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The application of average Hamiltonian theory (AHT) to magnetic resonance and quantum sensing informs pulse sequence design, for example, by providing efficient approximations of spin dynamics while retaining important physical characteristics of system evolution. However, AHT predictions break down in many common experimental conditions, including for sensing with solid-state spins. Here we establish that certain symmetries, such as rapid echos, allow AHT to remain accurate well beyond the perturbative limit. An exact method is presented to determine the sensor response to a target signal, which stays valid beyond the regime of AHT convergence. This beyond AHT approach enables new opportunities in quantum control techniques that leverage complementary analytical and numerical methods, with applications in a variety of quantum sensing platforms, Hamiltonian engineering, and probes of quantum many-body phenomena., Comment: 6 pages, 4 figures

The reconstruction of electrical current densities from magnetic field measurements is an important technique with applications in materials science, circuit design, quality control, plasma physics, and biology. Analytic reconstruction methods exist for planar currents, but break down in the presence of high spatial frequency noise or large standoff distance, restricting the types of systems that can be studied. Here, we demonstrate the use of a deep convolutional neural network for current density reconstruction from two-dimensional (2D) images of vector magnetic fields acquired by a quantum diamond microscope (QDM) utilizing a surface layer of Nitrogen Vacancy (NV) centers in diamond. Trained network performance significantly exceeds analytic reconstruction for data with high noise or large standoff distances. This machine learning technique can perform quality inversions on lower SNR data, reducing the data collection time by a factor of about 400 and permitting reconstructions of weaker and three-dimensional current sources., Comment: 17 pages, 10 figures. Includes Supplemental Information

The quantum diamond microscope (QDM) is a recently developed technology for near-field imaging of magnetic fields with micron-scale spatial resolution. In the present work, we integrate a QDM with a narrowband measurement protocol and a lock-in camera; and demonstrate imaging of radiofrequency (RF) magnetic field patterns produced by microcoils, with spectral resolution $\approx1$\,Hz. This RF-QDM provides multi-frequency imaging with a central detection frequency that is easily tunable over the MHz-scale, allowing spatial discrimination of both crowded spectral peaks and spectrally well-separated signals. The present instrument has spatial resolution $\approx2\,\mathrm{\mu m}$, field-of-view $\approx300\times300\,\mathrm{\mu m^2}$, and per-pixel sensitivity to narrowband fields $\sim{1}\,$nT$\cdot$Hz$^{-1/2}$. Spatial noise can be reduced to the picotesla scale by signal averaging and/or spatial binning. The RF-QDM enables simultaneous imaging of the amplitude, frequency, and phase of narrowband magnetic field patterns at the micron-scale, with potential applications in real-space NMR imaging, AC susceptibility mapping, impedance tomography, analysis of electronic circuits, and spatial eddy-current-based inspection.

Galactic double white dwarf (DWD) binaries are among the guaranteed sources for the Laser Interferometer Space Antenna (LISA), an upcoming space-based gravitational wave (GW) detector. Most DWDs in the LISA band are far from merging and emit quasimonochromatic GWs. As these sources are distributed throughout the Milky Way, they experience different accelerations in the Galactic gravitational potential, and therefore each DWD exhibits an apparent GW frequency chirp due to differential acceleration between the source and LISA. We examine how Galactic acceleration influences parameter estimation for these sources; and investigate how LISA observations could provide insight into the distribution of matter in the Galaxy., Comment: 20 pages, 7 figures

