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This study explores nonlinear optical effects in diamond crystals doped with nitrogen-vacancy (NV) centers, focusing on the optical Kerr effect in the infrared spectral region. By employing the Z-scan technique with 230 fs laser pulses at a wavelength of 1032~nm, we investigate the nonlinear refractive index of high-purity and NV-containing diamond crystals at NV concentrations of 0.3 ppm and 4.5 ppm. The results demonstrate a pronounced anisotropy in the nonlinear refractive index, which exhibits a four-fold rotational symmetry, with its amplitude reduced by the NV concentration. The reduction in non-linear susceptibility is linked to the negative contribution of NV centers, modeled as two-level systems upon a strong, laser field, red-detuned relative to their resonance frequency. These findings provide new insights into the interplay between NV centers and nonlinear optical properties of diamond, offering potential pathways for tunable nonlinear optics applications., Comment: 10 pages, 5 figure

We employ an optical fiber doped with randomly oriented fluorescent sub-micron diamonds and the novel zero-field resonance protocol to collect information on the localization and orientation of a magnetic-field source and its distribution. Many previous demonstrations of diamond-based magnetic field sensing achieved ultrahigh sensitivities down to the fT range warranted by manipulating spin states of the diamond nitrogen vacancy (NV) centers with externally applied radio or microwaves. The application of such oscillating fields is problematic in distributed magnetic-field measurements and may be incompatible with specific targets. Instead of relying on these approaches, we leveraged cross-relaxations of particular spin-state populations of the NV center under a magnetic field, thus observing zero-field resonances and making external radio frequency fields redundant. Combined with an optical fiber sensitive to the magnetic field along its entire length, remote sensing was realized that returned information on the spatial field distribution without using any moving mechanical elements in the detection system. Variation of the spatial parameters of the investigated field was achieved simply by controlling the current in a pair of induction coils easily integrable with optical fibers without limiting the fiber-specific functionality of the optical readout taking place at a fixed location at the optical fiber output. Lifting of the requirements related to the mechanical scanning of the fiber, the application of external fields, and the orientation of the NV centers against the measured field mark a very practical step forward in optically driven magnetic field sensing, not easily achievable with earlier implementations., Comment: 7 pages, 3 figures

Magnetometry using Nitrogen-Vacancy (NV) color centers in diamond predominantly relies on microwave spectroscopy. However, microwaves may hinder certain studies involving biological systems or thin conductive samples. This work demonstrates a wide-field, microwave-free imaging magnetometer utilizing NV centers in nanodiamonds by exploiting the cross-relaxation feature near zero magnetic fields under ambient conditions without applying microwaves. For this purpose, we measure the center shift, contrast, and linewidth of the zero-field cross-relaxation in 140 nm nanodiamonds drop-cast on a current-carrying conductive pattern while scanning a background magnetic field, achieving a sensitivity of 4.5 $\mathrm{\mu T/\sqrt{Hz}}$. Our work allows for applying the NV zero-field feature in nanodiamonds for magnetic field sensing in the zero and low-field regimes and highlights the potential for microwave-free all-optical wide-field magnetometry based on nanodiamonds., Comment: 8 pages, 5 figures

Existing explanation methods for image classification struggle to provide faithful and plausible explanations. This paper addresses this issue by proposing a post-hoc natural language explanation method that can be applied to any CNN-based classifier without altering its training process or affecting predictive performance. By analysing influential neurons and the corresponding activation maps, the method generates a faithful description of the classifier's decision process in the form of a structured meaning representation, which is then converted into text by a language model. Through this pipeline approach, the generated explanations are grounded in the neural network architecture, providing accurate insight into the classification process while remaining accessible to non-experts. Experimental results show that the NLEs constructed by our method are significantly more plausible and faithful. In particular, user interventions in the neural network structure (masking of neurons) are three times more effective than the baselines., Comment: Findings of EMNLP 2024

