Hyperfine Research Articles

Accurate hyperfine tensors for solid state quantum applications: case of the NV center in diamond

The decoherence of point defect qubits is often governed by the electron spin-nuclear spin hyperfine interaction that can be parameterized by using ab inito calculations in principle. So far most of the theoretical works have focused on the hyperfine interaction of the closest nuclear spins, while the accuracy of the predictions for distinct nuclear spins is barely discussed. Here we demonstrate for the case of the NV center in diamond that the absolute relative error of the computed hyperfine parameters can exceed 100% using an industry standards first-principles code. To overcome this issue, we implement an alternative method and report on significantly improved hyperfine values with O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{O}}}}}}}}$$\\end{document}(1%) relative mean error at all distances. The provided accurate hyperfine data for the NV center enables high-precision simulation of NV quantum nodes for quantum information processing and positioning of nuclear spins by comparing experimental and theoretical hyperfine data.

Nuclear magnetic resonance studies in a model transverse field Ising system

The suppression of ferroquadrupolar order in TmVO4 in a magnetic field is well-described by the transverse field Ising model, enabling detailed studies of critical dynamics near the quantum phase transition. We describe nuclear magnetic resonance measurements in pure and Y-doped single crystals. The non-Kramers nature of the ground state doublet leads to a unique form of the hyperfine coupling that exclusively probes the transverse field susceptibility. Our results show that this quantity diverges at the critical field, in contrast to the mean-field prediction. Furthermore, we find evidence for quantum critical fluctuations present near Tm-rich regions in Y-doped crystals at levels beyond which long-range order is suppressed, suggesting the presence of quantum Griffiths phases.

Isotope shifts in electron affinities and in binding energies of Pb and hyperfine structure of 207Pb.

The isotope shifts in electron affinities of Pb were measured by Walter et al. [Phys. Rev. A 106, L010801 (2022)] to be -0.002(4) meV for 207-208Pb and -0.003(4) meV for 206-208Pb by scanning the threshold of the photodetachment channel Pb-(S3/2◦4) - Pb (3P0), while Chen and Ning reported 0.015(25) and -0.050(22) meV for the isotope shifts on the binding energies measured relative to 3P2 using the SEVI method [J. Chem. Phys. 145, 084303 (2016)]. Here we revisited these isotope shifts by using our second-generation SEVI spectrometer and obtained -0.001(15) meV for 207-208Pb and -0.001(14) meV for 206-208Pb, respectively. In order to aid the experiment by theory, we performed the first abinitio theoretical calculations of isotope shifts in electron affinities and binding energies of Pb, as well as the hyperfine structure of 207Pb-, by using the MCDHF and RCI methods. The isotope shifts in electron affinities of 207-208Pb and 206-208Pb are -0.0023(8) and -0.0037(13) meV for the 3P0 channel, respectively, in good agreement with Walter et al.'s measurements. The isotope shifts in binding energies relative to 3P1,2, -0.0015(8) and -0.0026(13) meV for 207-208Pb and 206-208Pb, respectively, are compatible with the present measurements. The hyperfine constant for the ground state of 207Pb- obtained by the present calculations, A(S3/2◦4)=-1118 MHz, differs by a factor of 3 from the previous estimation by Bresteau et al. [J. Phys. B: At., Mol. Opt. Phys. 52, 065001 (2019)]. The reliability is supported by the good agreement between the theoretical and experimental hyperfine parameters of 209Bi.

On the “contact” hyperfine interaction

When Enrico Fermi analyzed the magnetic interaction between the electron and Na, Cs, and Rb nuclei in 1930, he used the Dirac equation to compute the energy of an electron interacting with a point charge and magnetic dipole (the nucleus) fixed at the origin. After the mathematical dust had settled, he found an interaction that appeared to act only at a single point: the center of the electron wavefunction; it has been called a contact interaction. In 1936, Casimir analyzed the magnetic interaction of proton and neutron spins in the ground state of the deuteron using the Schrödinger equation and classical electrodynamics. Using symmetries appropriate only to s states, and performing an integration by parts, he found that they, too, seemed to interact only at a single common point of the proton and neutron: their center-of-mass. When applied to hydrogen, his result agreed with Fermi's. We present an expanded version of Casimir's important but little-known calculation.

