Hyperfine Research Articles

Sweet-spot operation of a germanium hole spin qubit with highly anisotropic noise sensitivity

Spin qubits defined by valence band hole states are attractive for quantum information processing due to their inherent coupling to electric fields, enabling fast and scalable qubit control. Heavy holes in germanium are particularly promising, with recent demonstrations of fast and high-fidelity qubit operations. However, the mechanisms and anisotropies that underlie qubit driving and decoherence remain mostly unclear. Here we report the highly anisotropic heavy-hole g-tensor and its dependence on electric fields, revealing how qubit driving and decoherence originate from electric modulations of the g-tensor. Furthermore, we confirm the predicted Ising-type hyperfine interaction and show that qubit coherence is ultimately limited by 1/f charge noise, where f is the frequency. Finally, operating the qubit at low magnetic field, we measure a dephasing time of T2*\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${T}_{2}^{* }$$\\end{document} = 17.6 μs, maintaining single-qubit gate fidelities well above 99% even at elevated temperatures of T > 1 K. This understanding of qubit driving and decoherence mechanisms is key towards realizing scalable and highly coherent hole qubit arrays.

An electric-field-assisted magnetic trap for cold molecular evaporative cooling: Toward molecular Bose–Einstein condensation

Ultracold molecules provide fundamental new insights into molecular interaction dynamics in the quantum regime and represent a new platform for chemical physics where quantum behaviors play a dominant role in molecular interaction and dynamics. An electric-field-assisted magnetic trap for trapping and further evaporative cooling of cold molecules to ultracold regime is proposed utilizing the perturbation of the hyperfine levels in a mixed field, and the depth of the trap can be tuned by adjusting the assisted electric field rapidly. Thus, the evaporative cooling of [Formula: see text]I[Formula: see text]Br molecules in the [Formula: see text] state of the rovibronic ground state is simulated. It shows that IBr molecules would be cooled from 26[Formula: see text][Formula: see text]K to 556[Formula: see text]nK within 598.9[Formula: see text]ms and eventually we would obtain a number of [Formula: see text] molecules in a volume of [Formula: see text][Formula: see text]cm3 with the number density of [Formula: see text][Formula: see text]cm[Formula: see text]. The Bose–Einstein condensation of the alkali diatomic molecules would probably be realized in the proposed trap if the present experimentally available samples are loaded.

Relativistic Quantum Chemical Investigation of Actinide Covalency Measured by Electron Paramagnetic Resonance Spectroscopy.

We investigate actinide covalency effects in two [AnCptt3] (An = Th, U) complexes recently studied with pulsed electron paramagnetic resonance spectroscopy, using the Hyperion package to obtain relativistic hyperfine coupling constants from relativistic multiconfigurational wave functions. 1H and 13C HYSCORE simulations using the computed parameters show excellent agreement with the experimental data, highlighting the accuracy of modern relativistic ab initio methods. The extent of covalency indicated from the calculations on [ThCptt3] is in agreement with the original report based on traditional spectral fitting methods, while the covalency in [UCptt3] is found to be previously overestimated. The latter is due to the paramagnetic spin-orbit effect that arises naturally in a relativistic theory of hyperfine coupling and yet was not accounted for in the original study, thus highlighting the necessity of relativistic approaches for the interpretation of magnetic resonance data pertaining to actinides.

Analysis of early intermediate states of the nitrogenase reaction by regularization of EPR spectra

Due to the complexity of the catalytic FeMo cofactor site in nitrogenases that mediates the reduction of molecular nitrogen to ammonium, mechanistic details of this reaction remain under debate. In this study, selenium- and sulfur-incorporated FeMo cofactors of the catalytic MoFe protein component from Azotobacter vinelandii are prepared under turnover conditions and investigated by using different EPR methods. Complex signal patterns are observed in the continuous wave EPR spectra of selenium-incorporated samples, which are analyzed by Tikhonov regularization, a method that has not yet been applied to high spin systems of transition metal cofactors, and by an already established grid-of-error approach. Both methods yield similar probability distributions that reveal the presence of at least four other species with different electronic structures in addition to the ground state E0. Two of these species were preliminary assigned to hydrogenated E2 states. In addition, advanced pulsed-EPR experiments are utilized to verify the incorporation of sulfur and selenium into the FeMo cofactor, and to assign hyperfine couplings of 33S and 77Se that directly couple to the FeMo cluster. With this analysis, we report selenium incorporation under turnover conditions as a straightforward approach to stabilize and analyze early intermediate states of the FeMo cofactor.

