Electron-nuclear Hyperfine Coupling Research Articles

An electrically driven single-atom "flip-flop" qubit.

The spins of atoms and atom-like systems are among the most coherent objects in which to store quantum information. However, the need to address them using oscillating magnetic fields hinders their integration with quantum electronic devices. Here, we circumvent this hurdle by operating a single-atom "flip-flop" qubit in silicon, where quantum information is encoded in the electron-nuclear states of a phosphorus donor. The qubit is controlled using local electric fields at microwave frequencies, produced within a metal-oxide-semiconductor device. The electrical drive is mediated by the modulation of the electron-nuclear hyperfine coupling, a method that can be extended to many other atomic and molecular systems and to the hyperpolarization of nuclear spin ensembles. These results pave the way to the construction of solid-state quantum processors where dense arrays of atoms can be controlled using only local electric fields.

Large 31P-NMR enhancements in liquid state dynamic nuclear polarization through radical/target molecule non-covalent interaction.

Dynamic nuclear polarization (DNP) is a method to enhance the low sensitivity of nuclear magnetic resonance (NMR) via spin polarization transfer from electron spins to nuclear spins. In the liquid state, this process is mediated by fast modulations of the electron-nuclear hyperfine coupling and its efficiency depends strongly on the applied magnetic field. A peculiar case study is triphenylphosphine (PPh3) dissolved in benzene and doped with BDPA radical because it gives 31P-NMR signal enhancements of two orders of magnitude up to a magnetic field of 14.1 T. Here we show that the large 31P enhancements of BDPA/PPh3 in benzene at 1.2 T (i) decrease when the moieties are dissolved in other organic solvents, (ii) are strongly reduced when using a nitroxide radical, and (iii) vanish with pentavalent 31P triphenylphosphine oxide. Those experimental observations are rationalized with numerical calculations based on density functional theory that show the tendency of BDPA and PPh3 to form a weak complex via non-covalent interaction that leads to large hyperfine couplings to 31P (ΔAiso ≥ 13 MHz). This mechanism is hampered in other investigated systems. The case study of 31P-DNP in PPh3 is an important example that extends the current understanding of DNP in the liquids state: non-covalent interactions between radical and target can be particularly effective to obtain large NMR signal enhancements.

Ab-initio calculations of shallow dopant qubits in silicon from pseudopotential and all-electron mixed approach

Obtaining an accurate first-principle description of the electronic properties of dopant qubits is critical for engineering and optimizing high-performance quantum computing. However, density functional theory (DFT) has had limited success in providing a full quantitative description of these dopants due to their large wavefunction extent. Here, we build on recent advances in DFT to evaluate phosphorus dopants in silicon on a lattice comprised of 4096 atoms with hybrid functionals on a pseudopotential and all-electron mixed approach. Remarkable agreement is achieved with experimental measurements including: the electron-nuclear hyperfine coupling (115.5 MHz) and its electric field response (−2.65 × 10−3 μm2/V2), the binding energy (46.07 meV), excited valley-orbital energies of 1sT2 (37.22 meV) and 1sE (35.87 meV) states, and super-hyperfine couplings of the proximal shells of the silicon lattice. This quantitative description of spin and orbital properties of phosphorus dopant simultaneously from a single theoretical framework will help as a predictive tool for the design of qubits.

Primary donor triplet states of Photosystem I and II studied by Q-band pulse ENDOR spectroscopy

The photoexcited triplet state of the “primary donors” in the two photosystems of oxygenic photosynthesis has been investigated by means of electron-nuclear double resonance (ENDOR) at Q-band (34 GHz). The data obtained represent the first set of 1H hyperfine coupling tensors of the 3P700 triplet state in PSI and expand the existing data set for 3P680. We achieved an extensive assignment of the observed electron-nuclear hyperfine coupling constants (hfcs) corresponding to the methine α-protons and the methyl group β-protons of the chlorophyll (Chl) macrocycle. The data clearly confirm that in both photosystems the primary donor triplet is located on one specific monomeric Chl at cryogenic temperature. In comparison to previous transient ENDOR and pulse ENDOR experiments at standard X-band (9–10 GHz), the pulse Q-band ENDOR spectra demonstrate both improved signal-to-noise ratio and increased resolution. The observed ENDOR spectra for 3P700 and 3P680 differ in terms of the intensity loss of lines from specific methyl group protons, which is explained by hindered methyl group rotation produced by binding site effects. Contact analysis of the methyl groups in the PSI crystal structure in combination with the ENDOR analysis of 3P700 suggests that the triplet is located on the Chl aʹ (PA) in PSI. The results also provide additional evidence for the localization of 3P680 on the accessory ChlD1 in PSII.

