high-fidelity spin control over a gigahertz bandwidth, allowing characterization of the spin-wave band at multiple gigahertz above the sensor-spin frequency. The pump-tunable, hybrid diamond-magnet sensor chip opens the way for spin-based gigahertz material characterizations at small magnetic bias fields.

Coherence protection of spin qubits in hexagonal boron nitride

Spin defects in foils of hexagonal boron nitride are an attractive platform for magnetic field imaging, since the probe can be placed in close proximity to the target. However, as a III-V material the electron spin coherence is limited by the nuclear spin environment, with spin echo coherence times of ∽100 ns at room temperature accessible magnetic fields. We use a strong continuous microwave drive with a modulation in order to stabilize a Rabi oscillation, extending the coherence time up to ∽ 4μs, which is close to the 10 μs electron spin lifetime in our sample. We then define a protected qubit basis, and show full control of the protected qubit. The coherence times of a superposition of the protected qubit can be as high as 0.8 μs. This work establishes that boron vacancies in hexagonal boron nitride can have electron spin coherence times that are competitive with typical nitrogen vacancy centres in small nanodiamonds under ambient conditions.

Picotesla magnetometry of microwave fields with diamond sensors

Developing robust microwave-field sensors is both fundamentally and practically important with a wide range of applications from astronomy to communication engineering. The nitrogen vacancy (NV) center in diamond is an attractive candidate for such purpose because of its magnetometric sensitivity, stability, and compatibility with ambient conditions. However, the existing NV center-based magnetometers have limited sensitivity in the microwave band. Here, we present a continuous heterodyne detection scheme that can enhance the sensor's response to weak microwaves, even in the absence of spin controls. Experimentally, we achieve a sensitivity of 8.9 pT Hz^-1/2 for microwaves of 2.9 GHz by simultaneously using an ensemble of n_NV ~ 2.8 × 10¹³ NV centers within a sensor volume of 4 × 10^-2 mm³. Besides, we also achieve 1/t scaling of frequency resolution up to measurement time t of 10,000 s. Our scheme removes control pulses and thus will greatly benefit practical applications of diamond-based microwave sensors.

Relaxation of a dense ensemble of spins in diamond under a continuous microwave driving field

Decoherence of Rabi oscillation in a two-level quantum system consists of two components, a simple exponential decay and a damped oscillation. In dense-ensemble spin systems like negatively charged nitrogen-vacancy (NV⁻) centers in diamond, fast quantum state decoherence often obscures clear observation of the Rabi nutation. On the other hand, the simple exponential decay (or baseline decay) of the oscillation in such spin systems can be readily detected but has not been thoroughly explored in the past. This study investigates in depth the baseline decay of dense spin ensembles in diamond under continuously driving microwave (MW). It is found that the baseline decay times of NV⁻ spins decrease with the increasing MW field strength and the MW detuning dependence of the decay times shows a Lorentzian-like spectrum. The experimental findings are in good agreement with simulations based on the Bloch formalism for a simple two-level system in the low MW power region after taking into account the effect of inhomogeneous broadening. This combined investigation provides new insight into fundamental spin relaxation processes under continuous driving electromagnetic fields and paves ways to better understanding of this underexplored phenomena using single NV⁻ centers, which have shown promising applications in quantum computing and quantum metrology.

Heterodyne sensing of microwaves with a quantum sensor

Diamond quantum sensors are sensitive to weak microwave magnetic fields resonant to the spin transitions. However, the spectral resolution in such protocols is ultimately limited by the sensor lifetime. Here, we demonstrate a heterodyne detection method for microwaves (MW) leading to a lifetime independent spectral resolution in the GHz range. We reference the MW signal to a local oscillator by generating the initial superposition state from a coherent source. Experimentally, we achieve a spectral resolution below 1 Hz for a 4 GHz signal far below the sensor lifetime limit of kilohertz. Furthermore, we show control over the interaction of the MW-field with the two-level system by applying dressing fields, pulsed Mollow absorption and Floquet dynamics under strong longitudinal radio frequency drive. While pulsed Mollow absorption leads to improved sensitivity, the Floquet dynamics allow robust control, independent from the system’s resonance frequency. Our work is important for future studies in sensing weak microwave signals in a wide frequency range with high spectral resolution.