The second "Mineral Detection of Neutrinos and Dark Matter" (MDvDM'24) meeting was held January 8-11, 2024 in Arlington, VA, USA, hosted by Virginia Tech's Center for Neutrino Physics. This document collects contributions from this workshop, providing an overview of activities in the field. MDvDM'24 was the second topical workshop dedicated to the emerging field of mineral detection of neutrinos and dark matter, following a meeting hosted by IFPU in Trieste, Italy in October 2022. Mineral detectors have been proposed for a wide variety of applications, including searching for dark matter, measuring various fluxes of astrophysical neutrinos over gigayear timescales, monitoring nuclear reactors, and nuclear disarmament protocols; both as paleo-detectors using natural minerals that could have recorded the traces of nuclear recoils for timescales as long as a billion years and as detectors recording nuclear recoil events on laboratory timescales using natural or artificial minerals. Contributions to this proceedings discuss the vast physics potential, the progress in experimental studies, and the numerous challenges lying ahead on the path towards mineral detection. These include a better understanding of the formation and annealing of recoil defects in crystals; identifying the best classes of minerals and, for paleo-detectors, understanding their geology; modeling and control of the relevant backgrounds; developing, combining, and scaling up imaging and data analysis techniques; and many others. During the last years, MDvDM has grown rapidly and gained attention. Small-scale experimental efforts focused on establishing various microscopic readout techniques are underway at institutions in North America, Europe and Asia. We are looking ahead to an exciting future full of challenges to overcome, surprises to be encountered, and discoveries lying ahead of us., Comment: Summary and proceedings of the MDvDM'24 conference, Jan 8-11 2024

Nitrogen-vacancy (NV) centers in diamond are a leading modality for magnetic sensing and imaging under ambient conditions. However, these sensors suffer from degraded performance due to paramagnetic impurities and regions of stress in the diamond crystal lattice. This work demonstrates a quantum diamond microscope (QDM) for simultaneous mapping and spatial correlation of key properties of a millimeter-scale NV-diamond sensor chip, including: NV ensemble photoluminescence (PL) amplitude, spin-lattice relaxation time (T$_1$), and homogeneous and inhomogeneous spin coherence lifetimes (T$_2$ and T$_2^*$), as well as lattice stress/strain, birefringence magnitude, and birefringence angle of the diamond crystal., Comment: 8 pages main text, 8 pages supplemental text, 5 figures main text, 4 figures supplemental text

The nitrogen vacancy (NV) center in diamond is an increasingly popular quantum sensor for microscopy of electrical current, magnetization, and spins. However, efficient NV-sample integration with a robust, high-quality interface remains an outstanding challenge to realize scalable, high-throughput microscopy. In this work, we characterize a diamond micro-chip (DMC) containing a (111)-oriented NV ensemble; and demonstrate its utility for high-resolution quantum microscopy. We perform strain imaging of the DMC and find minimal detrimental strain variation across a field-of-view of tens of micrometer. We find good ensemble NV spin coherence and optical properties in the DMC, suitable for sensitive magnetometry. We then use the DMC to demonstrate wide-field microscopy of electrical current, and show that diffraction-limited quantum microscopy can be achieved. We also demonstrate the deterministic transfer of DMCs with multiple materials of interest for next-generation electronics and spintronics. Lastly, we develop a polymer-based technique for DMC placement. This work establishes the DMC's potential to expand the application of NV quantum microscopy in materials, device, geological, biomedical, and chemical sciences., Comment: Includes supplementary materials section

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

Nitrogen vacancy (NV) centers in diamond enable nuclear magnetic resonance (NMR) spectroscopy of samples at the nano- and micron scales. However, at typical tesla-scale NMR magnetic field strengths, NV-NMR protocols become difficult to implement due to the challenge of driving fast NV pulse sequences sensitive to nuclear Larmor frequencies above a few megahertz. We perform simulations and theoretical analysis of the experimental viability of NV-NMR at tesla-scale magnetic fields using a new measurement protocol called DRACAERIS (Double Rewound ACquisition Amplitude Encoded Radio Induced Signal). DRACAERIS detects the NMR sample's longitudinal magnetization at a much lower driven Rabi frequency, more suitable technically for NV detection. We discuss how pulse errors, finite pulse lengths, and nuclear spin-spin couplings affect the resulting NMR spectra. We find that DRACAERIS is less susceptible to pulse imperfections and off-resonance effects than previous protocols for longitudinal magnetization detection. We also identify reasonable parameters for experimental implementation.