Molecular Dynamics in Ionic Liquid/Radical Systems.

Molecular dynamics of the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethyl sulfonyl)imide (Emim-Tf2N) with either of the four organic stable radicals, TEMPO, 4-benzoyloxy-TEMPO, BDPA, and DPPH, is studied by using Nuclear Magnetic Resonance (NMR) and Dynamic Nuclear Polarization (DNP). In complex fluids at ambient temperature, NMR signal enhancement by DNP is frequently obtained by a combination of several mechanisms, where the Overhauser effect and solid effect are the most common. Understanding the interactions of free radicals with ionic liquid molecules is of particular significance due to their complex dynamics in these systems, influencing the properties of the ion-radical interaction. A combined analysis of EPR, DNP, and NMR relaxation dispersion is carried out for cations and anions containing, respectively, the NMR active nuclei 1H or 19F. Depending on the size and the chemical properties of the radical, different interaction processes are distinguished, namely, the Overhauser effect and solid effect, driven by dominating dipolar or scalar interactions. The resulting NMR relaxation dispersion is decomposed into rotational and translational contributions, allowing the identification of the corresponding correlation times of motion and interactions. The influence of electron relaxation time and electron-nuclear spin hyperfine coupling is discussed.

Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device

Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single-donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second. However, manufacturing a scalable quantum processor with this method is considered challenging, because of the exponential sensitivity of the exchange interaction that mediates the coupling between the qubits. Here we demonstrate the conditional, coherent control of an electron spin qubit in an exchange-coupled pair of 31P donors implanted in silicon. The coupling strength, J = 32.06 ± 0.06 MHz, is measured spectroscopically with high precision. Since the coupling is weaker than the electron-nuclear hyperfine coupling A ≈ 90 MHz which detunes the two electrons, a native two-qubit controlled-rotation gate can be obtained via a simple electron spin resonance pulse. This scheme is insensitive to the precise value of J, which makes it suitable for the scale-up of donor-based quantum computers in silicon that exploit the metal-oxide-semiconductor fabrication protocols commonly used in the classical electronics industry.

Extraction of isotropic electron-nuclear hyperfine coupling constants of paramagnetic point defects from near-zero field magnetoresistance spectra via least squares fitting to models developed from the stochastic quantum Liouville equation

We report on a method by which we can systematically extract spectroscopic information such as isotropic electron–nuclear hyperfine coupling constants from near-zero field magnetoresistance (NZFMR) spectra. The method utilizes a least squares fitting of models developed from the stochastic quantum Liouville equation. We applied our fitting algorithm to two distinct material systems: Si/SiO2 metal oxide semiconductor field effect transistors and a-Si:H metal insulator semiconductor capacitors. Our fitted results and hyperfine parameters are in reasonable agreement with existing knowledge of the defects present in the systems. Our work indicates that the NZFMR response and fitting of the NZFMR spectrum via models developed from the stochastic quantum Liouville equation could be a relatively simple yet powerful addition to the family of spin-based techniques used to explore the chemical and structural nature of point defects in semiconductor devices and insulators.