We implanted Fe$^+$ ions in nanodiamond (ND) powder containing negatively charged nitrogen-vacancy (NV-) centers and studied their Raman spectra and optically detected magnetic resonance (ODMR) in various applied magnetic fields with green light (532 nm) excitation. In Raman spectra, we observed a blue shift of the NV$^-$ peak associated with the conversion of the electronic sp$^3$ configuration to the disordered sp$^2$ one typical for the carbon/graphite structure. In the ODMR spectra, we observed a red shift of the resonance position caused by local heating by an absorptive environment that recovers after annealing. To reveal the red shift mechanism in ODMR, we created a controlled absorptive environment around ND by adding iron-based Fe$_2$O$_3$ and graphitic sp$^2$ powders to the ND suspension. This admixture caused a substantial increase in the observed shift proportional to the applied laser power, corresponding to an increase in the local temperature by 150-180 K. This surprisingly large shift is absent in non-irradiated NV-ND powders, is associated only with the modification of the local temperature by the absorptive environment of NV-NDs and can be studied using ODMR signals of NV$^-$., Comment: 21 pages, 6 figures

Cells and tissues are constantly exposed to various chemical and physical signals that intricately regulate various physiological and pathological processes. This study explores the integration of two biophysical methods, Traction Force Microscopy (TFM) and Optically-Detected Magnetic Resonance (ODMR), to concurrently assess cellular traction forces and local relative temperature. We present a novel elastic substrate with embedded nitrogen-vacancy microdiamonds, that facilitate ODMR-TFM measurements. Optimization efforts have focused on minimizing the sample illumination and experiment duration to mitigate biological perturbations. Our hybrid ODMR-TFM technique yields precise TFM maps and achieves approximately 1K accuracy in relative temperature measurements. Notably, our setup, employing a simple wide-field fluorescence microscope with standard components, demonstrates the broader feasibility of these techniques in life-science laboratories. By elucidating the physical aspects of cellular behavior beyond the existing methods, this approach opens avenues for a deeper understanding and may inspire diverse biomedical applications., Comment: 19 pages, 5 figures

We study the fluorescence of nanodiamond ensembles as a function of static external magnetic field and observe characteristic dip features close to the zero field with potential for magnetometry applications. We analyze the dependence of the features width and contrast of the feature on the size of the diamond (in the range 30 nm to 3 um) and on the strength of a bias magnetic field applied transversely to the field being scanned. We also perform optically detected magnetic resonance (ODMR) measurements to quantify the strain splitting of the zero-field ODMR resonance across various nanodiamond sizes and compare it with the width and contrast measurements of the zero-field fluorescence features for both nanodiamonds and bulk samples. The observed properties provide compelling evidence of cross-relaxation effects in the NV system occurring close to zero magnetic fields. Finally, the potential of this technique for use in practical magnetometry is discussed., Comment: 9 pages, 5 figures

Preparation of an atomic ensemble in a particular Zeeman state is a critical step of many protocols for implementing quantum sensors and quantum memories. These devices can also benefit from optical fibre integration. In this work we describe experimental results supported by a theoretical model of single-beam optical pumping of $^{87}$Rb atoms within a hollow-core photonic crystal fibre. The observed 50% population increase in the pumped F=2, m$_F$=2 Zeeman substate along with the depopulation of remaining Zeeman substates enabled us to achieve a 3 times improvement in the relative population of the m$_F$=2 substate within the F=2 manifold, with 60% of the F=2 population residing in the m$_F$=2 dark sublevel. Based on our theoretical model, we also propose methods to further improve the pumping efficiency in alkali-filled hollow-core fibres.

We present the results of work on a hybrid material composed of a tellurite glass rod doped with nanodiamonds containing nitrogen-vacancy-nitrogen and paramagnetic nitrogen-vacancy color centers. The reported results include details on tellurite glass and cane fabrication, confocal and wide-field imaging of the nanodiamond distribution in their volume, as well as on the spectroscopic characterization of their fluorescence and Optically Detected Magnetic Resonance measurements of magnetic fields and temperatures. Magnetic fields up to 50 G were examined with a sensitivity of 10$^{-5}$ T Hz$^{-1/2}$ whereas temperature measurements were simultaneously performed with a sensitivity of 74 kHz K$^{-1}$ within the 8 Kelvin range at room temperature. In that way, we demonstrate the suitability of such systems for fiber magneto- and thermometry with a reasonable performance already in the form of glass rods. At the same time, the rods constitute an interesting starting point for further processing into photonic components such as microstructured fibers or fiber tapers for the realization of specialized sensing modalities., Comment: 16 pages, 3 figures

