Zeeman Effect Research Articles

Optical properties of a hollow cylindrical quantum wire in a parallel applied magnetic field

In this theoretical study, we investigate optical properties of a hollow cylindrical quantum wire in the presence of a homogeneous magnetic field. The magnetic field is applied parallel to the axis of the quantum wire. The investigations were achieved by solving the Schrödinger equation within the effective mass approximation. The optical properties studied were absorption coefficient (AC) of electromagnetic radiation and changes in refractive index (CRI) of the hollow cylinder. The parallel applied magnetic field lifts the degeneracy of states of opposite angular momentum (the ±|m|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm |m |$$\\end{document} states, m being the angular momentum quantum number) known as the Zeeman splitting. As such, in the presence of magnetic field, AC splits into two branches, one corresponding to a transition involving the positive m states and the other corresponding to a transition involving the negative m states. Increase in intensity of the electromagnetic radiation reduces the magnitude of the AC. Presence of inner radius of the hollow cylindrical wire lowers transition energies. Apart from absorption due to the (m=0→±1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(m=0 \\rightarrow \\pm 1)$$\\end{document} transitions, the presence of the inner radius also facilitates absorption due the (m=-1→0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(m=-1\\rightarrow 0)$$\\end{document} transition as the magnetic field strength increases, a phenomenon that does not happen in solid cylindrical quantum wires. The presence of the inner radius also enhances AC in strong magnetic field. Increase in intensity of the electromagnetic radiation affects the CRI (here considered up to third order), introducing a normal dispersion region in an otherwise anomalous region. The parallel magnetic field also splits the CRI depending on the sign of the m states involved in the transitions.

Full Stokes-vector Inversion of the Solar Mg ii h and k Lines

The polarization of the Mg ii h and k resonance lines is the result of the joint action of scattering processes and the magnetic field–induced Hanle, Zeeman, and magneto-optical effects, thus holding significant potential for the diagnostic of the magnetic field in the solar chromosphere. The Chromospheric LAyer Spectro-Polarimeter sounding-rocket experiment, carried out in 2019, successfully measured at each position along the 196″ spectrograph slit the wavelength variation of the four Stokes parameters in the spectral region of this doublet around 280 nm, both in an active-region plage and in a quiet region close to the limb. We consider some of these CLASP2 Stokes profiles and apply to them the recently developed HanleRT Tenerife Inversion Code, which assumes a one-dimensional model atmosphere for each spatial pixel under consideration (i.e., it neglects the effects of horizontal radiative transfer). We find that the nonmagnetic causes of symmetry breaking, due to the horizontal inhomogeneities and the gradients of the horizontal components of the macroscopic velocity in the solar atmosphere, have a significant impact on the linear polarization profiles. By introducing such nonmagnetic causes of symmetry breaking as parameters in our inversion code, we can successfully fit the Stokes profiles and provide an estimation of the magnetic field vector. For example, in the quiet region pixels, where no circular polarization signal is detected, we find that the magnetic field strength in the upper chromosphere varies between 1 and 20 G.

Giant Valley Zeeman Splitting in Vanadium-Doped WSe2 Monolayers.

2D dilute magnetic semiconductors (DMS) based on transition metal dichalcogenides (TMD) offer an innovative pathway for advancing spintronic technologies, including the potential to exploit phenomena such as the valley Zeeman effect. However, the impact of magnetic ordering on the valley degeneracy breaking and on the enhancement of the optical transitions g-factors of these materials remains an open question. Here, a giant effective g-factors ranging between ≈-27 and -69 for the bound exciton at 4K in vanadium-doped WSe2 monolayers, obtained through magneto-photoluminescence (PL) experiments is reported. This giant g-factor disappears at room temperature, suggesting that this response is associated with a magnetic ordering of the vanadium impurity states at low temperatures. Ab initio calculations for the vanadium-doped WSe2 monolayer confirm the existence of magnetic ordering of the vanadium states, which leads to degeneracy breaking of the valence bands at K and K'. A phenomenological analysis is employed to correlate this splitting with the measured enhanced effective g-factor. The findings shed light on the potential of defect engineering of 2D materials for spintronicapplications.

Measurement of microwave polarization using two polarization orthogonal local microwave electric fields in a Rydberg atom-based mixer

We propose and demonstrate what we believe to be a novel method for measuring the polarization direction of a microwave electric field in a single measurement using a Rydberg atom-based mixer with two orthogonally polarized local microwave electric fields. This approach eliminates the need for physical rotation of the local field, allowing the polarization angle of the signal field to be determined directly by measuring the ratio of the two beat signals. Furthermore, introducing a weak static magnetic field enables the utilization of the Zeeman effect and exploitation of polarization asymmetry. This distinction allows for determining the polarization direction of the microwave field is θ or 180° – θ within the 0 to 180-degree range. The capability to measure microwave polarization in real-time across this range is very valuable for applications in microwave sensing and information transmission.

