Compact magneto-optical traps using planar optics

Magneto-optical traps (MOTs) composed of magnetic fields and light fields have been widely utilized to cool andconfine microscopic particles. Practical technology applications require miniaturized MOTs. The advancement of planaroptics has promoted the development of compact MOTs. In this article, we review the development of compact MOTs basedon planar optics. First, we introduce the standardMOTs. We then introduce the gratingMOTs with micron structures, whichhave been used to build cold atomic clocks, cold atomic interferometers, and ultra-cold sources. Further, we introducethe integrated MOTs based on nano-scale metasurfaces. These new compact MOTs greatly reduce volume and powerconsumption, and provide new opportunities for fundamental research and practical applications.

Magneto-optical Kerr Effect of Mono-layer NiX_(2)(X=Cl,Br,I):A Density Functional Theory Study

The full-potential linearized augmented plane wave plus local orbital method is utilized for exploring the electronic,magnetic,and magneto-optical properties of the NiX_(2)(X=Cl,Br,and I)single layer.The first-principles calculation demonstrates that these compounds are ferromagnetic indirect semiconductors,and the energy band gaps of NiX_(2)for X=Cl,Br,and I are 3.888,3.134,and 2.157 eV,respectively.The magnetic moments of Ni atoms in NiX_(2)monolayer are 1.656,1.588,1.449μB,and their magneto-crystalline anisotropy energies are 0.167,0.029,0.090 meV,respectively.Based on the macro-linear response theory,we systematically studied the influences of the external magnetic field and out-of-plane strain on the magneto-optical Kerr effect(MOKE)spectrum of the NiX_(2)single layer.It is found that,when the external magnetic field is perpendicular to the sample plane,the value of the Kerr rotation angle reaches the maximum,and the single-layer NiI_(2)material has a Kerr rotation angle of 1.89°at the photon energy of 1.986 eV.Besides,the Kerr rotation spectrum of NiCl_(2)and NiBr_(2)monolayers redshift as the out-of-plane strain increases,while NiI_(2)monolayer blueshifts.Accurate computation of the MOKE spectrum of NiX_(2)materials provides an opportunity for applications of 2D magnetic material ranging from sensing to data storing.

Classic analogue of Autler–Townes-splitting transparency using a single magneto-optical ring resonator

We show that an optical transparency can be obtained by using only one single magneto-optical ring resonator. This effect is based on the splitting of counterclockwise and clockwise modes in the ring resonator. Within a proposed resonator-waveguide configuration the superposition between the two degeneracy broken modes produces a transparency window,which can be closed, open, and modified by tuning the applied magnetic field. This phenomenon is an analogue of Autler–Townes splitting, and the magnetic field is equivalent to the strong external pump field. We provide a theoretic analysis on the induced transparency, and numerically demonstrate the effect using full-wave simulation. Feasible implication of this effect and its potential applications are also discussed.

Magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulators

Control and detection of antiferromagnetic topological materials are challenging since the total magnetization vanishes.Here we investigate the magneto-optical Kerr and Faraday effects in bilayer antiferromagnetic insulator Mn Bi2Te4.We find that by breaking the combined mirror symmetries with either perpendicular electric field or external magnetic moment,Kerr and Faraday effects occur.Under perpendicular electric field,antiferromagnetic topological insulators(AFMTI)show sharp peaks at the interband transition threshold,whereas trivial insulators show small adjacent positive and negative peaks.Gate voltage and Fermi energy can be tuned to reveal the differences between AFMTI and trivial insulators.We find that AFMTI with large antiferromagnetic order can be proposed as a pure magneto-optical rotator due to sizable Kerr(Faraday)angles and vanishing ellipticity.Under external magnetic moment,AFMTI and trivial insulators are significantly different in the magnitude of Kerr and Faraday angles and ellipticity.For the qualitative behaviors,AFMTI shows distinct features of Kerr and Faraday angles when the spin configurations of the system change.These phenomena provide new possibilities to optically detect and manipulate the layered topological antiferromagnets.

