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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

Quantum computing has tremendous potential to overcome some of the fundamental limitations present in classical information processing. Yet, today's technological limitations in the quality and scaling prevent exploiting its full potential. Quantum computing based on superconducting quantum processing units (QPUs) is among the most promising approaches towards practical quantum advantage. In this article the basic technological approach of IQM Quantum Computers is described covering both the QPU and the rest of the full-stack quantum computer. In particular, the focus is on a 20-qubit quantum computer featuring the Garnet QPU and its architecture, which we will scale up to 150 qubits. We also present QPU and system-level benchmarks, including a median 2-qubit gate fidelity of 99.5% and genuinely entangling all 20 qubits in a Greenberger-Horne-Zeilinger (GHZ) state.

Crossed optical dipole traps (ODTs) provide three-dimensional confinement of cold atoms and other optically trappable particles. However, the need to maintain the intersection of the two trapping beams poses strict requirements on alignment stability, and limits the ability to move the trap. Here we demonstrate a novel crossed ODT design that features inherent stability of the beam crossing, allowing the trap to move and remain aligned. The trap consists of a single high-power laser beam, imaged back onto itself at an angle to form a crossed trap. Self-aligning behavior results from employing an imaging system with positive magnification tuned precisely to unity. We employ laser-cooled samples of $^6$Li atoms to demonstrate that the trap remains well-aligned over a 4.3 mm travel range along an axis approximately perpendicular to the plane containing the crossed beams. Our scheme can be applied to bring an atomic cloud held in a crossed ODT close to a surface or field source for various applications in quantum simulation, sensing, and information processing., Comment: 9 pages, 5 figures

We give a complete invariant for shift equivalence for Boolean matrices (equivalently finite relations), in terms of the period, the induced partial order on recurrent components, and the cohomology class of the relation on those components.

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

Lunar sulfides and oxides are a significant source of noble and base metals and will be vital for future human colonies' self-sustainability. Sulfide detection (pyrite and troilite) applies to many technological fields and use cases, for example, as a raw material source (available in situ on the Lunar surface) for new solar panel production methods. Ilmenite is the primary iron and titanium ore on the Moon and can provide helium-3 for nuclear fusion and oxygen for rocket fuel. The most important ore minerals have prominent absorption peaks in a narrow far-infrared (FIR) wavelength range of 20-40 $\mu$m, much stronger than the spectral features of other common minerals, including significant silicates, sulfates, and carbonates. Our simulations based on the linear mixing of pyrite with the silicates mentioned above indicated that areas containing at least 10-20% pyrite could be detected from the orbit in the FIR range. MIRORES, Multiplanetary far-IR ORE Spectrometer, proposed here, would operate with a resolution down to <5 m, enabling the detection of areas covered by 2-3 m$^2$ of pyrite (or ilmenite) on a surface of ~17 m$^2$ from an altitude of 50 km, creating possibilities for detecting large and local smaller orebodies along with their stockworks. The use of the Cassegrain optical system achieves this capability. MIRORES will measure radiation in eight narrow bands (0.3 $\mu$m in width) that can include up to five bands centered on the ore mineral absorption bands, for example, 24.3, 24.9, 27.6, 34.2, and 38.8 $\mu$m for pyrite, marcasite, chalcopyrite, ilmenite, and troilite, respectively. The instrument size is 32 $\times$ 32 $\times$ 42 cm, and the mass is <10 kg, which fits the standard microsatellite requirements., Comment: 41 pages, 14 figures

The disparate nature of thermal-nonthermal energy partition during flares, particularly during weak flares, is still an open issue. Following the Neupert effect, quantifying the relative yield of X-ray emission in different energy bands can enable inferring the underlying energy release mechanism. During September 20-25, 2021, the Solar Orbiter mission - being closer to the Sun ($\sim$0.6 AU) and having a moderate separation angle (<40$^{\circ}$) from the Sun-Earth line provided a unique opportunity to analyze multi-wavelength emission from $\sim$200 (mostly weak) flares, commonly observed by the Spectrometer Telescope for Imaging X-rays (STIX), STEREO-A, GOES, and SDO observatories. Associating the quotient (q$_{f}$) of hard X-ray fluence (12-20 keV) and soft X-ray flux (4-10 keV) with the peak SXR flux enabled us to identify strongly non-thermal flares. Multi-wavelength investigation of spectral and imaging mode observations of the 20 strongly non-thermal weak flares reveals an inverse relationship of q$_{f}$ with the emission measure (EM) (and density), and a positive relationship with the flare plasma temperature. This indicates that plasma in tenuous loops attains higher temperatures compared to that in the denser loops, in response to nonthermal energy deposition. This is in agreement with the plasma parameters of the coronal loops, as derived by applying the one-dimensional Palermo Harvard (PH) hydrodynamical code to the coronal loop plasma having different initial coronal loop base pressures when subjected to similar heating input. Our investigation, therefore, indicates that the plasma parameters of the flaring loop in the initial phase have a decisive role in thermal-nonthermal energy partitioning., Comment: The Astrophysical Journal - Accepted for Publication