Wide-field imaging of magnetic signals using ensembles of nitrogen-vacancy (NV) centers in diamond has garnered increasing interest due to its combination of micron-scale resolution, millimeter-scale field of view, and compatibility with diverse samples from across the physical and life sciences. Recently, wide-field NV magnetic imaging based on the Ramsey protocol has achieved uniform and enhanced sensitivity compared to conventional measurements. Here, we integrate the Ramsey-based protocol with spin-bath driving to extend the NV spin dephasing time and improve magnetic sensitivity. We also employ a high-speed camera to enable dynamic wide-field magnetic imaging. We benchmark the utility of this quantum diamond microscope (QDM) by imaging magnetic fields produced from a fabricated wire phantom. Over a $270\times270 \hspace{0.08333em} \mu\mathrm{m}$$^2$ field of view, a median per-pixel magnetic sensitivity of $4.1(1)\hspace{0.08333em}\mathrm{nT}$$/\sqrt{\mathrm{Hz}}$ is realized with a spatial resolution $\lesssim\hspace{0.08333em}10\hspace{0.08333em}\mu\mathrm{m}$ and sub-millisecond temporal resolution. Importantly, the spatial magnetic noise floor can be reduced to the picotesla scale by time-averaging and signal modulation, which enables imaging of a magnetic-field pattern with a peak-to-peak amplitude difference of about $300\hspace{0.08333em}\mathrm{pT}$. Finally, we discuss potential new applications of this dynamic QDM in studying biomineralization and electrically-active cells., Comment: 18 Pages, 13 figures

We propose a novel experimental method for probing light dark matter candidates. We show that an electro-optical material's refractive index is modified in the presence of a coherently oscillating dark matter background. A high-precision resonant Michelson interferometer can be used to read out this signal. The proposed detection scheme allows for the exploration of an uncharted parameter space of dark matter candidates over a wide range of masses -- including masses exceeding a few tens of microelectronvolts, which is a challenging parameter space for microwave cavity haloscopes., Comment: 6+4 pages, 2 figures

Minerals are solid state nuclear track detectors - nuclear recoils in a mineral leave latent damage to the crystal structure. Depending on the mineral and its temperature, the damage features are retained in the material from minutes (in low-melting point materials such as salts at a few hundred degrees C) to timescales much larger than the 4.5 Gyr-age of the Solar System (in refractory materials at room temperature). The damage features from the $O(50)$ MeV fission fragments left by spontaneous fission of $^{238}$U and other heavy unstable isotopes have long been used for fission track dating of geological samples. Laboratory studies have demonstrated the readout of defects caused by nuclear recoils with energies as small as $O(1)$ keV. This whitepaper discusses a wide range of possible applications of minerals as detectors for $E_R \gtrsim O(1)$ keV nuclear recoils: Using natural minerals, one could use the damage features accumulated over $O(10)$ Myr$-O(1)$ Gyr to measure astrophysical neutrino fluxes (from the Sun, supernovae, or cosmic rays interacting with the atmosphere) as well as search for Dark Matter. Using signals accumulated over months to few-years timescales in laboratory-manufactured minerals, one could measure reactor neutrinos or use them as Dark Matter detectors, potentially with directional sensitivity. Research groups in Europe, Asia, and America have started developing microscopy techniques to read out the $O(1) - O(100)$ nm damage features in crystals left by $O(0.1) - O(100)$ keV nuclear recoils. We report on the status and plans of these programs. The research program towards the realization of such detectors is highly interdisciplinary, combining geoscience, material science, applied and fundamental physics with techniques from quantum information and Artificial Intelligence., Comment: 115 pages, many pictures of tracks. Please see the source file for higher resolution versions of some plots. v2: matches the published version

Chern numbers are gaining traction as they characterize topological phases in various physical systems. However, the resilience of the system topology to external perturbations makes it challenging to experimentally investigate transitions between different phases. In this study, we demonstrate the transitions of Chern number from 0 to 3, synthesized in an electronic-nuclear spin system associated with the nitrogen-vacancy (NV) centre in diamond. The Chern number is characterized by the number of degeneracies enclosed in a control Hamiltonian parameter sphere. The topological transitions between different phases are depicted by varying the radius and offset of the sphere. We show that the measured topological phase diagram is not only consistent with the numerical calculations but can also be mapped onto an interacting three-qubit system. The NV system may also allow access to even higher Chern numbers, which can be applied to exploring exotic topology or topological quantum information.