Theoretical insights into long-range coupling of electron-hole pairs in TCTA–PO-T2T exciplex

This work reports theoretical investigations concerning long-range coupling of electron-hole pairs in spatially separated exciplex (SSE) systems via Density Functional Theory and Time-Dependent Density Functional Theory. Based on TCTA−PO-T2T parent exciplex, where 4,4′,4″-Tris(carbazol-9-yl)triphenylamine (TCTA) serves as donor (D) and 2,4,6-Tris[3-(diphenylphosphinyl)phenyl]-1,3,5-triazine (PO-T2T) as acceptor (A), SSEs are constructed by intentionally tuning the D−A distance. The calculation results demonstrate that all SSEs, even if the D−A distance is over 14 Å, exhibit the clear and strong charge transfer character in terms of DCT, qCT, and t indexes. As the D−A distance increases, the energy gap of SSEs is increased, resulting in the blueshift of emission spectra. Calculation and experiment results show a good consistency, indicating that our model could well describe SSEs. Meanwhile, the reduced energy gap between CT and 3LE and more degenerate states could boost reverse intersystem crossing via vibronic coupling and hyperfine coupling, eventually improving the electroluminescent performance of SSEs. Our study suggests that manipulation of relative energy alignment via controlling D−A distance not only promotes the properties of exciplexes, but also offers guidance for designing thermally activated delayed fluorescence emitters through-space charge transfer.

Effect of charge on the rotation of prolate nitroxide spin probes in room-temperature ionic liquids

We have studied the rotational diffusion of two prolate nitroxide probes, the doubly negatively charged peroxylamine disulfonate (Frémy's salt − FS) and neutral di-tert-butyl nitroxide (DTBN), in a series of 1-alkyl-3-methylimidazolium tetrafluoroborate room-temperature ionic liquids (RTILs) having alkyl chain lengths from two to eight carbons using electron paramagnetic resonance (EPR) spectroscopy. Though the size and shape of the probes are reasonably similar, they behave differently due to the charge difference. The rotation of FS is anisotropic, and the rotational anisotropy increases with the alkyl chain length of the cation, while the rotation of DTBN is isotropic. The hyperfine coupling constant of DTBN decreases as a function of the alkyl chain length and is proportional to the relative permittivity of ionic liquids. On the other hand, the hyperfine coupling constant of FS increases with increasing chain length. These behaviors indicate the location of each probe in RTILs. FS is likely located in the polar region near the network of charged imidazolium ions. DTBN molecules are predominately distributed in the nonpolar domains.

Dual-mode rectangular microwave cavity for precision spectroscopy of hyperfine structure in muonium

Precision microwave spectroscopy of the ground-state hyperfine structure in muonium provides a stringent test of the Standard Model in particle physics. The MuSEUM collaboration is preparing for such a measurement, aiming for precision down to ≈1ppb, utilizing the world’s most intense pulsed muon beam at J-PARC. The measurement of the Zeeman-split structure with an external magnetic field of 1.7T also precisely determines the muon’s magnetic moment (≈10ppb). In the future, improved precision of the magnetic moment can be potentially obtained by measurements with different magnetic field strengths, however, it entails upgrading current cylindrical microwave cavities to rectangular ones. As the first step for the upgrade, we have developed a dual-mode rectangular cavity for the measurement with 2.9T field. The electromagnetic design and production have been established, and frequency sweeping with two desired modes has been successfully demonstrated. Moreover, the overall performance of the measurement at 2.9T field was evaluated with Monte Carlo simulations. These studies pave the way for a further extension of the MuSEUM experiment at various strengths of the magnetic fields.