Influence of linearly polarized light on the transverse relaxation of ground-state 133Cs atoms

In order to obtain an understanding of the relationship between the optical absorption and the transverse relaxation, the influences of linearly polarized light respectively at 133Cs D1 and D2 lines on the transverse relaxation of ground-state 133Cs atoms are studied. Under different vapor temperatures, light intensities and light frequencies, transverse spin relaxation times are separately measured for 133Cs atoms in different hyperfine levels. For theoretically analyzing the measuring results, especially for an unusual trend that the transverse spin relaxation time rises with the increase of light intensity, photon absorption cross-sections of linearly polarized light by 133Cs atoms are simulated. The experimental results show that through influencing the optical absorption and spin-exchange collisions, the linearly polarized light plays a remarkable role in the transverse spin relaxation. The results obtained by this paper can provide a guide to find the optimal intensity and frequency of linearly polarized light in practical applications for decreasing the influences of linearly polarized light on the transverse relaxation.

Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations

Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron correlation effects. In multiconfiguration calculations, the wave functions are expanded in terms of configuration state functions (CSFs) built from sets of one-electron orbitals. The orbital sets are typically enlarged within the layer-by-layer approach. The calculations are energy-driven, and orbitals in each new layer of correlation orbitals are spatially localized in regions where the weighted total energy decreases the most, overlapping and breaking up different closed core subshells in an irregular pattern. As a result, hyperfine structure constants, computed as expectation values of the hyperfine operators, often show irregular or oscillating convergence patterns. Large orbital sets, and associated large CSF expansions, are needed to obtain converged values of the hyperfine structure constants. We analyze the situation for the states of the {2s22p3,2s22p23p,2s22p24p} odd and {2s22p23s,2s2p4,2s22p24s,2s22p23d} even configurations in N I, and show that the convergence with respect to the increasing sets of orbitals is radically improved by introducing separately optimized orbital sets targeted for describing the spin- and orbital-polarization effects of the 1s and 2s core subshells that are merged with, and orthogonalized against, the ordinary energy-optimized orbitals. In the layer-by-layer approach, the spectroscopic orbitals are kept frozen from the initial calculation and are not allowed to relax in response to the introduced layers of correlation orbitals. To compensate for this lack of variational freedom, the orbitals are transformed to natural orbitals prior to the final calculation based on single and double substitutions from an increased multireference set. The use of natural orbitals has an important impact on the states of the 2s22p23s configuration, bringing the corresponding hyperfine interaction constants in closer agreement with experiment. Relying on recent progress in methodology, the multiconfiguration calculations are based on configuration state function generators, cutting down the time for spin-angular integration by factors of up to 50, compared to ordinary calculations.

A Reappraisal of the S2 State of Nature's Water Oxidizing Complex in Its Low and High Spin Forms.

Density functional theory calculated 14N hyperfine couplings are obtained for the Mn1 ligated π-N of residue His332 of the photosystem 2 water oxidizing complex. An open cubane, O4H, model closely matches the experimental coupling obtained for the high spin S = 5/2 form of the S2 state, supporting an open cubane structure for this state. We also investigate the unusual geometric features for the S2 state obtained by X-ray free electron laser structure determinations and rationalize it as an equilibrium occurring at room temperature between W1/O4 deprotonated and protonated forms of the open cubane structure.