Nitrogen-vacancy (NV) spin ensembles in diamond provide an advanced magnetic sensing platform, with applications in both the physical and life sciences. The development of isotopically engineered $^{15}$NV diamond offers advantages over naturally occurring $^{14}$NV for magnetometry, due to its simpler hyperfine structure. However, for sensing modalities requiring a bias magnetic field not aligned with the sensing NV axis, the absence of a quadrupole moment in the $^{15}$N nuclear spin leads to pronounced envelope modulation effects in time-dependent measurements of $^{15}$NV spin evolution. While such behavior in spin echo experiments are well studied, analogous effects in Ramsey measurements and the implications for magnetometry remain under-explored. Here, we derive the modulated $^{15}$NV Ramsey response to a misaligned bias field, using a simple vector description of the effective magnetic field on the nuclear spin. The predicted modulation properties are then compared to experimental results, revealing significant magnetic sensitivity loss if unaddressed. We demonstrate that double-quantum coherences of the NV $S=1$ electronic spin states dramatically suppress these envelope modulations, while additionally proving resilient to other parasitic effects such as strain heterogeneity and temperature shifts., Comment: Main text: 9 pages, 5 figures

This paper presents a method for hardware trojan detection in integrated circuits. Unsupervised deep learning is used to classify wide field-of-view (4x4 mm$^2$), high spatial resolution magnetic field images taken using a Quantum Diamond Microscope (QDM). QDM magnetic imaging is enhanced using quantum control techniques and improved diamond material to increase magnetic field sensitivity by a factor of 4 and measurement speed by a factor of 16 over previous demonstrations. These upgrades facilitate the first demonstration of QDM magnetic field measurement for hardware trojan detection. Unsupervised convolutional neural networks and clustering are used to infer trojan presence from unlabeled data sets of 600x600 pixel magnetic field images without human bias. This analysis is shown to be more accurate than principal component analysis for distinguishing between field programmable gate arrays configured with trojan free and trojan inserted logic. This framework is tested on a set of scalable trojans that we developed and measured with the QDM. Scalable and TrustHub trojans are detectable down to a minimum trojan trigger size of 0.5% of the total logic. The trojan detection framework can be used for golden-chip free detection, since knowledge of the chips' identities is only used to evaluate detection accuracy, Comment: 25 pages, 17 figures

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve a factor of 30 improvement in signal-to-noise ratio, translating to a sensitivity enhancement exceeding an order of magnitude. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous bias and control fields, ensuring that all of the ${\sim}10^9$ two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 dynamical decoupling and correlation spectroscopy, using a synthetic AC magnetic field. The results are independent of the nature of the target signal and broadly applicable to metrology using NV centers and other solid-state ensembles. This work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity., Comment: 7 pages, 5 figures; Supplemental: 4 pages, 3 figures

We present a summary of future prospects for direct detection of dark matter within the GeV/c2 to TeV/c2 mass range. This is paired with a new definition of the neutrino fog in order to better quantify the rate of diminishing returns on sensitivity due to irreducible neutrino backgrounds. A survey of dark matter candidates predicted to fall within this mass range demonstrates that fully testing multiple well-motivated theo-ries will require expanding the currently-funded generation of experiments down to and past the neutrino fog. We end with the status and plans for next-generation exper-iments and novel R&D concepts which will get us there., Comment: contribution to Snowmass 2021

Strong interactions between spins in many-body solid-state quantum system is a crucial resource for exploring and applying non-classical states. In particular, electronic spins associated with defects in diamond system are a leading platform for the study of collective quantum phenomena and for quantum technology applications. While such solid-state quantum defect systems have the advantage of scalability and operation under ambient conditions, they face the key challenge of controlling interactions between the defects spins, since the defects are spatially fixed inside the host lattice with relative positions that cannot be well controlled during fabrication. In this work, we present a dressed-state approach to control the effective dipolar coupling between solid-state spins; and then demonstrate this scheme experimentally using two strongly-coupled nitrogen vacancy (NV) centers in diamond. Including Rabi driving terms between the m$_s$ = 0 and $\pm$1 states in the NV spin Hamiltonian allows us to turn on and off or tune the effective dipolar coupling between two NV spins. Through Ramsey spectroscopy, we detect the change of the effective dipolar field generated by the control NV spin prepared in different dressed states. To observe the change of interaction dynamics, we then deploy spin-lock-based polarization transfer measurements via a Hartmann-Hahn matching condition between two NV spins in different dressed states. We perform simulations that indicate the promise for this robust scheme to control the distribution of interaction strengths in strongly-interacting spin systems, including interaction strength homogenization in a spin ensemble, which can be a valuable tool for studying non-equilibrium quantum phases and generating high fidelity multi-spin correlated states for quantum-enhanced sensing.

