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Quantum sensors that use solid state spin defects have emerged as effective probes of weak alternating magnetic signals. By recording the phase of a signal relative to an external clock, these devices can resolve signal frequencies to a precision orders of magnitude longer than the spin state lifetime. However, these quantum heterodyne protocols suffer from sub-optimal sensitivity, as they are currently limited to pulsed spin control techniques, which are susceptible to cumulative pulse-area errors, or single continuous drives which offer no protection of the spin coherence. Here, we present a control scheme based on a continuous microwave drive that extends spin coherence towards the effective $T_2 \approx \frac{1}{2}T_1$ limit and can resolve the frequency, amplitude and phase of GHz magnetic fields. The scheme is demonstrated using an ensemble of boron vacancies in hexagonal boron nitride, and achieves an amplitude sensitivity of $\eta \approx 3-5 \:\mathrm{\mu T \sqrt{Hz}}$ and phase sensitivity of $\eta_{\phi} \approx 0.076 \:\mathrm{rads \sqrt{Hz}}$. By repeatedly referencing the phase of a resonant signal against the coherent continuous microwave drive in a quantum heterodyne demonstration, we measure a GHz signal with a resolution $<$1 Hz over a 10 s measurement. Achieving this level of performance in a two-dimensional material platform could have broad applications, from probing nanoscale condensed matter systems to integration into heterostructures for quantum networking.

Sensors based on spin qubits in 2D crystals offer the prospect of nanoscale sensing volumes, where the close proximity of the sensor and source could provide access to otherwise inaccessible signals. For AC magnetometry, the sensitivity and frequency range is typically limited by the noise spectrum, which determines the qubit coherence time. This poses a problem for III-V materials, as the non-zero spin of the host nuclei introduces a considerable source of magnetic noise. Here, we overcome this with a sensing protocol based on phase modulated continuous concatenated dynamic decoupling, which extends the coherence time towards the $T_1$ limit at room temperature and enables tuneable narrowband AC magnetometry. We demonstrate the protocol with an ensemble of negatively charged boron vacancies in hexagonal boron nitride, detecting in-plane AC fields within $\pm 150~\mathrm{MHz}$ of the electron spin resonance, and out-of-plane fields in the range of $\sim10-150~\mathrm{MHz}$. We measure an AC magnetic field sensitivity of $\sim1~\mathrm{\mu T/\sqrt{Hz}}$ at $\sim2.5~\mathrm{GHz}$, for a sensor volume of $\sim0.1~\mathrm{\mu m^3}$, and demonstrate that the sensor can reconstruct the AC magnetic field from a wire loop antenna. This work establishes the viability of spin defects in 2D materials for high frequency magnetometry, demonstrating sensitivities that are comparable to nitrogen vacancy centres in diamond for microscopic sensing volumes, and with wide-ranging applications across science and technology.

Control over the shape and polarization of the beam emitted by a laser source is important in applications such as optical communications, optical manipulation and high-resolution optical imaging. In this paper, we present the inverse design of monolithic whispering-gallery nanolasers which emit along their axial direction with a tailored laser beam shape and polarization. We design and experimentally verify three types of sub-micron cavities, each one emitting into a different laser radiation mode: an azimuthally polarized doughnut beam, a radially polarized doughnut beam and a linearly polarized gaussian-like beam. The measured output laser beams yield a field overlap with respect to the target mode of 92%, 96% and 85% for the azimuthal, radial and linearly polarized cases, respectively, thereby demonstrating the generality of the method in the design of ultra-compact lasers with tailored beams.

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 time of $\sim100~\mathrm{ns}$ 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 $\sim4~\mathrm{\mu s}$, which is close to the 10-$\mathrm{\mu s}$ 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 $0.8~\mathrm{\mu s}$. This work establishes that boron vacancies in hexagonal boron nitride can have electron spin coherence times that are competitive with typical NV-centers in small nanodiamonds under ambient conditions.

We report optically detected magnetic resonance (ODMR) measurements of an ensemble of spin-1 negatively charged boron vacancies in hexagonal boron nitride. The photoluminescence decay rates are spin-dependent, with inter-system crossing rates of $1.02~\mathrm{ns^{-1}}$ and $2.03~\mathrm{ns^{-1}}$ for the $m_s=0$ and $m_s=\pm 1$ states, respectively. Time-gating the photoluminescence enhances the ODMR contrast by discriminating between different decay rates. This is particularly effective for detecting the spin of the optically excited state, where a zero-field splitting of $\vert D_{ES}\vert=2.09~\mathrm{GHz}$ is measured. The magnetic field dependence of the time-gated photoluminescence exhibits dips corresponding to the Ground (GSLAC) and excited-state (ESLAC) anti-crossings. Additional dips corresponding to anti-crossings with nearby spin-1/2 parasitic impurities are also observed. The ESLAC dip is sensitive to the angle of the external magnetic field. Comparison to a model suggests that the anti-crossings are mediated by the interaction with nuclear spins, and allow an estimate of the ratio of the spin-dependent relaxation rates from the singlet back into the triplet ground state of $\kappa_0/\kappa_1=0.34$. This work provides important spectroscopic signatures of the boron vacancy, and information on the spin pumping and read-out dynamics.