Electron-nuclear hyperfine coupling in quantum kagome antiferromagnets from first-principles calculation and a reflection of the defect effect

The discovery of ideal spin-1/2 kagome antiferromagnets Herbertsmithite and Zn-doped Barlowite represents a breakthrough in the quest for quantum spin liquids (QSLs), and nuclear magnetic resonance (NMR) spectroscopy plays a prominent role in revealing the quantum paramagnetism in these compounds. However, interpretation of NMR data that is often masked by defects can be controversial. Here, we show that the most significant interaction strength for NMR, i.e. the hyperfine coupling (HFC) strength, can be reasonably reproduced by first-principles calculations for these proposed QSLs. Applying this method to a supercell containing Cu-Zn defects enables us to map out the variation and distribution of HFC at different nuclear sites. This predictive power is expected to bridge the missing link in the analysis of the low-temperature NMR data.

(Invited) Metallofullerenes – Enabling Long-Lived Radical Ion Pair States

The “holy grail” of artificial photosynthesis is the realization of long lived radical ion pair states that power catalytic centers and, consequently, the production of solar fuels. Notably, magnetic field effects, especially internal magnetic field effects, are rarely employed in this context. Here, we report on severalelectron donor-acceptor conjugates, in which the presence of the Lu3N cluster in electron donating Lu3N@Ih -C80 exerts an appreciable electron nuclear hyperfine coupling on the charge transfer dynamics. As such, a fairly efficient radical ion pair intersystem crossing converts the initially formed singlet radical ion pair state, 1[(Lu3N@Ih -C80)•+-PDI•-]/ 1[(Lu3N@Ih -C80)•+-C60 •-], to the corresponding triplet radical ion pair state, 3[(Lu3N@Ih -C80)•+-PDI•-] / 3[(Lu3N@Ih -C80)•+-C60 •-]. Most notably, the radical ion pair state lifetime of the latter is up to 1000 times longer than that of the earlier.

Elucidating the Role of Zinc-Bacteriochlorophyll A' in the Primary Photochemistry of Chloroacidobacterium thermophilum Reaction Centers

Chloracidobacterium (Cab.) thermophilum is a microaerophilic, chlorophototrophic species in the phylum of Acidobacteria that contains homodimeric Type I reaction centers (RC). Photosynthetic RCs in bacteria convert light energy into chemical energy using (bacterio)chlorophyll ((B)Chl) cofactors. In addition to participating in energy transfer in the light-harvesting complexes, the (B)Chl molecules also act as the primary electron donor and primary electron acceptor in Type I RCs. Previously, reversed-phase high-performance liquid chromatography of Cab. thermophilum RCs revealed the presence of (B)Chl a, Chl a, and Zn2+-(B)Chl a' in a ratio of about 12.8:8.0:2.0. Moreover, it was shown that Cab. thermophilum uses chlorosomes and FMO for light harvesting, and synthesizes (B)Chl c in addition to (B)Chl a, Chl a, and Zn2+-(B)Chl a'. It has been demonstrated that Chl a is the primary electron acceptor in Cab. thermophilum RC and since Zn2+-(B)Chl a' is only present in the RC, it was suggested that it could function as the primary electron donor. In this study, we utilize high-resolution, two-dimensional (2D) 14N and 67Zn hyperfine sublevel correlation (HYSCORE) spectroscopy to determine the electronic and geometric structure of the primary donor cation, P840+, in the Cab. thermophilum RC. Additionally, we perform density functional theory (DFT) calculations to determine the electron spin-density distribution and electron-nuclear hyperfine coupling parameters of P840+ for comparison with the parameters that are obtained from the experimental 2D HYSCORE measurements. Our studies indicate that that the primary donor, P840, of the Cab. RC is comprised of Zn2+-sBChl a' molecules.

Effect of Electron-Nuclear Hyperfine Interactions on Multiple-Quantum Coherences in Photogenerated Covalent Radical (Qubit) Pairs.