Long-lived photoinduced charge separation in adamantane-bridged donor-acceptor dyads: A case of adamantane bridge conferring orthogonal donor-acceptor orientation and restricted rotation

Design of compact donor-acceptor dyads that can exhibit charge separated (CS) state lifetimes extending to the microsecond time domain remains a major challenge even today. A simple but effective design strategy that can lead to long CS state lifetimes, in at least a few compact dyads, is still elusive. Herein we propose that use of adamantane (AD) as bridge can enhance CS state lifetimes in small molecule donor-acceptor dyads. This paper reports AD-bridged dyads, AN-AD-NB and PY-AD-NB, wherein the anthracene (or pyrene) donor and nitrobenzene acceptor are attached to bridgehead positions of AD. The singlet CS states generated upon irradiation were long-lived (lifetimes >1 μs) and decayed to the ground and local triplet states, simultaneously. Electron transfer reactions of the CS state with secondary donor and acceptor established that the CS state is sufficiently long-lived to participate in intermolecular reactions. X-ray crystal structure of the AN-AD-NB dyad reveals that the donor and acceptor are orthogonally oriented, which reduces the donor-acceptor interaction, and thereby the charge recombination rate, significantly. By analysing the X-ray structure, we predict that all adamantane-bridged compact dyads will have orthogonal donor-acceptor orientation and exhibit long-lived CS states. We also report studies with bisadamantyl-substituted dyads and the results confirmed that the local triplets are formed from the CS state through hyperfine interaction. Based on our work we propose that the hyperfine interaction, which is not expected to occur in compact dyads because of the short donor-acceptor separation, can indeed occur if the CS state is sufficiently long-lived.

Magnetic hyperfine interactions of probe 57Fe atoms within the hexagonal manganite ScMnO3

Here we present the Mössbauer study of the combined magnetic and electrical hyperfine interactions of the probe 57Fe nuclei localized in the hexagonal manganite ScMnO3. The hyperfine interactions were measured in the temperature range where ScMnO3 demonstrates spin ordering: 15 K <T <TN (∼ 130 K). By analyzing the hyperfine parameters of 57Fe nuclei, we evaluated the oxidation state of the iron ions, their local crystal environment, and the orientation of the magnetic moments μFe in the structure of ScMn0.99657Fe0.004O3 at T <<TN. The temperature-dependent evolution of Zeeman structures in Mössbauer spectra was analyzed using the stochastic relaxation model, and indicates the presence of frustration of the superexchange interactions Fe3+−O−Mn3+. The temperature dependence of the hyperfine magnetic field Bhf(T) was described using critical indices, whose values reflect the reduced dimensionality of the magnetic system under study. It was shown that the observed sharp temperature-dependent change of the quadrupole shift of the Zeeman structure components may be attributed to the spin reorientation process, resulting in antiferromagnetism with a weak ferromagnetic component.

The excitation energies and hyperfine structures for 2l, 3l states in lithiumlike ions

Combining the multi-configuration Dirac–Hartree–Fock method and the model-quantum electrodynamics (QED) approach, the wave functions, transition energies and hyperfine structure constants for 2l, 3l states in Li-like Ne7+, Mg9+, Al10+, P12+, Ar15+ and Ca17+ ions are calculated. The effects of electron correlation, Breit interactions, nuclear recoil and QED effects are analyzed in detail. We find that the contribution of the non-diagonal elements of the self-energy is significant for the 2p1/2→2s1/2 and 2p3/2→2s1/2 transitions. However, for the 3l→2s1/2 transitions, the contribution of non-diagonal elements is small. The accuracy of the currently calculated hyperfine structure constants is expected to be within 1%.