Stimulated emission depletion, or STED microscopy is a well-established super-resolution technique, but is ultimately limited by the chosen flourophore. Here we demonstrate STED microscopy with color centers in nanoscale flakes of hexagonal boron nitride using time-gated continuous wave STED. For color centers with zero phonon line emission around 580 nm we measure a STED cross-section of (5.5 $\pm$ 3.2) x $10^{-17} \mbox{cm}^{2}$, achieve a resolution of $\sim$ 50 nm and resolve two color centers separated by 250 nm, which is less than the diffraction limit. The achieved resolution is limited by the numerical aperture of the objective lens (0.8) and the available laser power, and we predict that a resolution of sub-10 nm can be achieved with an oil immersion objective lens, similar to state-of-the-art resolution obtained with nitrogen vacancy centers in diamond., Comment: 20 pages, 6 figures, SI included in the main text

We demonstrate the use of Stimulated Emission Depletion (STED) spectroscopy to map the electron-optical-phonon sideband of the ground state of the radiative transition of color centers in hexagonal boron nitride emitting at 2.0-2.2 eV, with in-plane linear polarization. The measurements are compared to Photoluminescence of Excitation (PLE) spectra, that maps the electron-optical-phonon sideband of the excited state. The main qualitative difference is a red-shift in the longitudinal optical phonon peak associated with $E_{1u}$ symmetry at the zone center. We argue that this is consistent with recent findings for a carbon-based line defect with admixture of energetically similar excited states.

We report on multicolor excitation experiments with color centers in hexagonal boron nitride at cryogenic temperatures. We demonstrate controllable optical switching between bright and dark states of color centers emitting around 2eV. Resonant, or quasi-resonant excitation also pumps the color center, via a two-photon process, into a dark state, where it becomes trapped. Photoluminescence excitation spectroscopy reveals a defect dependent energy threshold for repumping the color center into the bright state of between 2.2 and 2.6eV. Photoionization and photocharging of the defect is the most plausible explanation for this behaviour, with the negative and neutral charge states of the boron vacancy potential candidates for the bright and dark states, respectively. Furthermore, a second zero phonon line, detuned by +0.4eV, is observed in absorption with orthogonal polarization to the emission, evidencing an additional energy level in the color center., Comment: 19 pages, 4 figures

Metamaterials and plasmonics are powerful tools for unconventional manipulation and harnessing of light. Metamaterials can be engineered to possess intriguing properties lacking in natural materials, such as negative refractive index. Plasmonics offers capabilities to confine light in subwavelength dimensions and to enhance light-matter interactions. Recently,graphene-based plasmonics has revealed emerging technological potential as it features large tunability, higher field-confinement and lower loss compared to metal-based plasmonics. Here,we introduce hybrid structures comprising graphene plasmonic resonators efficiently coupled to conventional split-ring resonators, thus demonstrating a type of highly tunable metamaterial, where the interaction between the two resonances reaches the strong-coupling regime. Such hybrid metamaterials are employed as high-speed THz modulators, exhibiting over 60% transmission modulation and operating speed in excess of 40 MHz. This device concept also provides a platform for exploring cavity-enhanced light-matter interactions and optical processes in graphene plasmonic structures for applications including sensing, photo-detection and nonlinear frequency generation.

We study plasmonic resonances in electrostatically gated graphene nanoribbons on silicon dioxide substrates. Absorption spectra are measured in the mid-far infrared and reveal multiple peaks, with width-dependent resonant frequencies. We calculate the dielectric function within the random phase approximation and show that the observed spectra can be explained by surface-plasmon-phonon-polariton modes, which arise from coupling of the graphene plasmon to three surface optical phonon modes in the silicon dioxide.

Non-classical light sources offer a myriad of possibilities in fundamental science and applications including quantum cryptography and quantum lithography. Single photons can encode quantum information and multi-qubit gates in silica waveguide circuits have been used to demonstrate linear optical quantum computing. Scale-up requires miniaturisation of the waveguide circuit and multiple photon sources. Silicon photonics, driven by the incentive of optical interconnects, is a highly promising platform for the passive components, but integrated light sources are limited by silicon's indirect band-gap. III-V semiconductor quantum-dots, on the other hand, are proven quantum emitters. Here we demonstrate single-photon emission from quantum-dots coupled to photonic crystal nanocavities fabricated from III-V material grown directly on silicon substrates. The high quality of the III-V material and photonic structures is emphasized by observation of the strong-coupling regime. This work opens-up the advantages of silicon photonics to the integration and scale-up of solid-state quantum optical systems.

A scalable optical quantum information processor is likely to be a waveguide circuit with integrated sources, detectors, and either deterministic quantum-logic or quantum memory elements. With microsecond coherence times, ultrafast coherent control, and lifetime-limited transitions, semiconductor quantum-dot spins are a natural choice for the static qubits. However their integration with flying photonic qubits requires an on-chip spin-photon interface, which presents a fundamental problem: the spin-state is measured and controlled via circularly-polarised photons, but waveguides support only linear polarisation. We demonstrate here a solution based on two orthogonal photonic nanowires, in which the spin-state is mapped to a path-encoded photon, thus providing a blue-print for a scalable spin-photon network. Furthermore, for some devices we observe that the circular polarisation state is directly mapped to orthogonal nanowires. This result, which is physically surprising for a non-chiral structure, is shown to be related to the nano-positioning of the quantum-dot with respect to the photonic circuit.