Ultrafast photodriven electron transfer reactions starting from an excited singlet state in an organic donor-acceptor molecule can generate a spin-correlated radical pair (RP) with an initially entangled spin state that may prove useful as a two-qubit pair in quantum information protocols. Here we investigate the effects of modulating electron-nuclear hyperfine coupling by rapidly transferring an electron between two equivalent sites comprising the reduced acceptor of the RP. A covalent electron donor-acceptor molecule including a tetrathiafulvalene (TTF) donor, a 4-aminonaphthalene-1,8-imide (ANI) chromophoric primary acceptor, and an m-xylene bridged cyclophane having two equivalent pyromellitimides (PI2), TTF-ANI-PI2, as a secondary acceptor was synthesized along with an analogous molecule having one pyromellitimide (PI) acceptor, TTF-ANI-PI. Photoexcitation of ANI within each molecule results in sub-nanosecond formation of TTF+•-ANI-PI-• and TTF+•-ANI-PI2-•. The effect of reducing electron-nuclear hyperfine interactions in TTF+•-ANI-PI2-• relative to TTF+•-ANI-PI-• on decoherence of multiple-quantum coherences has been measured by pulse-EPR spectroscopy. This contribution is especially relevant in the absence of modulation of exchange or dipolar interactions, as with the RP at a fixed distance in the molecules in this work. The theoretical prediction of the contribution from an ensemble of hyperfine interactions to decoherence in these RPs is shown to be less than the full width at half-maximum of the quantum beat frequencies measured experimentally. Pulse bandwidth and off-resonant excitation by square microwave pulses are proposed as larger contributors to decoherence in these molecules than the hyperfine interactions, and specific pulse shapes relevant to arbitrary waveform generation are introduced.

Optimization and prediction of the electron-nuclear dipolar and scalar interaction in 1H and 13C liquid state dynamic nuclear polarization.

During the last 10-15 years, dynamic nuclear polarization (DNP) has evolved as a powerful tool for hyperpolarization of NMR and MRI nuclides. However, it is not as well appreciated that solution-state dynamic nuclear polarization is a powerful approach to study intermolecular interactions in solution. For solutions and fluids, the 1H nuclide is usually dominated by an Overhauser dipolar enhancement and can be significantly increased by decreasing the correlation time (τc) of the substrate/nitroxide interaction by utilizing supercritical fluids (SF CO2). For molecules containing the ubiquitous 13C nuclide, the Overhauser enhancement is usually a profile of both scalar and dipolar interactions. For carbon atoms without an attached hydrogen, a dipolar enhancement usually dominates as we illustrate for sp2 hybridized carbons in the fullerenes, C60 and C70. However, the scalar interaction is dependent on a Fermi contact interaction which does not have the magnetic field dependence inherent in the dipolar interaction. For a comprehensive range of molecular systems we show that molecules that exhibit weakly acidic complexation interaction(s) with nitroxides provide corresponding large scalar enhancements. For the first time, we report that sp hybridized (H-C) alkyne systems, for example, the phenylacetylene-nitroxide system exhibit very large scalar dominated enhancements. Finally, we demonstrate for a wide range of molecular systems that the Fermi contact interaction can be computationally predicted via electron-nuclear hyperfine coupling and correlated with experimental 13C DNP enhancements.

Fast photo-driven electron spin coherence transfer: the effect of electron-nuclear hyperfine coupling on coherence dephasing

A covalently-linked electron donor–acceptor–acceptor molecule was utilized to study the effect of electron-nuclear hyperfine coupling on the dephasing of the zero quantum coherence in spin correlated radical pairs.

Overhauser effects in insulating solids.

We report magic angle spinning, dynamic nuclear polarization (DNP) experiments at magnetic fields of 9.4 T, 14.1 T, and 18.8 T using the narrow line polarizing agents 1,3-bisdiphenylene-2-phenylallyl (BDPA) dispersed in polystyrene, and sulfonated-BDPA (SA-BDPA) and trityl OX063 in glassy glycerol/water matrices. The (1)H DNP enhancement field profiles of the BDPA radicals exhibit a significant DNP Overhauser effect (OE) as well as a solid effect (SE) despite the fact that these samples are insulating solids. In contrast, trityl exhibits only a SE enhancement. Data suggest that the appearance of the OE is due to rather strong electron-nuclear hyperfine couplings present in BDPA and SA-BDPA, which are absent in trityl and perdeuterated BDPA (d21-BDPA). In addition, and in contrast to other DNP mechanisms such as the solid effect or cross effect, the experimental data suggest that the OE in non-conducting solids scales favorably with magnetic field, increasing in magnitude in going from 5 T, to 9.4 T, to 14.1 T, and to 18.8 T. Simulations using a model two spin system consisting of an electron hyperfine coupled to a (1)H reproduce the essential features of the field profiles and indicate that the OE in these samples originates from the zero and double quantum cross relaxation induced by fluctuating hyperfine interactions between the intramolecular delocalized unpaired electrons and their neighboring nuclei, and that the size of these hyperfine couplings is crucial to the magnitude of the enhancements. Microwave power dependent studies show that the OE saturates at considerably lower power levels than the solid effect in the same samples. Our results provide new insights into the mechanism of the Overhauser effect, and also provide a new approach to perform DNP experiments in chemical, biophysical, and physical systems at high magnetic fields.