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

Motivated by the study of the recurrent orbits in a Morse set of a Morse decomposition, we introduce the concept of Morse predecomposition of an isolated invariant set in the setting of combinatorial and classical dynamical systems. We prove that a Morse predecomposition indexed by a poset is a Morse decomposition and we show how a Morse predecomposition may be condensed back to a Morse decomposition., Comment: 29 pages (31 with bibliography), 9 figures

Taking a discrete approach to functions and dynamical systems, this paper integrates the combinatorial gradients in Forman's discrete Morse theory with persistent homology to forge a unified approach to function simplification. The two crucial ingredients in this effort are the Lefschetz complex, which focuses on the homology at the expense of the geometry of the cells, and the shallow pairs, which are birth-death pairs that can double as vectors in discrete Morse theory. The main new concept is the depth poset on the birth-death pairs, which captures all simplifications achieved through canceling shallow pairs. One of its linear extensions is the ordering by persistence.

We develop Conley's theory for multivalued maps on finite topological spaces. More precisely, for discrete-time dynamical systems generated by the iteration of a multivalued map which satisfies appropriate regularity conditions, we establish the notions of isolated invariant sets and index pairs, and use them to introduce a well-defined Conley index. In addition, we verify some of its fundamental properties such as the Wazewski property and continuation.

Connection matrices are a generalization of Morse boundary operators from the classical Morse theory for gradient vector fields. Developing an efficient computational framework for connection matrices is particularly important in the context of a rapidly growing data science that requires new mathematical tools for discrete data. Toward this goal, the classical theory for connection matrices has been adapted to combinatorial frameworks that facilitate computation. We develop an efficient persistence-like algorithm to compute a connection matrix from a given combinatorial (multi) vector field on a simplicial complex. This algorithm requires a single-pass, improving upon a known algorithm that runs an implicit recursion executing two-passes at each level. Overall, the new algorithm is more simple, direct, and efficient than the state-of-the-art. Because of the algorithm's similarity to the persistence algorithm, one may take advantage of various software optimizations from topological data analysis.

We present a photoluminescence (PL) and Raman spectroscopy study of various diamond samples that have high concentrations of nitrogen-vacancy (NV) color centers up to multiple parts per million (ppm). With green red, and near infrared (NIR) light excitation, we demonstrate that while for samples with a low density of NV centers the signals are primarily dominated by Raman scattering from the diamond lattice, for higher density of NVs we observe a combination of Raman scattering from the diamond lattice and fluorescence from the NV centers, while for the highest NV densities the Raman signals from diamond are completely overwhelmed by the intense NVs fluorescence. However, under NIR excitation, Raman diamond signatures can be observed for some diamonds. These observations reveal different roles of two mechanisms of light emission and contradict the naive belief that Raman scattering enables complete characterisation of a diamond crystalline sample.

This paper presents the universal address sequence generator (UASG) for memory built-in-self-test. The studies are based on the proposed universal method for generating address sequences with the desired properties for multirun march memory tests. As a mathematical model, a modification of the recursive relation for quasi-random sequence generation is used. For this model, a structural diagram of the hardware implementation is given, of which the basis is a storage device for storing so-called direction numbers of the generation matrix. The form of the generation matrix determines the basic properties of the generated address sequences. The proposed UASG generates a wide spectrum of different address sequences, including the standard ones, such as linear, address complement, gray code, worst-case gate delay, $2^i$, next address, and pseudorandom. Examples of the use of the proposed methods are considered. The result of the practical implementation of the UASG is presented, and the main characteristics are evaluated.

Magnetometry with nitrogen-vacancy color centers in diamond has gained significant interest among researchers in recent years. Absolute knowledge of the three-dimensional orientation of the magnetic field is necessary for many applications. Conventional magnetometry measurements are usually performed with NV ensembles in a bulk diamond with a thin NV layer or a scanning probe in the form of a diamond tip, which requires a smooth sample surface and proximity of the probing device, often limiting the sensing capabilities. Here, we present a method for determining the three-dimensional orientation of the magnetic field vector relative to the diamond crystal lattice. We demonstrate that NV centers in arbitrarily oriented submicrometer-sized diamond powder deposited on a planar surface can be used for sensing the magnetic field. Our work can be extended to irregular surfaces, which shows a promising path for nanodiamond-based photonic sensors., Comment: 10 pages + 2 pages in supplementary. Article published in Scientific Reports

The Szymczak functor is a tool used to construct the Conley index for dynamical systems with discrete time. We present an algorithmizable classification of isomorphism classes in the Szymczak category over the category of finite sets with arbitrary relations as morphisms. The research is the first step towards the construction of Conley theory for relations., Comment: New coauthor, disproved Conjecture 6.40, added "Final Remarks" section and minor changes

