Arbitrary Field Research Articles

Joint quantum sensing of vector magnetic field and temperature with nitrogen-vacancy centers in diamond

Quantum diamond sensors of multiple physical quantities, especially magnetic field and temperature, have great application prospects in materials science, biophysics, and engineering. Here, we demonstrate joint quantum sensing of vector magnetic field and temperature based on ensembles of nitrogen-vacancy (NV) centers in the diamond. Combining the intrinsic C3ν symmetry of diamond crystals and multiple-frequency excitation technique, we can directly measure frequency-modulated optically detected magnetic resonance (ODMR) spectra for three different NV orientations and then obtain the Zeeman splittings and the center frequency movement of the electron spin. An artificially generated underlying external magnetic field is used to eliminate degeneracy and facilitate coordinate transformations. The six-channel phase-locked amplification technology enables simultaneous detection of vector magnetic field and temperature with a sensitivity of about 0.87 nT/Hz1/2 and 0.32 mK/Hz1/2; meanwhile, a 23 dB isolation between magnetic and temperature signals is kept. This technology realizes the simultaneous measurement of arbitrary vector magnetic field and temperature, which can be used to study the temperature-varying magnetic phase transition.

Nearly Ideal Transparency with Artificially Designed Meta-Atoms.

The ideal electromagnetic transparency refers to the ability of an object to remain scatteringless to any incoming waves, resulting in vacuum invisibility. However, natural solid substances can hardly be transparent in free space as they are responsive to external polarizations. Completely eliminating the polarization effect of an obstacle under arbitrary field illumination is a long-standing scientific challenge. Here, it is shown that a subwavelength meta-atom can be nearly ideally transparent in the vacuum. The overall vacuum-like property of the meta-atom is achieved through judiciously designing its internal polarization and magnetization. Remarkably, any large-scale objects made by stacking the meta-atoms inherit the vacuum-like property and are scatteringless in free space. By both the simulations and experiments, the meta-atom's peculiar property is reasonably verified. The proposed meta-atoms are excellent candidates for a wide range of applications, such as perfect radar radomes, scatteringless walls, filtering devices, and self-stealth materials.

A Classification of 2-Dimensional Endo-Commutative Straight Algebras of Rank 1 over a non-Trivial Field

An endo-commutative algebra is a nonassociative algebra in which the square mapping preserves multiplication. In this paper, we give a complete classification of 2-dimensional endo-commutative straight algebras of rank one over an arbitrary non-trivial field, where a straight algebra of dimension 2 satisfies the condition that there exists an element x such that x and x2 are linearly independent. We list all multiplication tables of the algebras up to isomorphism.

Bounded Rank Perturbations of Quasi-Regular Pencils Over Arbitrary Fields

Bounded Rank Perturbations of Quasi-Regular Pencils Over Arbitrary Fields

Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields.

Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ±J models, Sherrington-Kirkpatrick models, and only locally connected J1-J2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high-power efficiency Boltzmann sampling to a generalized large-scale Ising model.

Sound field control in a rectangular closed space using multiple selected room modes

Sound field control using multiple loudspeakers is essential for many applications such as sound field reproduction for delivering an immersive sound experience and noise control. These sound field controls are generally required in closed spaces, such as living rooms or factories, where eigenmodes are prominent at low frequencies. Many studies on the control of a few modes in closed spaces have been conducted in the field of noise control. In this study, we attempted to reproduce arbitrary sound fields, such as plane and spherical waves, from virtual sound sources using simultaneous multiple eigenmodes based on room-mode matching (RMM). Because most rooms are generally considered rectangular at low frequencies, we expanded the target sound field with discrete cosine transform (DCT) by approximating the eigenmodes as cosine functions. We proposed a method for extracting the control modes necessary to reproduce the desired sound field considering the mode strength at a target frequency. The simulation results verified that the proposed method can reproduce propagating plane waves with loudspeaker arrays placed on both sides of the closed space while maintaining the loudspeaker filter gains at appropriate values.