Spin dynamics of radical pairs with restricted geometries and strong exchange coupling: the role of hyperfine coupling.

Subnanosecond radical pair (RP) formation by electron transfer from an excited singlet state or by bond breaking produces two correlated spins coupled by their spin-spin exchange (J) and magnetic dipole (D) interactions. In the high magnetic field limit, the two-spin system can be described by a singlet state (S) and three triplet states (T₀, T(+1), T(-1)). When J is small relative to the electron Zeeman interaction, |T₀⟩ is the only triplet state that is populated by coherent spin mixing with the |S⟩ state because the |T(+1)⟩ and |T(-1)⟩ states are well-separated from |S⟩ by a large energy gap. Herein, we describe the spin dynamics for RPs having restricted geometries in which J is similar in magnitude to the electron Zeeman interaction and does not fluctuate significantly. Under these circumstances, depending on the sign of J, the energies of |T(+1)⟩ or |T(-1)⟩ are close to that of |S⟩ so that weak isotropic electron-nuclear hyperfine coupling leads to population of |T(+1)⟩ or |T(-1)⟩. An approximate relationship for the triplet quantum yield is developed for a RP in the large J regime, where one or both electrons interact with nearby spin-1/2 nuclei. This relationship also yields the net spin polarization transfer to the nuclear spins.

A Metallofullerene Electron Donor that Powers an Efficient Spin Flip in a Linear Electron Donor–Acceptor Conjugate

The dream target of artificial photosynthesis is the realization of long-lived radical ion pair states that power catalytic centers and, consequently, the production of solar fuels. Notably, magnetic field effects, especially internal magnetic field effects, are rarely employed in this context. Here, we report on a linear Lu3N@Ih-C80-PDI electron donor-acceptor conjugate, in which the presence of the Lu3N cluster exerts an appreciable electron nuclear hyperfine coupling on the charge transfer dynamics. As such, a fairly efficient radical ion pair intersystem crossing converts the initially formed singlet radical ion pair state, (1)[(Lu3N@Ih-C80)(•+)-PDI(•-)], to the corresponding triplet radical ion pair state, (3)[(Lu3N@Ih-C80)(•+)-PDI(•-)]. Most notably, the radical ion pair state lifetime of the latter is nearly 1000 times longer than that of the former.

Mass-Independent Isotope Effects

Three fundamental properties of atomic nuclei-mass, spin (and related magnetic moment), and volume-are the source of isotope effects. The mostly deserved and popular, with almost hundred-year history, is the mass-dependent isotope effect. The first mass-independent isotope effect which chemically discriminates isotopes by their nuclear spins and nuclear magnetic moments rather than by their masses was detected in 1976. It was named as the magnetic isotope effect because it is controlled by magnetic interaction, i.e., electron-nuclear hyperfine coupling in the paramagnetic species, the reaction intermediates. The effect follows from the universal physical property of chemical reactions to conserve angular momentum (spin) of electrons and nuclei. It is now detected for oxygen, silicon, sulfur, germanium, tin, mercury, magnesium, calcium, zinc, and uranium in a great variety of chemical and biochemical reactions including those of medical and ecological importance. Another mass-independent isotope effect was detected in 1983 as a deviation of isotopic distribution in reaction products from that which would be expected from the mass-dependent isotope effect. On the physical basis, it is in fact a mass-dependent effect, but it surprisingly results in isotope fractionation which is incompatible with that predicted by traditional mass-dependent effects. It is supposed to be a function of dynamic parameters of reaction and energy relaxation in excited states of products. The third, nuclear volume mass-independent isotope effect is detected in the high-resolution atomic and molecular spectra and in the extraction processes, but there are no unambiguous indications of its importance as an isotope fractionation factor in chemical reactions.