High-sensitivity phase imaging eddy current magneto-optical system for carbon fiber reinforced polymers detection

This paper proposed a high-sensitivity phase imaging eddy current magneto-optical (PI-ECMO) system for carbon fiber reinforced polymer (CFRP) defect detection. In contrast to other eddy current-based detection systems, the proposed system employs a fixed position excitation coil while enabling the detection point to move within the detection region. This configuration effectively mitigates the interference caused by the lift-off effect, which is commonly observed in systems with moving excitation coils. Correspondingly, the relationship between the defect characteristics (orientation and position) and the surface vertical magnetic field distribution (amplitude and phase) is studied in detail by theoretical analysis and numerical simulations. Experiments conducted on woven CFRP plates demonstrate that the designed PI-ECMO system is capable of effectively detecting both surface and internal cracks, as well as impact defects. The excitation current is significantly reduced compared with traditional eddy current magneto-optical (ECMO) systems.

Convergence Phenomenon with Fourier Series of tg(x2)and Alike

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

Single atoms transferring between a magneto-optical trap and a far-off-resonance optical dipole trap

Based on our work on single cesium atoms trapped in a large-magnetic-gradient vapour-cell magneto-optical trap （MOT）, the signal-to-noise ratio （SNR） is remarkably improved. Also a far-off-resonance optical dipole trap （FORT） formed by a strongly-focused 1064 nm single frequency Nd：YVO4 laser beam is introduced. One cesium atom is prepared in the MOT, and then it can transfer successfully between the MOT and the FORT which is overlapped with the MOT. Utilizing the effective transfer, the lifetime of single atoms trapped in the FORT is measured to be 6.9± 0.3 s. Thus we provide a system where the atomic qubit can be coherently manipulated.

Observation of single neutral atoms in a large-magnetic-gradient vapour-cell magneto-optical trap

Single caesium atoms in a large-magnetic-gradient vapour-cell magneto-optical trap have been identified. The trapping of individual atoms is marked by the steps in fluorescence signal corresponding to the capture or loss of single atoms. The typical magnetic gradient is about 29 mT/cm, which evidently reduces the capture rate of magneto-optical trap.

Continuously transferring cold atoms in caesium double magneto-optical trap

We have established a caesium double magneto-optical trap （MOT） system for cavity-QED experiment, and demonstrated the continuous transfer of cold caesium atoms from the vapour-cell MOT with a pressure of - 1 × 10^-6 Pa to the ultra-high-vacuum （UHV） MOT with a pressure of - 8 × 10^-8 Pa via a focused continuous-wave transfer laser beam. The effect of frequency detuning as well as the intensity of the transfer beam is systematically investigated, which makes the transverse cooling adequate before the atoms leak out of the vapour-cell MOT to reduce divergence of the cold atomic beam. The typical cold atomic flux got from vapour-cell MOT is - 2 × 10^7 atoms/s. About 5 × 10^6 caesium atoms are recaptured in the UHV MOT.

Enhanced cold mercury atom production with two-dimensional magneto-optical trap

A cold atom source is important for quantum metrology and precision measurement.To reduce the quantum projection noise limit in optical lattice clock,one can increase the number of cold atoms and reduce the dead time by enhancing the loading rate.In this work,we realize an enhanced cold mercury atom source based on a two-dimensional(2D)magnetooptical trap(MOT).The vacuum system is composed of two titanium chambers connected with a differential pumping tube.Two stable cooling laser systems are adopted for the 2D-MOT and the three-dimensional(3D)-MOT,respectively.Using an optimized 2D-MOT and push beam,about 1.3×10^(6)atoms,which are almost an order of magnitude higher than using a pure 3D-MOT,are loaded into the 3D-MOT for202Hg atoms.This enhanced cold mercury atom source is helpful in increasing the frequency stability of a neutral mercury lattice clock.

