High-Field Phenomena of Qubits

Electron and nuclear spins are very promising candidates to serve as quantum bits (qubits) for proposed quantum computers, as the spin degrees of freedom are relatively isolated from their surroundings and can be coherently manipulated, e.g., through pulsed electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). For solid-state spin systems, impurities in crystals based on carbon and silicon in various forms have been suggested as qubits, and very long relaxation rates have been observed in such systems. We have investigated a variety of these systems at high magnetic fields in our multifrequency pulsed EPR/ENDOR (electron nuclear double resonance) spectrometer. A high magnetic field leads to large electron spin polarizations at helium temperatures, giving rise to various phenomena that are of interest with respect to quantum computing. For example, it allows the initialization of both the electron spin as well as hyperfine-coupled nuclear spins in a well-defined state by combining millimeter and radio-frequency radiation. It can increase the T ₂ relaxation times by eliminating decoherence due to dipolar interaction and lead to new mechanisms for the coherent electrical readout of electron spins. We will show some examples of these and other effects in Si:P, SiC:N and nitrogen-related centers in diamond.     

Probing of the shallow donor and acceptor wave functions in silicon carbide and silicon through an EPR study of crystals with a modified isotopic composition

The spatial distributions of the unpaired-electron wave functions of shallow N donors in SiC crystals and of shallow P and As donors in silicon crystals were determined by studying crystals with a modified content of the ²⁹Si and ¹³C isotopes having a nonzero nuclear magnetic moment. As follows from the present EPR and available ENDOR data, the distribution of donor electrons in SiC depends substantially on the polytype and position in the lattice; indeed, in 4H-SiC, the unpaired electrons occupy primarily the Si s and p orbitals, whereas in 6H-SiC these electrons reside primarily in the s orbitals of C. The electron distributions for the N donor in the hexagonal position, which has a shallow level close to that obtained for this material in the effective-mass approximation, and for the donor occupying the quasi-cubic position differ substantially. The EPR spectrum of N in quasi-cubic positions was observed to have a hyperfine structure originating from a comparatively strong coupling with the first two coordination shells of Si and C, which were unambiguously identified. The effective-mass approximation breaks down close to the N donor occupying the quasi-cubic position, and the donor structure and the donor electron distribution become less symmetric. In silicon, reduction of the ²⁹Si content brought about a substantial narrowing of the EPR line of the shallow P and As donors and an increase in the EPR signal intensity, as well as a noticeable increase in the spin-lattice relaxation time T₁. This offers the possibility of selectively studying these spectra by optically exciting a region of the crystal in order to shorten T₁ and thereby precluding EPR signal saturation only in the illuminated part of the material. This method may be used to advantage in developing materials for quantum computers based on donors in silicon and SiC.     

High-Frequency EPR and ENDOR Spectroscopy on Semiconductor Quantum Dots

It is shown that high-frequency electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy are excellent tools for the investigation of the electronic properties of semiconductor quantum dots (QDs). The great attractions of these techniques are that, in contrast to optical methods, they allow the identification of the dopants and provide information about the spatial distribution of the electronic wave function. This latter aspect is particularly attractive because it allows for a quantitative measurement of the effect of confinement on the shape and properties of the wave function. In this contribution EPR and ENDOR results are presented on doped ZnO QDs. Shallow donors (SDs), related to interstitial Li and Na and substitutional Al atoms, have been identified in this material by pulsed high-frequency EPR and ENDOR spectroscopy. The shallow character of the wave function of the donors is evidenced by the multitude of ENDOR transitions of the ⁶⁷Zn nuclear spins and by the hyperfine interaction of the ⁷Li, ²³Na and ²⁷Al nuclear spins that are much smaller than for atomic lithium, sodium and aluminium. The EPR signal of an exchange-coupled pair consisting of a shallow donor and a deep Na-related acceptor has been identified in ZnO nanocrystals with radii smaller than 1.5 nm. From ENDOR experiments it is concluded that the deep Na-related acceptor is located at the interface of the ZnO core and the Zn(OH)₂ capping layer, while the shallow donor is in the ZnO core. The spatial distribution of the electronic wave function of a shallow donor in ZnO semiconductor QDs has been determined in the regime of quantum confinement by using the nuclear spins as probes. Hyperfine interactions as monitored by ENDOR spectroscopy quantitatively reveal the transition from semiconductor to molecular properties upon reduction of the size of the nanoparticles. In addition, the effect of confinement on the g-factor of SDs in ZnO as well as in CdS QDs is observed. Finally, it is shown that an almost complete dynamic nuclear polarization (DNP) of the ⁶⁷Zn nuclear spins in the core of ZnO QDs and of the ¹H nuclear spins in the Zn(OH)₂ capping layer can be obtained. This DNP is achieved by saturating the EPR transition of SDs present in the QDs with resonant high-frequency microwaves at low temperatures. This nuclear polarization manifests itself as a hole and an antihole in the EPR absorption line of the SD in the QDs and a shift of the hole (antihole). The enhancement of the nuclear polarization opens the possibility to study semiconductor nanostructures with nuclear magnetic resonance techniques.     