High-resolution microwave detection with NV centers in diamond is currently applicable to signals with frequencies below 10 MHz, thus limiting their range of applications. Here, the authors demonstrate detection of GHz signals with sub-Hz spectral resolution, not limited by the quantum sensor lifetime.

Extension of the Coherence Time by Generating MW Dressed States in a Single NV Centre in Diamond

Nitrogen-vacancy (NV) centres in diamond hold promise in quantum sensing applications. A major interest in them is an enhancement of their sensitivity by the extension of the coherence time (T₂). In this report, we experimentally generated more than four dressed states in a single NV centre in diamond based on Autler-Townes splitting (ATS). We also observed the extension of the coherence time to T₂ ~ 1.5 ms which is more than two orders of magnitude longer than that of the undressed states. As an example of a quantum application using these results we propose a protocol of quantum sensing, which shows more than an order of magnitude enhancement in the sensitivity.

Initialization of Single Spin Dressed States using Shortcuts to Adiabaticity

We demonstrate the use of shortcuts to adiabaticity protocols for initialization, read-out, and coherent control of dressed states generated by closed-contour, coherent driving of a single spin. Such dressed states have recently been shown to exhibit efficient coherence protection, beyond what their two-level counterparts can offer. Our state transfer protocols yield a transfer fidelity of ∼99.4(2)% while accelerating the transfer speed by a factor of 2.6 compared to the adiabatic approach. We show bidirectionality of the accelerated state transfer, which we employ for direct dressed state population read-out after coherent manipulation in the dressed state manifold. Our results enable direct and efficient access to coherence-protected dressed states of individual spins and thereby offer attractive avenues for applications in quantum information processing or quantum sensing.

Clock transition by continuous dynamical decoupling of a three-level system

We present a novel continuous dynamical decoupling scheme for the construction of a robust qubit in a three-level system. By means of a clock transition adjustment, we first show how robustness to environmental noise is achieved, while eliminating drive-noise, to first-order. We demonstrate this scheme with the spin sub-levels of the NV-centre's electronic ground state. By applying drive fields with moderate Rabi frequencies, the drive noise is eliminated and an improvement of 2 orders of magnitude in the coherence time is obtained compared to the pure dephasing time. We then show how the clock transition adjustment can be tuned to eliminate also the second-order effect of the environmental noise with moderate drive fields. A further detailed theoretical investigation suggests an additional improvement of more than 1 order of magnitude in the coherence time which is supported by simulations. Hence, our scheme predicts that the coherence time may be prolonged towards the lifetime-limit using a relatively simple experimental setup.

Quantum sensing of weak radio-frequency signals by pulsed Mollow absorption spectroscopy

Quantum sensors—qubits sensitive to external fields—have become powerful detectors for various small acoustic and electromagnetic fields. A major key to their success have been dynamical decoupling protocols which enhance sensitivity to weak oscillating (AC) signals. Currently, those methods are limited to signal frequencies below a few MHz. Here we harness a quantum-optical effect, the Mollow triplet splitting of a strongly driven two-level system, to overcome this limitation. We microscopically understand this effect as a pulsed dynamical decoupling protocol and find that it enables sensitive detection of fields close to the driven transition. Employing a nitrogen-vacancy center, we detect GHz microwave fields with a signal strength (Rabi frequency) below the current detection limit, which is set by the center’s spectral linewidth \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1{\rm{/}}T_2^*$$\end{document}1∕T2*. Pushing detection sensitivity to the much lower 1/T₂ limit, this scheme could enable various applications, most prominently coherent coupling to single phonons and microwave photons.

Dynamical decoupling protocols can enhance the sensitivity of quantum sensors but this is limited to signal frequencies below a few MHz. Here, Joas et al. use the Mollow triplet splitting in a nitrogen-vacancy centre to overcome this limitation, enabling sensitive detection of signals in the GHz range.