Zeeman Splitting of Torsional Oscillation Frequencies of Magnetars

Magnetars form a special class of neutron stars possessing superstrong magnetic fields and demonstrating power flares triggered by these fields. Observations of such flares reveal the presence of quasi-periodic oscillations (QPOs) at certain frequencies; they are thought to be excited in the flares. QPOs carry potentially important information on magnetar structure, magnetic field, and mechanisms of magnetar activity. We calculate frequencies of torsional (magneto-elastic) oscillations of the magnetar crust treating the magnetic field effects in the first order of perturbation theory. The theory predicts the splitting of non-magnetic oscillation frequencies into Zeeman components. Zeeman splitting of the torsional oscillation spectrum of magnetars was suggested, clearly described and estimated by Shaisultanov and Eichler (2009), but their work has not been given considerable attention. To extend it, we suggest the technique of calculating oscillation frequencies, including Zeeman splitting at not too strong magnetic fields for arbitrary magnetic field configuration. Zeeman splitting enriches the oscillation spectrum and simplifies the theoretical interpretation of observations. We calculate several low-frequency oscillations of magnetars with a pure dipole magnetic field in the crust. The results qualitatively agree with the low-frequency QPOs detected in the hyperflare of SGR 1806–20 and in the giant flare of SGR 1900+14.

Continuous-stage adapted exponential methods for charged-particle dynamics with arbitrary magnetic fields

Continuous-stage adapted exponential methods for charged-particle dynamics with arbitrary magnetic fields

Tailoring light-induced charge transfer and intersystem crossing in FeCO using time-dependent spin-orbit configuration interaction.

Real-time (RT) electronic structure methods provide a natural framework for describing light-matter interactions in arbitrary time-dependent electromagnetic fields (EMF). Optically induced excited state transitions are of particular interest, which require tuned EMF to drive population transfer to and from the specific state(s) of interest. Intersystem crossing, or spin-flip, may be driven through shaped EMF or laser pulses. These transitions can result in long-lived "spin-trapped" excited states, which are especially useful for materials requiring charge separation or protracted excited state lifetimes. Time-dependent configuration interaction (TDCI) is unique among RT methods in that it may be implemented in a basis of eigenstates, allowing for rapid propagation of the time-dependent Schrödinger equation. The recent spin-orbit TDCI (TD-SOCI) enables a real-time description of spin-flip dynamics in an arbitrary EMF and, therefore, provides an ideal framework for rational pulse design. The present study explores the mechanism of multiple spin-flip pathways for a model transition metal complex, FeCO, using shaped pulses designed to drive controlled intersystem crossing and charge transfer. These results show that extremely tunable excited state dynamics can be achieved by considering the dipole transition matrix elements between the states of interest.

On nonsingular bilinear maps over different fields

The investigation of nonsingular bilinear forms originates from the classification of division algebras over the real number field. Building upon this foundation, researchers have delved into the study of nonsingular bilinear forms over real number fields, leading to significant results such as Hopfs theorem. However, the interest in understanding nonsingular bilinear forms extends beyond real number fields, prompting a desire to explore other fields as well. When it comes to algebraically closed fields, the theorem becomes well-understood, with essence captured by the Hopf-Smith theorem. Inspired by these established studies, we are motivated to further the comprehension of nonsingular bilinear forms over arbitrary fields. Given a field , we study in this article numerical constraints on for the existence of nonsingular bilinear maps for not only algebraically closed fields and the real number field but also the rational number field and finite fields. We reach the final conclusion mainly through algebro-geometric techniques and the use of determinantal varieties. We reprove a result of HopfSmith which states that the minimal possible value of is when is an algebraically closed field. When is the real number field, we prove that under a combinatorial condition, the minimal possible value of is still . We also show that when is the rational number field or a finite field, the minimal possible value of is .

Particle-pair creation by high-harmonic laser fields

We consider the dynamical pair-creation by intense electric fields in vacuum, based on exact solutions of the Dirac equation using the temporal Klein process. This approach gives a simple interpretation of the QED processes associated with arbitrary time-varying electric fields, and leads to the standard quantum kinetic equation. As an application, we consider the case of an intense laser field containing a large spectrum of coherent high-harmonics (HH). The role of the fast field oscillations is discussed. We show that HH pulses eventually lead to an enhancement of pair-creation and can be described as a sequence of dynamically equivalent Sauter pulses.