Magnetic field-engineered optical nonlinearity in germanene nanotubes

Abstract The linear and nonlinear optical properties of germanene nanotubes (GeNTs) under the influence of magnetic fields are investigated through theoretical analysis. By employing a tight-binding model beyond the Dirac cone approximation, the electronic band structure, density of states, dipole matrix elements, and third-order nonlinear optical susceptibilities are calculated. The application of a magnetic field induces a Zeeman splitting of the energy levels, breaking the band degeneracy. Consequently, the dipole matrix elements exhibit a magnetic field dependence, altering the intensity and number of allowed transitions. In the infrared and ultraviolet energy regions, the linear optical absorption spectrum displays the splitting of peaks into dual neighboring peaks, with the splitting distance linearly dependent on the magnetic field strength. The third-order nonlinear optical susceptibilities, χTHG(3)3ω and χIDIR(3)ω, reveal the emergence of multiple resonance peaks in different energy regions due to two-photon and three-photon absorption processes. The magnetic field significantly influences the number, position, and height of these optical peaks, enabling effective control over the nonlinear optical response. By investigating the scaled energy (E/E_g) dependence, a universal behavior is observed for the three- and two photon resonance peaks, where their positions remain constant, but their peak intensities are significantly enhanced under the influence of the magnetic field. These findings demonstrate the potential of GeNTs as tunable nonlinear optical materials, with the magnetic field serving as an effective parameter for engineering their optical properties for various applications in optoelectronics, photonics, and related fields.

Constructing the Fulde-Ferrell-Larkin-Ovchinnikov State in a CrOCl/NbSe2 van der Waals Heterostructure.

Time reversal symmetry breaking in superconductors, resulting from external magnetic fields or spontaneous magnetization, often leads to unconventional superconducting properties. In this way, an intrinsic phenomenon called the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state may be realized by the Zeeman effect. Here, we construct the FFLO state in an artificial CrOCl/NbSe2 van der Waals (vdW) heterostructure by utilizing the superconducting proximity effect of NbSe2 flakes. The proximity-induced superconductivity demonstrates a considerably weak gap of about 0.12 meV, and the in-plane upper critical field reveals the behavior of the FFLO state. First-principles calculations uncover the origin of the proximitized superconductivity, which indicates the importance of Cr vacancies or line defects in CrOCl. Moreover, the FFLO state could be induced by the inherent large spin splitting in CrOCl. Our findings not only provide a practical scheme for constructing the FFLO state but also inspire the discovery of an exotic FFLO state in other two-dimensional vdW heterostructures.

The Spatial Correlation between CN-line- and Dust-continuum-emitting Regions in High-mass Star-forming Clouds

Measuring the strength of a three-dimensional (3D) magnetic field vector is challenging as it is not easy to recognize whether its line-of-sight (LOS) and plane-of-sky (POS) components are obtained from the same region. CN (N = 1–0) emission has been used to get the LOS component of a magnetic field (B LOS) from its Zeeman splitting lines, while dust continuum emission has been used to get the POS component of a magnetic field (B POS). We use the CN (N = 1–0) data observed with the Taeduk Radio Astronomy Observatory 14 m telescope and the dust continuum data from the Herschel archive toward six high-mass star-forming regions in order to test whether CN line and dust continuum emission can trace a similar region and thus can be used for inferring 3D magnetic field strength. Our comparison between CN and H2 column densities for all targets indicates that CN line emission tends to be strong toward bright continuum regions. The positions of peak CN column densities are particularly well correlated with those of peak H2 column densities, at least over the H2 column density of 8.0 × 1022 cm−2 within one or two telescope beam sizes in all targets, implying that CN-line- and dust-continuum-emitting regions are likely spatially coincident. This enabled us to make the reliable measurement of the 3D magnetic field strengths of five targets by taking a vector sum of their B LOS and B POS, helping to decide the magnetical criticality of the targets as supercritical or transcritical.

Direct Detection of the Magnetic Force and Field Coupling of Electronic Spins Using Photoinduced Magnetic Force Microscopy.