Integration of optically-active nanodiamonds with glass fibers is a powerful method of scaling of diamond magnetic sensing functionality. We propose a novel approach for integration of nanodiamonds containing nitrogen-vacancy centers directly into the fiber core. The core is fabricated using nanostructurization, that is by stacking the preform from 790 soft glass canes, drawn from a single rod dip-coated with nanodiamonds suspended in isopropyl alcohol. This enables manual control over distribution of nanoscale features, here - the nanodiamonds across and along the fiber core. We verify this by mapping the nanodiamond distribution in the core using confocal microscopy. The nanodiamonds are separated longitudinally either by 15 microns or 24 microns, while in the transverse plane separation of approximately 1 micron is observed, corresponding to the individual cane diameter in the final fiber, without significant agglomeration. Filtered, red fluorescence is observed with naked eye uniformly along the fiber. Its magnetic sensitivity is confirmed by in optically detected magnetic resonance recorded with a coiled, 60-cm-long fiber sample with readout contrast limited mainly by microwave antenna coverage. NV fluorescence intensity in 0 to 35 mT magnetic field is also demonstrated, allowing magnetometry applications with a large B-field dynamic range in absence of microwaves., Comment: 12 pages, 7 figures, 1 table

The ability to perform noninvasive, non-contact measurements of electric signals produced by action potentials is essential in biomedicine. A key method to do this is to remotely sense signals by the magnetic field they induce. Existing methods for magnetic field sensing of mammalian tissue, used in techniques such as magnetoencephalography of the brain, require cryogenically cooled superconducting detectors. These have many disadvantages in terms of high cost, flexibility and limited portability as well as poor spatial and temporal resolution. In this work we demonstrate an alternative technique for detecting magnetic fields generated by the current from action potentials in living tissue using nitrogen vacancy centres in diamond. With 50pT/$\sqrt{Hz}$ sensitivity, we show the first measurements of sensing from mammalian tissue with a diamond sensor using mouse muscle optogenetically activated with blue light. We show these measurements can be performed in an ordinary, unshielded lab environment and that the signal can be easily recovered by digital signal processing techniques.

Driving an open spin system by two strong, nearly degenerate fields enables addressing populations of individual spin states, characterisation of their interaction with thermal bath, and measurements of their relaxation/decoherence rates. With such addressing we observe nested magnetic resonances having nontrivial dependence on microwave field intensity: while the width of one of the resonances undergoes a strong power broadening, the other one exhibits a peculiar field-induced stabilization. We also observe light-induced narrowing of such composite resonances. The observations are explained by the dynamics of bright and dark superposition states and their interaction with reservoir., Comment: Replaced with major revisions. Current version: 14 pages including 5 figures + supplemental information (7 pages). Original version: 13 pages including 5 figures + supplemental information (6 pages)

We demonstrate a technique for precision sensing of temperature or the magnetic field by simultaneously driving two hyperfine transitions involving distinct electronic states of the nitrogen-vacancy center in diamond. Frequency modulation of both driving fields is used with either the same or opposite phase, resulting in the immunity to fluctuations in either the magnetic field or the temperature, respectively. In this way, a sensitivity of 1.4 nT Hz$^{-1/2}$ or 430 $\mu$K Hz$^{-1/2}$ is demonstrated. The presented technique only requires a single frequency demodulator and enables the use of phase-sensitive camera imaging sensors. A simple extension of the method utilizing two demodulators allows for simultaneous, independent, and high-bandwidth monitoring of both the magnetic field and temperature., Comment: 5 pages, 4 figures