ON MODEL-THEORETIC CONNECTED GROUPS

AbstractWe introduce and study the model-theoretic notions of absolute connectedness and type-absolute connectedness for groups. We prove that groups of rational points of split semisimple linear groups (that is, Chevalley groups) over arbitrary infinite fields are absolutely connected and characterize connected Lie groups which are type-absolutely connected. We prove that the class of type-absolutely connected group is exactly the class of discretely topologized groups with the trivial Bohr compactification, that is, the class of minimally almost periodic groups.

Birational anabelian Grothendieck Conjecture for curves over arbitrary cyclotomic extension fields of number fields

In anabelian geometry, various strong/desired forms of Grothendieck Conjecture-type results for hyperbolic curves over relatively small arithmetic fields — for instance, finite fields, number fields, or p-adic local fields — have been obtained by many researchers, especially by A. Tamagawa and S. Mochizuki. Let us recall that, in their proofs, the Weil Conjecture or p-adic Hodge theory plays an essential role. Therefore, to obtain such Grothendieck Conjecture-type results, it appears that the condition that the cyclotomic characters of the absolute Galois groups of the base fields are highly nontrivial is indispensable. On the other hand, in an author's recent joint work with Y. Hoshi and S. Mochizuki, we introduced the notion of TKND-AVKF-field [concerning the divisible subgroups of the groups of rational points of semi-abelian varieties] and obtained the semi-absolute version of the Grothendieck Conjecture for higher dimensional (≥2) configuration spaces associated to hyperbolic curves of genus 0 over TKND-AVKF-fields contained in the algebraic closure of the field of rational numbers. For instance, every [possibly, infinite] cyclotomic extension field of a number field is such a TKND-AVKF-field. In particular, this Grothendieck Conjecture-type result suggests that the condition that the cyclotomic character of the absolute Galois group of the base field under consideration is sufficiently nontrivial is, in fact, not indispensable for strong/desired form of anabelian phenomena. In the present paper, to pose another evidence for this observation, we prove the relative birational version of the Grothendieck Conjecture for smooth curves over TKND-AVKF-fields with a certain mild condition that every cyclotomic extension field of a number field satisfies. From the viewpoint of the condition on base fields, this result may be regarded as a partial generalization of F. Pop and S. Mochizuki's results on the birational version of the Grothendieck Conjecture for smooth curves.

Fast norm computation in smooth-degree Abelian number fields

This paper presents a fast method to compute algebraic norms of integral elements of smooth-degree cyclotomic fields, and, more generally, smooth-degree Galois number fields with commutative Galois groups. The typical scenario arising in S-unit searches (for, e.g., class-group computation) is computing a Theta (nlog n)-bit norm of an element of weight n^{1/2+o(1)} in a degree-n field; this method then uses n(log n)^{3+o(1)} bit operations.An n(log n)^{O(1)} operation count was already known in two easier special cases: norms from power-of-2 cyclotomic fields via towers of power-of-2 cyclotomic subfields, and norms from multiquadratic fields via towers of multiquadratic subfields. This paper handles more general Abelian fields by identifying tower-compatible integral bases supporting fast multiplication; in particular, there is a synergy between tower-compatible Gauss-period integral bases and a fast-multiplication idea from Rader.As a baseline, this paper also analyzes various standard norm-computation techniques that apply to arbitrary number fields, concluding that all of these techniques use at least n^2(log n)^{2+o(1)} bit operations in the same scenario, even with fast subroutines for continued fractions and for complex FFTs. Compared to this baseline, algorithms dedicated to smooth-degree Abelian fields find each norm n/(log n)^{1+o(1)} times faster, and finish norm computations inside S-unit searches n^2/(log n)^{1+o(1)} times faster.