Glass-forming Ability and Chemical Stability of Magneto-optical Glass Heavily Doped with Rare Earth Oxide

The glass-forming region of B2O3-Al2O3-SiO2 （BAS） glass heavily doped with rare earth oxides was investigated by an effective method, and the chemical stability was investigated by powder method. Influences of rare earth oxides on the glass-forming ability and the chemical stability of the BAS glass were also discussed. The experimental results show that the BAS glass-forming region expands firstly with the increase of the Tb2O3 content up to 30mol% and then shrinks. The acid-resistant capacity of the BAS glass doped with rare earth oxides is the lowest, the water-resistant capacity is secondary, and the alkali-resistant capacity is the best. Besides, the glass chemical stability can be improved by doping appropriate amount of rare earth oxides. Moreover, the stronger the ionic polarization ability of the rare earth ions is, the better the chemical stability of the BAS glass will be.

Determination of the magnetic anisotropy constant of Cu/Fe/SiO_2/Si by a magneto-optical Kerr effect susceptometer

The magneto-optical Kerr effect susceptometry technique is proposed to determine the uniaxial magnetic anisotropy （UMA） constant Ku. The magnetic properties of Cu/Fe/SiO2/Si grown by dc magnetron sputtering were investigated. The in-plane uniaxial magnetic anisotropy was probed by the magneto-optical Kerr effect （MOKE）. The value of UMA, Ku = 2.5 x 103 J/m3, was simulated from the field dependence of ac susceptibility along the hard axis according to the Stoner-Wohlfarth （S-W） model, which is consistent with Ku = 2.7~ 103 J/m3 calculated from the magnetic hysteresis loops. Our results show that the magneto-optical Kerr effect susceptometry can be employed to determine the magnetic anisotropy constant owing to its high sensitivity.

A Single Folded Beam Magneto-Optical Trap System for Neutral Mercury Atoms

Mercury is a promising candidate for the optical lattice clock, due to its low sensitivity to the blackbody radiation. We develop a single folded beam magneto-optical trap for the neutral mercury optical lattice clock, with a 253. 7nm frequency quadrupled laser. Up to 1.7 × 10^6 （202Hg） or 1.5 × 10^6 （199Hg） atoms can be captured, and the atom temperature is lowered to 170μK （202Hg） or 50μK （199Hg）. The cold atom signals of all six rich abundant isotopes are observed in this system.

Study of magnetic and magneto-optical properties of heavily doped bismuth substitute yttrium iron garnet (Bi∶YIG) film

The magnetic and magneto-optical properties of heavily doped Bi∶YIG film were studied. The film was deposited by radio frequency magnetron sputtering method and crystallized by rapid recurrent thermal annealing (RRTA). The results show that the RRTA treated film has good properties both in microwave and optical wave band. The saturation magnetization of the film on different substrates varies from 135.7 to 138.6 kA·m-1. The coercive field of the film on GGG substrate is about 0.32 kA·m-1, while about 0.8-1.43 kA·m-1 on YAG substrate and 1.75 kA·m-1 on Al2O3 substrate. The Faraday angle is about 3-5 (°)·μm-1 when optical wavelength ranges at 450-600 nm. The transmission spectra of the Bi∶YIG films on three substrates has similar change as annealing temperature below 800 ℃. Specially, when annealing temperature is above 800 ℃ a step is observed between 550 and 650 nm wavelength for the film deposited on Al2O3 substrate.Three results are very useful in magneto-optical recording application and integrated microwave devices.

Influence of Magnetic Field Inhomogeneity on a Magneto-Optical Current Sensor

The growth in the capacity of electric power system creates a demand for the protection of relaying systems. Optical current transducers—OCT that are mainly made up of single mode optical fibers which are subjected to Faraday rotation are used as a replacement for electromagnetic transducers due to their immunity to electromagnetic interference. However, the principal parameter in this system, the sensitivity to magnetic fields or current, depends on the Verdet constant, which is low in the case of optical fibers. However, the optical path length can be increased to compensate for it by winding the fiber around a current carrying element a large number of turns. In this work, we study a current sensor, which is made up of a conductor coil with a fiber inside, thus increasing sensitivity. We study the effect of the inhomogeneity of the magnetic field induced by the current on the sensitivity of the optical fiber sensor.