The intrinsic spin of the electron and its associated magnetic moment can provide insights into spintronics. However, the interaction is extremely weak, as is the case with the coupling between an electron's spin and a magnetic field, and it poses significant experimental challenges. Here we demonstrate the direct measurement of polarized single NV- centers and their spin-spin coupling behaviors in diamond. By using photoinduced magnetic force microscopy, we obtain the extremely weak magnetic force coupling originating from the electron spin. The polarized spin state of NV- centers, transitioning from |0⟩ to |±1⟩, and their corresponding Zeeman effect can be characterized through their interaction with a magnetic tip. The result presents an advancement in achieving electron spin measurements by magnetic force, avoiding the need for manufacturing conductive substrates. This facilitates a better understanding and control of electron spin to novel electronic states for future quantum technologies.

Mapping the Sun's coronal magnetic field using the Zeeman effect.

Regular remote sensing of the magnetic field embedded within the million-degree solar corona is severely lacking. This reality impedes fundamental investigations of the nature of coronal heating, the generation of solar and stellar winds, and the impulsive release of energy into the solar system via flares and other eruptive phenomena. Resulting from advancements in large aperture solar coronagraphy, we report unprecedented maps of polarized spectra emitted at 1074 nm by Fe+12 atoms in the active corona. We detect clear signatures of the Zeeman effect that are produced by the coronal magnetic field along the optically thin path length of its formation. Our comparisons with global magnetohydrodynamic models highlight the valuable constraints that these measurements provide for coronal modeling efforts, which are anticipated to yield subsequent benefits for space weather research and forecasting.

Manipulation of anisotropic Zhang-Rice exciton in NiPS3 by magnetic field

The effect of external magnetic fields on the behavior of the Zhang-Rice exciton in NiPS3, which captures the physics of spin-orbital entanglement in 2D XY-type antiferromagnets, remains unclear. This study presents systematic study of angle-resolved and polarization-resolved magneto-optical photoluminescence spectra of NiPS3 in the Voigt geometry. We observed highly anisotropic, non-linear Zeeman splitting and polarization rotation of the Zhang-Rice exciton, which depends on the direction and intensity of the magnetic field and can be attributed to the spin-orbital coupling and field-induced spin reorientation. Furthermore, above the critical magnetic field, we detected additional splitting of the exciton peaks, indicating the coexistence of various orientations of Néel vector. This study characterizes orbital change of Zhang-Rice exciton and field-induced spin-reorientation phase transitions in a 2D hexagonal XY-type antiferromagnet, and it further demonstrates the continuous manipulation of the spin and polarization of the Zhang-Rice exciton.

Magnetic field diagnostics of prominences with the Mg II k line 3D Stokes inversions versus traditional methods

The Mg II k resonance line is commonly used for diagnosing the solar chromosphere. We theoretically investigated its intensity and polarization in solar prominences, taking 3D radiative transfer and Hanle and Zeeman effects into account. We used an optically thick 3D model representative of a solar prominence and applied several inversion methods to the synthetic Stokes profiles, clarifying their pros and cons for inferring prominence magnetic fields. We conclude that the self-consistent 3D inversion with radiative transfer is necessary to determine the magnetic field vector, although its geometry cannot be inferred with full fidelity. We also demonstrate that more traditional methods, such as those based on the weak field approximation or the constant-property slab assumption, can offer useful information under certain conditions.

AC Zeeman effect in microfabricated surface traps.

Quantum processors and atomic clocks based on trapped ions often utilize an ion's hyperfine transition as the qubit state or frequency reference, respectively. These states are a good choice because they are insensitive in first order to magnetic field fluctuations, leading to long coherence times and stable frequency splittings. In trapped ions, however, these states are still subject to the second order AC Zeeman effect due to the necessary presence of an oscillating magnetic field used to confine the ions in a Paul trap configuration. Here, we measure the frequency shift of the 2S1/2 hyperfine transition of a 171Yb+ ion caused by the radio frequency (RF) electromagnetic field used to create confinement in several microfabricated surface trap designs. By comparing different trap designs, we show that two key design modifications significantly reduce the AC Zeeman effect experienced by the ion: (1) an RF ground layer routed directly below the entire RF electrode, and (2) a symmetric RF electrode. Both of these changes lead to better cancellation of the AC magnetic field and, thus, overall reduced frequency shifts due to the AC Zeeman effect and reduced variation across the device. These improvements enable a more homogeneous environment for quantum computing and can reduce errors for precision applications such as atomic clocks.

Origin of Dopant-Carrier Exchange Coupling and Excitonic Zeeman Splitting in Mn2+-Doped Lead Halide Perovskite Nanocrystals.