Dynamic Nuclear Polarization in III–V Semiconductors

We report on electron spin resonance, nuclear magnetic resonance and Overhauser shift experiments on two of the most commonly used III–V semiconductors, GaAs and InP. Localized electron centers in these semiconductors have extended wavefunctions and exhibit strong electron–nuclear hyperfine coupling with the nuclei in their vicinity. These interactions not only play a critical role in electron and nuclear spin relaxation mechanisms, but also result in transfer of spin polarization from the electron spin system to the nuclear spin system. This transfer of polarization, known as dynamic nuclear polarization (DNP), may result in an enhancement of the nuclear spin polarization by several orders of magnitude under suitable conditions. We determine the critical range of doping concentration and temperature conducive to DNP effects by studying these semiconductors with varying doping concentration in a wide temperature range. We show that the electron spin system in undoped InP exhibits electric current-induced spin polarization. This is consistent with model predictions in zinc-blende semiconductors with strong spin–orbit effects.

Resident electron spin dynamics of II-VI quantum dots

The spin dynamics of single electrons resident to charged CdSe/ZnSe quantum dots is studied. The spin-orbit mediated spin lifetime is uncovered. It follows a magnetic-field dependence of τso=190 ms T4/B4. Below about B=2 T, the electron-nuclear hyperfine coupling takes over and the electron spin lifetime shortens. We analyze the temperature dependence of the spin transfer via hyperfine interaction and find that the efficiency for the formation of a nuclear dynamical polarization increases up to 100 K.

Direct detection of a hydrogen ligand in the [NiFe] center of the regulatory H2-sensing hydrogenase from Ralstonia eutropha in its reduced state by HYSCORE and ENDOR spectroscopy.

The regulatory H2-sensing [NiFe] hydrogenase of the beta-proteobacterium Ralstonia eutropha displays an Ni-C "active" state after reduction with H2 that is very similar to the reduced Ni-C state of standard [NiFe] hydrogenases. Pulse electron nuclear double resonance (ENDOR) and four-pulse ESEEM (hyperfine sublevel correlation, HYSCORE) spectroscopy are applied to obtain structural information on this state via detection of the electron-nuclear hyperfine coupling constants. Two proton hyperfine couplings are determined by analysis of ENDOR spectra recorded over the full magnetic field range of the EPR spectrum. These are associated with nonexchangeable protons and belong to the beta-CH(2) protons of a bridging cysteine of the NiFe center. The signals of a third proton exhibit a large anisotropic coupling (Ax = 18.4 MHz, Ay = -10.8 MHz, Az = -18 MHz). They disappear from the 1H region of the ENDOR spectra after exchange of H2O with 2H2O and activation with 2H2 instead of H2 gas. They reappear in the 2H region of the ENDOR and HYSCORE spectra. Based on a comparison with the spectroscopically similar [NiFe] hydrogenase of Desulfovibrio vulgaris Miyazaki F, for which the g-tensor orientation of the Ni-C state with respect to the crystal structure is known (Foerster et al. J. Am. Chem. Soc. 2003, 125, 83-93), an assignment of the 1H hyperfine couplings is proposed. The exchangeable proton resides in a bridging position between the Ni and Fe and is assigned to a formal hydride ion. After illumination at low temperature (T = 10 K), the Ni-L state is formed. For the Ni-L state, the strong hyperfine coupling observed for the exchangeable hydrogen in Ni-C is lost, indicating a cleavage of the metal-hydride bond(s). These experiments give first direct information on the position of hydrogen binding in the active NiFe center of the regulatory hydrogenase. It is proposed that such a binding situation is also present in the active Ni-C state of standard hydrogenases.