Metafiber transforming arbitrarily structured light

Structured light has proven useful for numerous photonic applications. However, the current use of structured light in optical fiber science and technology is severely limited by mode mixing or by the lack of optical elements that can be integrated onto fiber end-faces for wavefront engineering, and hence generation of structured light is still handled outside the fiber via bulky optics in free space. We report a metafiber platform capable of creating arbitrarily structured light on the hybrid-order Poincaré sphere. Polymeric metasurfaces, with unleashed height degree of freedom and a greatly expanded 3D meta-atom library, were 3D laser nanoprinted and interfaced with polarization-maintaining single-mode fibers. Multiple metasurfaces were interfaced on the fiber end-faces, transforming the fiber output into different structured-light fields, including cylindrical vector beams, circularly polarized vortex beams, and arbitrary vector field. Our work provides a paradigm for advancing optical fiber science and technology towards fiber-integrated light shaping, which may find important applications in fiber communications, fiber lasers and sensors, endoscopic imaging, fiber lithography, and lab-on-fiber technology.

Bounded rank perturbations of matrix pencils without nontrivial invariant factors

In this paper, we solve the bounded rank perturbation problem for matrix pencils without nontrivial homogeneous invariant factors, over arbitrary fields. The solution is based on reducing the problem to two minimal case matrix pencil completion problems. If there are no nontrivial homogeneous invariant factors involved, these two minimal completion problems allow treating column and row minimal indices separately. This is an example of the utility of completion tools in perturbation problems, when dealing with matrix pencils.

An approach for a polychromatic generalized Lorenz–Mie theory

In this work a polychromatic version of the generalized Lorenz–Mie theory stricto sensu (GLMT) is derived. In this new formalism, arbitrary time-dependent fields are expanded into partial waves using Bromwich scalar potentials and, instead of the usual expansion coefficients – the beam shape coefficients (BSCs) – found in the monochromatic GLMT, now one finds field shape spectra (FSSs) which are intrinsically frequency-dependent. Expressions for the incident, scattered and internal fields are presented, and it is shown how physical quantities defined and expressed in the monochromatic GLMT in terms of the BSCs are modified and redefined in terms of the FSSs in polychromatic light scattering problems, like scattered intensities and phase angles, absorption, extinction and scattering cross-sections, and radiation pressure cross-sections.

Heavy quarkonia in QGP medium in an arbitrary magnetic field

Heavy quarkonia in QGP medium in an arbitrary magnetic field

Mie scattering with 3D angular spectrum method.

Mie theory is a powerful method to model electromagnetic scattering from a multilayered sphere. Usually, the incident beam is expanded to its vector spherical harmonic representation defined by beam shape coefficients, and the multilayer sphere scattering is obtained by the T-matrix method. However, obtaining the beam shape coefficients for arbitrarily shaped incident beams has limitations on source locations and requires different methods when the incident beam is defined inside or outside the computational domain or at the scatterer surface. We propose a 3D angular spectrum method for defining beam shape coefficients from arbitrary source field distributions. This method enables the placement of the sources freely within the computational domain without singularities, allowing flexibility in beam design. We demonstrate incident field synthesis and spherical scattering by comparing morphology-dependent resonances to known values, achieving excellent matching and high accuracy. The proposed method has significant benefits for optical systems and inverse beam design. It allows for the analysis of electromagnetic forward/backward propagation between optical elements and spherical targets using a single method. It is also valuable for optical force beam design and analysis.

Reoptimization of single-joint motor patterns to non-Earth gravity torques induced by a robotic exoskeleton

Gravity is a ubiquitous component of our environment that we have learned to optimally integrate in movement control. Yet, altered gravity conditions arise in numerous applications from space exploration to rehabilitation, thereby pressing the sensorimotor system to adapt. Here, we used a robotic exoskeleton to reproduce the elbow joint-level effects of arbitrary gravity fields ranging from 1g to -1g, passing through Mars- and Moon-like gravities, and tested whether humans can reoptimize their motor patterns accordingly. By comparing the motor patterns of actual arm movements with those predicted by an optimal control model, we show that our participants () adapted optimally to each gravity-like torque. These findings suggest that the joint-level effects of a large range of gravities can be efficiently apprehended by humans, thus opening new perspectives in arm weight support training in manipulation tasks, whether it be for patients or astronauts.