Low-dimensional metal halide perovskites have unique optical and electrical properties that render them attractive for the design of diluted magnetic semiconductors. However, the nature of dopant-exciton exchange interactions that result in spin-polarization of host-lattice charge carriers as a basis for spintronics remains unexplored. Here, we investigate Mn2+-doped CsPbCl3 nanocrystals using magnetic circular dichroism spectroscopy and show that Mn2+ dopants induce excitonic Zeeman splitting which is strongly dependent on the nature of the band-edge structure. We demonstrate that the largest splitting corresponds to exchange interactions involving the excited state at the M-point along the spin-orbit split-off conduction band edge. This splitting gives rise to an absorption-like C-term excitonic MCD signal, with the estimated effective g-factor (geff) of ca. 70. The results of this work help resolve the assignment of absorption transitions observed for metal halide perovskite nanocrystals and allow for a design of new diluted magnetic semiconductor materials for spintronics applications.

Imagination in Scientific Reasoning: Theoretical Innovation and Scientific Explanation on the Example of Atomic Physics

This article aims to show the great variety of ways in which new ideas enter science; ideas that must pass both the critical examination of the scientific community and the filter of empirical contrast. The community itself is aware of the role that conjectures, intuitions, and imagination play in the advancement of science. A fundamental role in the context of discovery is played by abduction, a form of reasoning that serves the purposes of theoretical innovation and scientific explanation, which I illustrate by focusing on the anomalous Zeeman effect, which is very appropriate to the case. But I also point out that in preductive reasoning, a genuinely deductive form of inter-theoretical reasoning, imagination, and luck should not be excluded when choosing the theoretical elements whose step-by-step combination leads to a novel theoretical result.

Hexagonal Boron Nitride Quantum Simulator: Prelude to Spin and Photonic Qubits.

The quest for qubit operation at room temperature is accelerating the field of quantum information science and technology. Solid state quantum defects with spin-optical properties are promising spin- and photonic qubit candidates for room temperature operations. In this regard, a single boron vacancy within hexagonal boron nitride (h-BN) lattice such as VB- defect has coherent quantum interfaces for spin and photonic qubits owing to the large band gap of h-BN (6 eV) that can shield a computational subspace from environmental noise. However, for a VB- defect in h-BN to be a potential quantum simulator, the design and characterization of the Hamiltonian involving mutual interactions of the defect and other degrees of freedom are needed to fully understand the effect of defects on the computational subspace. Here, we studied the key coupling tensors such as zero-field splitting, Zeeman effect, and hyperfine splitting in order to build the Hamiltonian of the VB- defect. These eigenstates are spin triplet states that form a computational subspace. To study the phonon-assisted single photon emission in the VB- defect, the Hamiltonian is characterized by electron-phonon interaction with Jahn-Teller distortions. A theoretical demonstration of how the VB- Hamiltonian is utilized to relate these quantum properties to spin- and photonic-quantum information processing. For selecting promising host 2D materials for spin and photonic qubits, we present a data-mining perspective based on the proposed Hamiltonian engineering of the VB- defect in which h-BN is one of four materials chosen to be room temperature qubit candidates.

Spin-Degeneracy Breaking and Parity Transitions in Three-Terminal Josephson Junctions

Hybrid Josephson junctions (JJs) realized in superconductor-semiconductor heterostructures host fermionic modes known as Andreev bound states (ABSs). In these structures, a promising and yet unexplored avenue for harnessing spin and parity degrees of freedom is offered by JJs with three or more superconducting terminals, where phase-induced spin polarization and transitions of the ground state to an odd parity were predicted to arise. Here we spectroscopically probe the two-dimensional band structure of ABSs in a phase-controlled InAs/Al three-terminal JJ. Andreev bands show signatures of spin-degeneracy breaking, with level splitting in excess of ∼9 GHz, and zero-energy crossings associated to ground state fermion parity transitions. Spin splitting and parity transitions are enabled and controlled by locally applied magnetic fluxes, in the absence of Zeeman effect or Coulomb blockade. Our results underscore the potential of multiterminal hybrid devices for phase engineering ABSs, with significant implications for spin- and parity-based quantum devices. Published by the American Physical Society 2024