Resonant magneto-optical Kerr effect induced by hybrid plasma modes in ferromagnetic nanovoids

With nanovoids buried in Co films, resonant structures were observed in spectra of polar magneto-optical Kerr effect（MOKE）, where both a narrow bandwidth and high intensity were acquired. Through changing the thickness of Co films and the lattice of voids, different optical modes were introduced. For a very shallow array of voids, the resonant MOKE was induced by Ag plasma edge resonance, for deeper ones, hybrid plasma modes, such as void plasmons in the voids, surface lattice plasmons between the voids, and the co-action of them, etc. resulted in resonant MOKE. We found that resonant MOKE resulted from the void plasmons resonance which possesses the narrowest bandwidth for the lowest absorption of voids. The simulated electromagnetic field（EF） distribution consolidated different effects of these three optical modes on resonant MOKE modulation. Such resonant polar MOKE possesses high sensitivity, which might pave the way to on-chip MO devices.

Improvement on the magneto-optical Kerr effect of cobalt film with a quadrilayer structure

The magneto-optical Kerr effect of the HfO2/Co/HfO2/A1 multilayer structure is investigated in this work, and an ob- vious cavity enhancement of the Kerr response for the HfO2 semiconductor is found both theoretically and experimentally. Surprisingly, a maximum value of about -3 of the polar Kerr rotation for s-polarized incident light is observed in our experiment. We propose that this improvement on the Kerr effect can be attributed to the multiple reflection and optical interference in the cavity, which can also be proved by simulation using the finite element method.

Application of longitudinal generalized magneto-optical ellipsometry in magnetic ultrathin films

The longitudinal generalized magneto-optical ellipsometry （GME） method is extended to the measurement of three- layer ultrathin magnetic films. In this work, the theory of the reflection matrix is introduced into the GME measurement to obtain the reflective matrix parameters of ultrathin multilayer magnetic films with different thicknesses. After that, a spectroscopic ellipsometry is used to determine the optical parameter and the thickness of every layer of these samples, then the magneto-optical coupling constant of the multilayer magnetic ultrathin film can be obtained. After measurements of a series of ultrathin Fe films, the results show that the magneto-optical coupling constant Q is independent of the thickness of the magnetic film. The magneto-optical Kerr rotations and ellipticity are measured to confirm the validity of this experiment. Combined with the optical constants and the Q constant, the Kerr rotations and ellipticity are calculated in theory. The results show that the theoretical curve fits very well with the experimental data.

Magnetic and Magneto-Optical Properties in Paramagnetic NdF3 Under High Magnetic Field

In this paper, we first theoretically report the magnetic and magneto-opticalproperties in paramagnetic media under high external magnetic field. Considering the action of theexternal magnetic Geld H_e and indirect exchange interaction H_v, the characteristic of the magneticsaturation and the property of the Faraday rotation to be nonlinear with external magnetic Geld arepresented in paramagnetic NdF_3. In terms of our theory, the indirect exchange interaction plays auimportant role in the magnetization M and the Faraday rotation θ in NdF_3 under high externalmagnetic Geld. The theory is in good agreement with experimental results. On the other hand, areasonable explanation for the temperature dependence of the ratio of the Verdet constant to themagnetic susceptibility V/x is obtained.

Dependence of loading time on control parameters in a standard vapour-oaded magneto-optical trap

Loading time is one of the most important dynamic characteristics of a magneto-optical trap. In this paper, we primarily report on a detailed experimental study of the effects of some magneto-optical trap control parameters on loading time, including the background vacuum pressure, the magnetic field gradient, and the intensities of trapping and repumping lasers. We compare the results with previous theoretical and experimental results, and give qualitative analysis. These experimental investigations offer some useful guidelines to coatrol the loading time of magneto-optical traps. The controllable loading time achieved is helpful to enhance the signal-to-noise ratio of photoassociation spectroscopy, which is remarkably improved from 7 to 28.6.