We report on the creation, observation and optimization of superposition states of cold atoms. In our experiments, rubidium atoms are prepared in a magneto-optical trap and later, after switching off the trapping fields, Faraday rotation of a weak probe beam is used to characterize atomic states prepared by application of appropriate light pulses and external magnetic fields. We discuss the signatures of polarization and alignment of atomic spin states and identify main factors responsible for deterioration of the atomic number and their coherence and present means for their optimization, like relaxation in the dark with the strobe probing. These results may be used for controlled preparation of cold atom samples and in situ magnetometry of static and transient fields, Comment: 15 pages and 9 figures (including supplementary information)

We demonstrate magnetic field sensing using an ensemble of nitrogen-vacancy centers by recording the variation in the pump-light absorption due to the spin-polarization dependence of the total ground state population. Using a 532 nm pump laser, we measure the absorption of native nitrogen-vacancy centers in a chemical vapor deposited diamond placed in a resonant optical cavity. For a laser pump power of 0.4 W and a cavity finesse of 45, we obtain a noise floor of $\sim$ 100 nT/$\sqrt{\textrm{Hz}}$ spanning a bandwidth up to 125 Hz. We project a photon shot-noise-limited sensitivity of $\sim$ 1 pT/$\sqrt{\textrm{Hz}}$ by optimizing the nitrogen-vacancy concentration and the detection method., Comment: 7 pages and 5 figures

Sensitive, real-time optical magnetometry with nitrogen-vacancy centers in diamond relies on accurate imaging of small ($\ll 10^{-2}$) fractional fluorescence changes across the diamond sample. We discuss the limitations on magnetic-field sensitivity resulting from the limited number of photoelectrons that a camera can record in a given time. Several types of camera sensors are analyzed and the smallest measurable magnetic-field change is estimated for each type. We show that most common sensors are of a limited use in such applications, while certain highly specific cameras allow to achieve nanotesla-level sensitivity in $1$~s of a combined exposure. Finally, we demonstrate the results obtained with a lock-in camera that pave the way for real-time, wide-field magnetometry at the nanotesla level and with micrometer resolution., Comment: 7 pages, 4 figures

We suggest a novel approach for wide-field imaging of the neural network dynamics of brain slices that uses highly sensitivity magnetometry based on nitrogen-vacancy (NV) centers in diamond. In-vitro recordings in brain slices is a proven method for the characterization of electrical neural activity and has strongly contributed to our understanding of the mechanisms that govern neural information processing. However, traditional recordings can only acquire signals from a few positions simultaneously, which severely limits their ability to characterize the dynamics of the underlying neural networks. We suggest to radically extend the scope of this method using the wide-field imaging of the neural magnetic fields across the slice by means of NV magnetometry. Employing comprehensive computational simulations and theoretical analyses, we characterize the spatiotemporal characteristics of the neural magnetic fields and derive the required key performance parameters of an imaging setup based on NV magnetometry. In particular, we determine how the technical parameters determine the achievable spatial resolution for an optimal reconstruction of the neural currents from the measured field distributions. Finally, we compare the imaging of neural slice activity with that of a single planar pyramidal cell. Our results suggest that imaging of neural slice activity will be possible with the upcoming generation of NV magnetic field sensors, while imaging of the activity of a single planar cell remains more challenging., Comment: 28 pages, 8 figures; SI 11 pages, 4 figures

Magnetometers based on ensembles of nitrogen-vacancy centres are a promising platform for continuously sensing static and low-frequency magnetic fields. Their combination with phase-sensitive (lock-in) detection creates a highly versatile sensor with a sensitivity that is proportional to the derivative of the optical magnetic resonance lock-in spectrum, which is in turn dependant on the lock-in modulation parameters. Here we study the dependence of the lock-in spectral slope on the modulation of the spin-driving microwave field. Given the presence of the intrinsic nitrogen hyperfine spin transitions, we experimentally show that when the ratio between the hyperfine linewidth and their separation is $\gtrsim 1/4$, square-wave based frequency modulation generates the steepest slope at modulation depths exceeding the separation of the hyperfine lines, compared to sine-wave based modulation. We formulate a model for calculating lock-in spectra which shows excellent agreement with our experiments, and which shows that an optimum slope is achieved when the linewidth/separation ratio is $\lesssim 1/4$ and the modulation depth is less then the resonance linewidth, irrespective of the modulation function used., Comment: 13 pager and 6 figures