Odd-frequency superfluidity from a particle-number-conserving perspective

We investigate odd-in-time—or —pairing of fermions in equilibrium systems within the particle-number-conserving framework of Penrose, Onsager, and Yang, where superfluid order is defined by macroscopic eigenvalues of reduced density matrices. We show that odd-frequency pair correlations are synonymous with even fermion-exchange symmetry in a time-dependent correlation function that generalises the two-body reduced density matrix. Macroscopic even-under-fermion-exchange pairing is found to emerge from conventional Penrose-Onsager-Yang condensation in two-body or higher-order reduced density matrices through the symmetry-mixing properties of the Hamiltonian. We identify and characterize a matrix responsible for producing macroscopic even fermion-exchange correlations that coexist with a conventional Cooper-pair condensate, while a matrix is shown to be responsible for creating macroscopic even fermion-exchange correlations from hidden orders such as a multiparticle condensate. The transformer scenario is illustrated using the spin-balanced s-wave superfluid with Zeeman splitting as an example. The generator scenario is demonstrated by the composite-boson condensate arising for itinerant electrons coupled to magnetic excitations. Structural analysis of the transformer and generator matrices is shown to provide general conditions for odd-frequency pairing order to arise in a given system. Our formalism facilitates a fully general derivation of the Meissner effect for odd-frequency superconductors that holds also beyond the regime of validity for mean-field theory. Published by the American Physical Society 2024

The CXSFIT spectral fitting code: Past, present and future.

Magnetically confined plasma experiments generate a wealth of spectroscopic data. The first step toward extracting physical parameters is to fit a spectral model to the often complex spectra. The CXSFIT (Charge eXchange Spectroscopy FITting) spectral fitting code was originally developed for fitting charge exchange spectra on JET from the late 1980s onward and has been further developed over decades to keep up with the needs of the users. The primary use is to efficiently fit a large number of spectra with many constrained Gaussian spectral lines of which the physical parameters can be coupled in a user-friendly manner. More recent additions to the code include time-dependent couplings between parameters, flexible background subtraction, and a non-linear coupling scheme between fit parameters. The latter was a pre-requisite for implementing Zeeman and motional Stark effect multiplets in the library of spectral features. The ability to save and replay "fit recipes," even when multiple iterations are required, has ensured the traceability of the results and is one of the keys to the longevity and success of the code. The code is also in use on other tokamaks (AUG, ST-40) and to fit data from other spectroscopic diagnostics on JET. In this paper, we document the current capabilities and philosophy behind the structure of the code, including some of the algorithms used to calculate spectral features numerically efficiently. We also provide an outline of how CXSFIT could be transferred into a framework that would be able to meet the spectral fitting requirements of future devices, such as ITER.

An Air-Stable Carbon-Centered Triradical with a Well-Addressable Quartet Ground State.

Organic polyradicals with a high-spin ground state and quantum magnetic properties suitable for spin manipulation are valuable materials for diverse innovative technologies, including quantum devices. However, the typically high reactivity and low stability of conventional polyradicals present a major obstacle to such applications. In this study, a highly stable carbon-centered triradical TR with a quartet ground state and excellent stability (τ1/2 of ∼90 days in air-saturated toluene at room temperature) is achieved, which shows apposite magnetic anisotropy and Zeeman splitting partition with favorable addressability. By virtue of the optimal stability, thorough structural and magnetic characterizations are realized. With X-ray crystallography unambiguously proving the molecular structure, the quartet ground state (ΔED-Q = 0.78 kcal/mol) is confirmed by the SQUID measurements, while the cw- and pulsed EPR techniques offer additional supportive evidence for the high-spin nature. Remarkably, owing to the easily attained magnetic anisotropy, selective excitations between different Zeeman splitting levels are successfully demonstrated with TR in its frozen toluene solution without the requirement for special alignment, which is unprecedented for organic polyradicals. Along with the millisecond spin-lattice relaxation and microsecond coherence time manifested by TR, this triradical is promising for potential coherent spin manipulation applications as a multienergy-level quantum information carrier.

Josephson Diode Effect in Parallel-Coupled Double-Quantum Dots Connected to Unalike Majorana Nanowires.

We study theoretically the Josephson diode effect (JDE) when realized in a system composed of parallel-coupled double-quantum dots (DQDs) sandwiched between two semiconductor nanowires deposited on an s-wave superconductor surface. Due to the combined effects of proximity-induced superconductivity, strong Rashba spin-orbit interaction, and the Zeeman splitting inside the nanowires, a pair of Majorana bound states (MBSs) may possibly emerge at opposite ends of each nanowire. Different phase factors arising from the superconductor substrate can be generated in the coupling amplitudes between the DQDs and MBSs prepared at the left and right nanowires, and this will result in the Josephson current. We find that the critical Josephson currents in positive and negative directions are different from each other in amplitude within an oscillation period with respect to the magnetic flux penetrating through the system, a phenomenon known as the JDE. It arises from the quantum interference effect in this double-path device, and it can hardly occur in the system of one QD coupled to MBSs. Our results also show that the diode efficiency can reach up to 50%, but this depends on the overlap amplitude between the MBSs, as well as the energy levels of the DQDs adjustable by gate voltages. The present model is realizable within current nanofabrication technologies and may find practical use in the interdisciplinary field of Majorana and Josephson physics.