On the optimality of the radical-pair quantum compass

Quantum sensing enables the ultimate precision attainable in parameter estimation. Circumstantial evidence suggests that certain organisms, most notably migratory songbirds, also harness quantum-enhanced magnetic field sensing via a radical-pair-based chemical compass for the precise detection of the weak geomagnetic field. However, what underpins the acuity of such a compass operating in a noisy biological setting, at physiological temperatures, remains an open question. Here, we address the fundamental limits of inferring geomagnetic field directions from radical-pair spin dynamics. Specifically, we compare the compass precision, as derived from the directional dependence of the radical-pair recombination yield, to the ultimate precision potentially realisable by a quantum measurement on the spin system under steady-state conditions. To this end, we probe the quantum Fisher information and associated Cramér–Rao bound in spin models of realistic complexity, accounting for complex inter-radical interactions, a multitude of hyperfine couplings, and asymmetric recombination kinetics, as characteristic for the magnetosensory protein cryptochrome. We compare several models implicated in cryptochrome magnetoreception and unveil their optimality through the precision of measurements ostensibly accessible to nature. Overall, the comparison provides insight into processes honed by nature to realise optimality whilst constrained to operating with mere reaction yields. Generally, the inference of compass orientation from recombination yields approaches optimality in the limits of complexity, yet levels off short of the theoretical optimal precision bounds by up to one or two orders of magnitude, thus underscoring the potential for improving on design principles inherent to natural systems.

Ligand Effects on the Spin Relaxation Dynamics and Coherent Manipulation of Organometallic La(II) Potential Qudits.

We present pulsed electron paramagnetic resonance (EPR) studies on three La(II) complexes, [K(2.2.2-cryptand)][La(Cp')3] (1), [K(2.2.2-cryptand)][La(Cp″)3] (2), and [K(2.2.2-cryptand)][La(Cptt)3] (3), which feature cyclopentadienyl derivatives as ligands [Cp' = C5H4SiMe3; Cp″ = C5H3(SiMe3)2; Cptt = C5H3(CMe3)2] and display a C3 symmetry. Long spin-lattice relaxation (T1) and phase memory (Tm) times are observed for all three compounds, but with significant variation in T1 among 1-3, with 3 being the slowest relaxing due to higher s-character of the SOMO. The dephasing times can be extended by more than an order of magnitude via dynamical decoupling experiments using a Carr-Purcell-Meiboom-Gill (CPMG) sequence, reaching 161 μs (5 K) for 3. Coherent spin manipulation is performed by the observation of Rabi quantum oscillations up to 80 K in this nuclear spin-rich environment (1H, 13C, and 29Si). The high nuclear spin of 139La (I = 7/2), and the ability to coherently manipulate all eight hyperfine transitions, makes these molecules promising candidates for application as qudits (multilevel quantum systems featuring d quantum states; d >2) for performing quantum operations within a single molecule. Application of HYSCORE techniques allows us to quantify the electron spin density at ligand nuclei and interrogate the role of functional groups to the electron spin relaxation properties.

Finite nuclear mass correction to the hyperfine splitting in hydrogenic systems

Finite nuclear mass correction to the hyperfine splitting in hydrogenic systems

Morphology, physical, and structural aspects of copper nanoparticles induced- metal phosphate nanocompounds for gamma ray shielding and magnetic sensing applications

The inorganic nanocompounds were synthesized by solid state reaction with the composition 10Li2O+(30-x)Sb2O3 + xZnO + 59.5P2O5 + 0.5Cu (in mol%). SEM morphographs of the samples confirmed the grain size ≈0.5–2.5 μm. The EDAX spectra of the samples confirmed presence of copper (Cu) nanoparticles (<2 wt%) in the composition. The EDAX studies showed energy dispersion of Kα- photons by reactivity of elements P, Cu, and Zn, while the element Sb has shown dispersion of Lα- photons up to 10 keV. Mass attenuation coefficient (MAC) has exhibited a few discontinuities (bumps) at low energies (<10 keV) due to K, L- absorption edges of various elements (such as P, Cu, Zn, and Sb) presented in the samples. The shrinking of Phosphorous-Phosphorous separation (dP-P) from 4.716 Ao to 3.990 Ao indicated the greater solidity (or density) of the prepared nanocompounds at higher content of ZnO. XRD spectra showed the presence of major crystallites such as LiPO3, Li3PO4, Li6P6018, SbPO4, Cu3PO4, Cu2P2O7, Cu3[PO4]2, Zn[PO3]2, Zn2P2O7, ZnP4O11, and LiZnPO4 in the prepared nanocompounds. The average crystallite size was determined in the range of 35–83 nm. FTIR spectra of these compounds displayed the [PO2]−, [PO3]−, [PO4]3−, and [ZnO4] units along with linkages P─O─P, O─P─O, Sb─O─Sb, Cu─O─Cu, etc. A band due to vibrations of Cu─O bond has been observed in the range of 466–478 cm−1, which endorses the contribution of copper nanoparticles in the solid state reaction of the metal phosphate nanocompounds. A partially resolved hyperfine structure of magnetic resonance signals corresponding to g|| ≈2.4 and g⊥ ≈2.05 were observed due to the presence of an anisotropic hyperfine interaction of the electron spin (S = 1/2) with the nuclear spin (I = 3/2) of copper isotopes (63Cu and 65Cu) in the samples.