We outline the unique opportunities and challenges in the search for "ultraheavy" dark matter candidates with masses between roughly $10~{\rm TeV}$ and the Planck scale $m_{\rm pl} \approx 10^{16}~{\rm TeV}$. This mass range presents a wide and relatively unexplored dark matter parameter space, with a rich space of possible models and cosmic histories. We emphasize that both current detectors and new, targeted search techniques, via both direct and indirect detection, are poised to contribute to searches for ultraheavy particle dark matter in the coming decade. We highlight the need for new developments in this space, including new analyses of current and imminent direct and indirect experiments targeting ultraheavy dark matter and development of new, ultra-sensitive detector technologies like next-generation liquid noble detectors, neutrino experiments, and specialized quantum sensing techniques., Comment: Solicited community whitepaper for the Snowmass2021 process (Cosmic frontier, particle dark matter working group). 10 pages, 3 figures, many references. Comments welcome. v2: minor revisions based on comments

Next-generation dark matter (DM) detectors searching for weakly interacting massive particles (WIMPs) will be sensitive to coherent scattering from solar neutrinos, demanding an efficient background-signal discrimination tool. Directional detectors improve sensitivity to WIMP DM despite the irreducible neutrino background. Wide-bandgap semiconductors offer a path to directional detection in a high-density target material. A detector of this type operates in a hybrid mode. The WIMP or neutrino-induced nuclear recoil is detected using real-time charge, phonon, or photon collection. The directional signal, however, is imprinted as a durable sub-micron damage track in the lattice structure. This directional signal can be read out by a variety of atomic physics techniques, from point defect quantum sensing to x-ray microscopy. In this white paper, we present the detector principle and review the status of the experimental techniques required for directional readout of nuclear recoil tracks. Specifically, we focus on diamond as a target material; it is both a leading platform for emerging quantum technologies and a promising component of next-generation semiconductor electronics. Based on the development and demonstration of directional readout in diamond over the next decade, a future WIMP detector will leverage or motivate advances in multiple disciplines towards precision dark matter and neutrino physics., Comment: contribution to Snowmass 2021, 30 pages + references, 14 figures; v3: journal format (20 pages + references, 14 figures), journal reference added

The adoption of 3D packaging technology necessitates the development of new approaches to failure electronic device analysis. To that end, our team is developing a tool called the quantum diamond microscope (QDM) that leverages an ensemble of nitrogen vacancy (NV) centers in diamond, achieving vector magnetic imaging with a wide field-of-view and high spatial resolution under ambient conditions. Here, we present the QDM measurement of 2D current distributions in an 8-nm flip chip IC and 3D current distributions in a multi-layer PCB. Magnetic field emanations from the C4 bumps in the flip chip dominate the QDM measurements, but these prove to be useful for image registration and can be subtracted to resolve adjacent current traces in the die at the micron scale. Vias in 3D ICs display only Bx and By magnetic fields due to their vertical orientation and are difficult to detect with magnetometers that only measure the Bz component (orthogonal to the IC surface). Using the multi-layer PCB, we show that the QDM's ability to simultaneously measure Bx, By, and Bz is advantageous for resolving magnetic fields from vias as current passes between layers. We also show how spacing between conducting layers is determined by magnetic field images and how it agrees with the design specifications of the PCB. In our initial efforts to provide further z-depth information for current sources in complex 3D circuits, we show how magnetic field images of individual layers can be subtracted from the magnetic field image of the total structure. This allows for isolation of signal layers and can be used to map embedded current paths via solution of the 2D magnetic inverse. In addition, the paper also discusses the use of neural networks to identify 2D current distributions and its potential for analyzing 3D structures.