A Faraday laser locked to 87Rb D2 line

We present a single-frequency Faraday laser utilizing a 5-Torr-Ar-mixed 85Rb atomic filter as a frequency-selecting element, and lock it to 87Rb D2 line via modulation transfer spectroscopy (MTS). The wavelength of the free-running Faraday laser fluctuated between 780.2457 and 780.2470 nm, which was limited within the ultra-narrow transmission bandwidth (700 MHz) of the atomic filter. When the Faraday laser was stabilized to 87Rb 52S1/2 F = 2 → 52P3/2 F′ = 3 hyperfine transition line, the output wavelength of the laser was approximately 780.24602 nm, and the fractional frequency Allan deviation measured by residual error signal arrived at 2.87 × 10−14 at 1 s, then reached 1.25 × 10−14 at 100 s. The laser system is easy to be locked to 87Rb D2 line within the current range of laser diode (LD) from 75 to 140 mA, which has the potential to achieve a “turnkey” systems and is suitable for laser-pumped rubidium atomic clocks and laser-cooling experiments.

Magnetic ground states and hyperfine interactions in YMnO[formula omitted] using density functional theory

This study employs the Local Density functional theory (DFT) and the DFT+U extension, to better describe the localized d-Mn states, and therefore analyze six magnetic configurations of the Mn ions in hexagonal manganite YMnO3. The respective study was complemented through hyperfine interaction calculations of different atomic configurations. Our focus is on six distinct magnetic configurations, complemented by thorough Hyperfine Interactions (HFI) calculations targeting the most plausible configuration. We find the P6’3 and P63 configurations are the most probable, aligning with previous research in the field. These configurations also show a strong correlation with experimental observations of magnetic moments, providing new insights into the magnetic ordering of YMnO3. Our results highlight the intricate relationship between magnetic moments and the lattice structure of YMnO3, offering valuable insights into the material’s magnetic properties.

Rotational Spectrum of the Phenoxy Radical.

We report the hyperfine-resolved rotational spectrum of the gas-phase phenoxy radical in the 8-25 GHz frequency range using cavity Fourier transform microwave spectroscopy. A complete assignment of its complex but well-resolved fine and hyperfine splittings yielded a precisely determined set of rotational constants, spin-rotation parameters, and nuclear hyperfine coupling constants. These results are interpreted with support from high-level quantum chemical calculations to gain detailed insight into the distribution of the unpaired π electron in this prototypical resonance-stabilized radical. The accurate laboratory rest frequencies enable studies of the chemistry of phenoxy in both the laboratory and space. The prospects of extending the present experimental and theoretical techniques to investigate the rotational spectra of isotopic variants and structural isomers of phenoxy and other important gas-phase radical intermediates that are yet undetected at radio wavelengths are discussed.

Mechanisms of Ligand Hyperfine Coupling in Transition-Metal Complexes: σ and π Transmission Pathways.

Theoretical interpretation of hyperfine interactions was pioneered in the 1950s-1960s by the seminal works of McConnell, Karplus, and others for organic radicals and by Watson and Freeman for transition-metal (TM) complexes. In this work, we investigate a series of octahedral Ru(III) complexes with aromatic ligands to understand the mechanism of transmission of the spin density from the d-orbital of the metal to the s-orbitals of the ligand atoms. Spin densities and spin populations underlying ligand hyperfine couplings are analyzed in terms of π-conjugative or σ-hyperconjugative delocalization vs spin polarization based on symmetry considerations and restricted open-shell vs unrestricted wave function analysis. The transmission of spin density is shown to be most efficient in the case of symmetry-allowed π-conjugative delocalization, but when the π-conjugation is partially or fully symmetry-forbidden, it can be surpassed by σ-hyperconjugative delocalization. Despite a lower spin population of the ligand in σ-hyperconjugative transmission, the hyperfine couplings can be larger because of the direct involvement of the ligand s-orbitals in this delocalization pathway. We demonstrate a quantitative correlation between the hyperfine couplings of aromatic ligand atoms and the characteristics of the metal-ligand bond modulated by the trans substituent, a hyperfine trans effect.