Vanadium in silicon carbide: telecom-ready spin centres with long relaxation lifetimes and hyperfine-resolved optical transitions

Vanadium in silicon carbide (SiC) is emerging as an important candidate system for quantum technology due to its optical transitions in the telecom wavelength range. However, several key characteristics of this defect family including their spin relaxation lifetime (T1), charge state dynamics, and level structure are not fully understood. In this work, we determine the T1 of an ensemble of vanadium defects, demonstrating that it can be greatly enhanced at low temperature. We observe a large spin contrast exceeding 90% and long spin-relaxation times of up to 25 s at 100 mK, and of order 1 s at 1.3 K. These measurements are complemented by a characterization of the ensemble charge state dynamics. The stable electron spin furthermore enables high-resolution characterization of the systems’ hyperfine level structure via two-photon magneto-spectroscopy. The acquired insights point towards high-performance spin-photon interfaces based on vanadium in SiC.

New energy levels of atomic holmium discovered by laser spectroscopy in the near infrared spectral range

A combination of optogalvanic spectroscopy and laser-induced fluorescence spectroscopy with a continuous wave tunable single mode Ti-Sa laser was applied to find new energy levels of atomic holmium. Free and excited holmium atoms were produced in a liquid nitrogen-cooled hollow-cathode lamp. In this study, we examined 35 spectral lines of Ho I in the near-infrared wavelength range from 698 nm to 833 nm. Altogether, 16 new energy levels have been discovered, 5 levels of even parity and 11 levels of odd parity. Another four energy levels have been discovered but have already been published by another research group. Data on the hyperfine structure for the new levels are presented. Additionally, hyperfine structure data of three known levels of even parity were determined for the first time. The existence of the new energy levels was confirmed by analyzing 60 lines of previously measured Fourier transform spectra to precisely determine the energy of the levels.

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 = 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.

The heavy atom structure, "cis effect" on methyl internal rotation, and 14N nuclear quadrupole coupling of 1-cyanopropene from quantum chemical and microwave spectroscopic analysis.

The microwave spectrum of 1-cyanopropene (crotonitrile) was remeasured using two pulsed molecular jet Fourier transform microwave spectrometers operating from 2.0 to 40.0 GHz. The molecule exists in two isomer forms, E and Z, with respect to the orientation between the methyl and the cyano groups. The spectrum of the Z isomer is more intense. Due to internal rotation of the methyl group, doublets containing A and E torsional species were found for all rotational transitions. Hyperfine splittings arising from the 14N nuclear quadrupole coupling were resolved. The heavy atom structure of the Z isomer was determined by observation of 13C and 15N isotopologue spectra in natural abundances. The experimental results were supported by quantum chemistry. The complex spectral patterns were analyzed and fitted globally, and the barriers to methyl internal rotation are determined to be 478.325(28) cm-1 and 674.632(76) cm-1 for the Z and E isomers, respectively. The non-bonded intramolecular electrostatic attraction between the methyl group and the 1-cyano substituent overcomes steric hindrance, leading to higher stability of the Z isomer. The consequence is a slight opening of 3.2° of the C(1)-C(2)-C(3) angle and a radical decrease of the methyl torsional barrier in the Z isomer due to steric repulsion.

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.