Multivector fields and combinatorial dynamical systems have recently become a subject of interest due to their potential for use in computational methods. In this paper, we develop a method to track an isolated invariant set -- a salient feature of a combinatorial dynamical system -- across a sequence of multivector fields. This goal is attained by placing the classical notion of the "continuation" of an isolated invariant set in the combinatorial setting. In particular, we give a "Tracking Protocol" that, when given a seed isolated invariant set, finds a canonical continuation of the seed across a sequence of multivector fields. In cases where it is not possible to continue, we show how to use zigzag persistence to track homological features associated with the isolated invariant sets. This construction permits viewing continuation as a special case of persistence., Comment: Full version of SoCG 2022 paper

The thick-target model predicts that in flare foot points, we should observe lowering of HXR sources' altitude with increasing energy. The foot point of HXR sources result from the direct interaction of non-thermal electron beams with plasma in the lower part of the solar atmosphere, where the density increases rapidly. Therefore, we can estimate the plasma density distribution along the non-thermal electron beam directly from the observations of the altitude-energy relation obtained for the HXR foot point sources. The relation's shape is density-dependent and is also determined by the power-law distribution of non-thermal electrons. Additionally, during the impulsive phase these parameters may change dramatically. Thus, the interpretation of observed HXR foot point sources' altitudes is not straightforward and needs detailed numerical modelling of the electron precipitation process. The numerical model was calculated using the hydrodynamic 1D model with an application of the Fokker-Planck formalism for non-thermal beam precipitation. HXR data from RHESSI were used to trace chromospheric density changes during a non-thermal emission burst, in detail. We have found that the amount of mass that evaporated from the chromosphere is in good agreement with the ranges obtained from hydrodynamical modelling of a flaring loop, and from an analysis of observed emission measure in the loop top, and with specific scaling laws. Consistency between the obtained values shows that HXR images may provide an important constraint for models - a mass of plasma that evaporated due to a non-thermal electron beam depositing energy in the chromosphere. High-energy, non-thermal sources' (above 20 keV in this case) positions fit the column density changes obtained from the hydrodynamical model perfectly. Density changes seem to be less affected by the electrons' spectral index., Comment: Astronomy & Astrophysics, accepted

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

Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in discrete contexts, such as graph theory or in the recently developed field of combinatorial dynamics, is straightforward and computationally feasible. In this paper, we present an approach to study classical dynamical systems as given by semiflows or flows using techniques from combinatorial topological dynamics. More precisely, we present a general existence theorem for periodic orbits of semiflows which is based on suitable phase space decompositions, and indicate how combinatorial techniques can be used to satisfy the necessary assumptions. In this way, one can obtain computer-assisted proofs for the existence of periodic orbits and even certain chaotic behavior.

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

Multivector fields provide an avenue for studying continuous dynamical systems in a combinatorial framework. There are currently two approaches in the literature which use persistent homology to capture changes in combinatorial dynamical systems. The first captures changes in the Conley index, while the second captures changes in the Morse decomposition. However, such approaches have limitations. The former approach only describes how the Conley index changes across a selected isolated invariant set though the dynamics can be much more complicated than the behavior of a single isolated invariant set. Likewise, considering a Morse decomposition omits much information about the individual Morse sets. In this paper, we propose a method to summarize changes in combinatorial dynamical systems by capturing changes in the so-called Conley-Morse graphs. A Conley-Morse graph contains information about both the structure of a selected Morse decomposition and about the Conley index at each Morse set in the decomposition. Hence, our method summarizes the changing structure of a sequence of dynamical systems at a finer granularity than previous approaches.

The Spectrometer/Telescope for Imaging X-rays (STIX) is the HXR instrument onboard Solar Orbiter designed to observe solar flares over a broad range of flare sizes, between 4-150 keV. We report the first STIX observations of microflares recorded during the instrument commissioning phase in order to investigate the STIX performance at its detection limit. This first result paper focuses on the temporal and spectral evolution of STIX microflares occuring in the AR12765 in June 2020, and compares the STIX measurements with GOES/XRS, SDO/AIA, and Hinode/XRT. For the observed microflares of the GOES A and B class, the STIX peak time at lowest energies is located in the impulsive phase of the flares, well before the GOES peak time. Such a behavior can either be explained by the higher sensitivity of STIX to higher temperatures compared to GOES, or due to the existence of a nonthermal component reaching down to low energies. The interpretation is inconclusive due to limited counting statistics for all but the largest flare in our sample. For this largest flare, the low-energy peak time is clearly due to thermal emission, and the nonthermal component seen at higher energies occurs even earlier. This suggests that the classic thermal explanation might also be favored for the majority of the smaller flares. In combination with EUV and SXR observations, STIX corroborates earlier findings that an isothermal assumption is of limited validity. Future diagnostic efforts should focus on multi-wavelength studies to derive differential emission measure distributions over a wide range of temperatures to accurately describe the energetics of solar flares. Commissioning observations confirm that STIX is working as designed. As a rule of thumb, STIX detects flares as small as the GOES A class. For flares above the GOES B class, detailed spectral and imaging analyses can be performed., Comment: 19 pages, 11 figures