Magnetic hyperfine interaction made easier

We present two derivations of the hyperfine interaction in the ground state of hydrogen using classical electrodynamics. We calculate, at the site of the proton moment m→p, the magnetic field B→e due to the magnetization source M→e(r→) of the relatively extended 1 s electron state. This gives the magnetic interaction via −m→p·B→e. One derivation applies the Biot–Savart law to the bound 1 s electric current J→b=∇→×M→ to directly find B→e; the other derivation applies the magnetic version of the Coulomb Law to the bound 1 s magnetic charge density ρb=−∇→·M→ to first obtain μ0H→e and then adds μ0M→ to find B→e. We show, for any source M→, that these two approaches give the same B→(r→), as is expected within classical electrodynamics.

Phase locking and absolute frequency stabilization of laser sources for a Pr:YSO quantum memory

We propose a scheme to phase lock a quantum-memory control laser, frequency-conversion pump laser, and two-photon source over three octaves in frequency to operate a quantum memory. The absolute frequencies of the laser sources are determined based on a Doppler-free iodine hyperfine transition. The achieved relative frequency instability and uncertainty were ≤1 × 10–12 and 3 × 10–11, respectively, which are below the requirement for operating a Pr:YSO quantum memory. This scheme simplifies the instrumentation of laser sources in a quantum repeater, and increases the reliability of quantum communication systems.

Paramagnetic Effects in NMR Spectroscopy of Transition-Metal Complexes: Principles and Chemical Concepts.

ConspectusMagnetic resonance techniques represent a fundamental class of spectroscopic methods used in physics, chemistry, biology, and medicine. Electron paramagnetic resonance (EPR) is an extremely powerful technique for characterizing systems with an open-shell electronic nature, whereas nuclear magnetic resonance (NMR) has traditionally been used to investigate diamagnetic (closed-shell) systems. However, these two techniques are tightly connected by the electron-nucleus hyperfine interaction operating in paramagnetic (open-shell) systems. Hyperfine interaction of the nuclear spin with unpaired electron(s) induces large temperature-dependent shifts of nuclear resonance frequencies that are designated as hyperfine NMR shifts (δHF).Three fundamental physical mechanisms shape the total hyperfine interaction: Fermi-contact, paramagnetic spin-orbit, and spin-dipolar. The corresponding hyperfine NMR contributions can be interpreted in terms of through-bond and through-space effects. In this Account, we provide an elemental theory behind the hyperfine interaction and NMR shifts and describe recent progress in understanding the structural and electronic principles underlying individual hyperfine terms.The Fermi-contact (FC) mechanism reflects the propagation of electron-spin density throughout the molecule and is proportional to the spin density at the nuclear position. As the imbalance in spin density can be thought of as originating at the paramagnetic metal center and being propagated to the observed nucleus via chemical bonds, FC is an excellent indicator of the bond character. The paramagnetic spin-orbit (PSO) mechanism originates in the orbital current density generated by the spin-orbit coupling interaction at the metal center. The PSO mechanism of the ligand NMR shift then reflects the transmission of the spin polarization through bonds, similar to the FC mechanism, but it also makes a substantial through-space contribution in long-range situations. In contrast, the spin-dipolar (SD) mechanism is relatively unimportant at short-range with significant spin polarization on the spectator atom. The PSO and SD mechanisms combine at long-range to form the so-called pseudocontact shift, traditionally used as a structural and dynamics probe in paramagnetic NMR (pNMR). Note that the PSO and SD terms both contribute to the isotropic NMR shift only at the relativistic spin-orbit level of theory.We demonstrate the advantages of calculating and analyzing the NMR shifts at relativistic two- and four-component levels of theory and present analytical tools and approaches based on perturbation theory. We show that paramagnetic NMR effects can be interpreted by spin-delocalization and spin-polarization mechanisms related to chemical bond concepts of electron conjugation in π-space and hyperconjugation in σ-space in the framework of the molecular orbital (MO) theory. Further, we discuss the effects of environment (supramolecular interactions, solvent, and crystal packing) and demonstrate applications of hyperfine shifts in determining the structure of paramagnetic Ru(III) compounds and their supramolecular host-guest complexes with macrocycles.In conclusion, we provide a short overview of possible pNMR applications in the analysis of spectra and electronic structure and perspectives in this field for a general chemical audience.

Numerical studies on lutetium isotopic selective photoionization based on a three-step ionization scheme

Numerical studies of lutetium selective photoionization have been carried out based on a three-step photoionization scheme, 5d6s2 2D3/2 → 5d6s6p4Fo5/2 → 5d6s7s4D3/2 → (53,375 cm−1)1/2 → Lu+, by the density matrix theory. Atomic hyperfine structures and magnetic sublevels are considered in our photoionization dynamics model. To examine the effectiveness of this model, the simulated 176Lu ion strengths are compared with the experimental results, and the simulated excitation cross sections of 176Lu excitation channels are compared with the analytical and experimental results. Semi-quantitative agreements are acquired for these two cases. On this basis, selective photoionization processes of two lutetium isotopes are simulated and discussed. Considering the ionization probability and abundance of target isotope, the 8.5-9.5-8.5 two-step excitation channel is optimal for 176Lu enrichment from natural lutetium. The influences of laser parameters and atomic Doppler broadening are presented numerically and optimization excitation conditions are identified. For the co-propagating excitation lasers, extra-narrow laser bandwidth (at the magnitude of 0.1 GHz) and atomic Doppler broadening (smaller than 0.3 GHz) is required. A new time-delayed configuration is proposed to implement multiple counter-propagating laser exposures for high target isotope abundance at the larger atomic Doppler broadening.

Investigations on the defect structures for Mn2+ in CdSe nanocrystals and bulk materials and the criterion of occupation for Mn2+ in CdX (X = S, Se, Te) nanocrystals.

The spin Hamiltonian parameters and defect structures are theoretically studied for the substitutional Mn2+ at the core of CdSe nanocrystals and in the bulk materials from the perturbation calculations of spin Hamiltonian parameters for trigonal tetrahedral 3d5 clusters. Both the crystal-field and charge transfer contributions are taken into account in the calculations from the cluster approach. The impurity-ligand bond angles are found to be about 1.84° larger and 0.10° smaller in the CdSe:Mn2+ nanocrystals and bulk materials, respectively, than those (≈109.37°) of the host Cd2+ sites. The quantitative criterion of occupation (at the core or surface) for Mn2+ in CdX (X = S, Se, Te) nanocrystals is presented for the first time based on the inequations of hyperfine structure constants (HSCs). This criterion is well supported by the experimental HSCs data of Mn2+ in CdX nanocrystals. The previous assignments of signals SI as Mn2+ at the core of CdS nanocrystals are renewed as Mn2+ at the surface based on the above criterion. The present studies would be helpful to achieve convenient determination of occupation for Mn2+ impurities in CdX semiconductor nanocrystals by means of spectral (e.g., HSCs) analysis.

Rotational spectrum, structure, and quadrupole coupling of cyclopropylchloromethyldifluorosilane.

Cyclopropylchloromethyldifluorosilane, c-C3H5SiF2CH2Cl, has been synthesized, and its rotational spectrum has been recorded by chirped-pulse Fourier transform microwave spectroscopy. The spectral analysis of several isotopologues indicates the presence of two distinct conformations in the free-jet expansion, which are interconvertible through a rotation of the chloromethyl group. A partial substitution structure is presented for the lower energy conformation and is compared to the equilibrium structure obtained from quantum chemical calculations. Additionally, the presence of the chlorine nucleus leads to the rotational transitions splitting into multiple hyperfine components and χaa, a measure of the electric field gradient along the a axis, is unusually small at merely +0.1393(73) MHz. Various common abinitio and density functional theory methods fail to predict good quadrupole coupling constants (in the principal axis system) that adequately reproduce the observed hyperfine splitting, although diagonalizing the quadrupole coupling tensor from the principal axis system into a nucleus-centered axis system reveals that, overall, these methods calculate reasonably the electric field gradient about the chlorine nucleus. Finally, a total of nine electric dipole forbidden, quadrupole allowed transitions are observed in the rotational spectra of the parent species of the higher energy conformation and the 37Cl isotopologue of the lower energy conformation. These include those of x-type (no change in parity of Ka or Kc), which, to our knowledge, is the first time such transitions have been observed in a chlorine-containing molecule.