Angle-selective measurements of spin soliton in ladder polydiacetylene by pulsed 94 GHz EPR

Angle-selection experiments of a spin soliton in randomly oriented ladder polydiacetylene were carried out by pulsed electron paramagnetic resonance (EPR) at W-band. EPR measurement using 94 GHz microwaves increased the difference in the resonance field due tog anisotropy of the spin soliton to allow the orientation dependence of transient nutation, electron nuclear double resonance (ENDOR) and spin relaxations to be investigated. The shape of theg anisotropy-resolved nutation spectrum was discussed on the basis of the EPR transition moments and the differences between spin relaxation times. Reliable assignments of hyperfine couplings to the β protons (H_β) of the alkyl side chains were achieved with the support of W-band ENDOR measurements. No significant orientational dependence in theT ₁ andT ₂ processes was found in terms of isotropy of the H_β-hyperfine interaction.     

Electron paramagnetic resonance and 1H nuclear magnetic resonance study of Y-doping effect on the hydrogen shallow donors in ZnO nanoparticles

Hydrogen shallow donors in sol-gel-derived pristine and rare-earth Y-doped ZnO nanoparticles have been investigated by electron paramagnetic resonance (EPR) and high-resolution ¹H nuclear magnetic resonance (NMR). It is shown by EPR measurements that the energy level of the hydrogen shallow donors in the Y-doped ZnO is much deeper (E ～ 174 meV) than in the pristine ZnO (E ～ 75 meV). The temperature-dependent ¹H NMR chemical shift and linewidth measurements of the pristine and the Y-doped ZnO systems indicated that Y-doping effectively modifies the lattice environment and hinders the hydrogen motions in the ZnO nanoparticles.     

Pulse EPR spectroscopy of Cu2+-doped inorganic glasses

Two-frequency continuous-wave and pulse EPR (electron paramagnetic resonance) spectroscopical techniques are applied to determine static and dynamic EPR parameters of Cu²⁺ ions in oxide and fluoride glasses. The investigations are focussed on the analysis of strain effects in the glassy matrices, the identification of the magnetic nuclei in the vicinity of Cu²⁺ ions as well as the determination of the dependence of the phase memory timeT _M on temperature and resonance field. The results obtained by X-band continuous-wave EPR, X- and S-band echo-detected EPR, and X- and S-band electron spin echo envelope modulation studies of Cu²⁺-doped inorganic glasses yield information on the local symmetry of the Cu²⁺ coordination polyhedra, the chemical nature of the atoms in the second and higher coordination spheres, the distribution of the parameters of the static spin Hamiltonian and the low-temperature motions of the dopant-containing structural units. Special techniques like 2-D Mims ENDOR (electron nuclear double resonance) and hyperfine-correlated ENDOR are applied for the first time to doped inorganic glasses. From the spin relaxation measurements a stronger tendency of the Cu²⁺ ions to aggregate is found for fluoride glasses in comparison to aluminosilicate and phosphate glasses.     

Local structure of titanium pair centers in SrF2 crystals: EPR and ENDOR spectroscopic studies

The local structure of titanium pair centers in SrF₂: Ti crystals is investigated using electron paramagnetic resonance (EPR) and electron-nuclear double resonance (ENDOR) spectroscopy. It is found that titanium pair centers with spin moment S=2 and tetragonal symmetry of the magnetic properties are formed in SrF₂: Ti cubic crystals under certain growth conditions and during annealing. The tensor components of the fine and ligand hyperfine structures in the EPR and ENDOR spectra are determined. A model of the Ti⁺-Ti³⁺ paramagnetic dimer is proposed. This model provides an adequate interpretation of both the ferromagnetic nature of the exchange interaction and the observed displacements of four ligands in the first coordination sphere of titanium impurity ions in directions perpendicular to the impurity ion-ligand bonds.     

A Q-band pulsed ENDOR spectrometer for the study of transition metal ion complexes in solids

We describe the design of a pulsed electron nuclear double resonance (ENDOR) spectrometer operating at Q-band frequencies (35 GHz) for studies of transition metal ion complexes in the temperature range between 4.2 and 297 K. Specific features of the spectrometer are a microwave IMPATT generator, a homebuilt cavity, and a commercial Bruker magnet. Standard Davies and Mims ENDOR sequences have been implemented. The performance of the spectrometer is demonstrated for a broad radio frequency range by¹H,¹⁴N,³¹P,¹³³Cs, and²⁰⁷Pb pulsed ENDOR experiments of Cu²⁺, Cr⁵⁺, and V⁴⁺ transition metal ion complexes in both single crystals and disordered materials.     

Defects in Nanodiamonds: Application of High-Frequency cw and Pulse EPR,ODMR

Different aspects of applications of electron paramagnetic resonance (EPR) based techniques including high frequency (HF) electron spin echo (ESE), electron-nuclear double resonance (ENDOR) and optically detected magnetic resonance (ODMR) approaches to study diamond nanostructures are examined.     

Electron paramagnetic resonance in YbNiAl<Subscript>2</Subscript> single crystals with strong magnetic anisotropy

Anisotropy in the magnetic properties of YbNiAl₂ intermetallide has been studied. Electron paramagnetic resonance (EPR) signals assigned to the localized magnetic moments of trivalent ytterbium have been detected at temperatures below 20 K. Spin–lattice relaxation processes like the Orbach–Aminov process with participation of the first excited Stark sublevel of the Yb³⁺ ion with an energy of 96 K govern electron–spin dynamics and the disappearance of spectrum lines with a further increase in temperature. Strong magnetic anisotropy effects are discussed as a main reason for the appearance of electron paramagnetic resonance.     

Quantitative characterization of the Mn2+ complexes of ADP and ATPγS by W-band ENDOR

W-band (95 GHz) pulsed electron nuclear double resonance (ENDOR) measurements were carried out to determine quantitatively the first coordination shell of Mn²⁺ with ADP and ATPγS. The intensity of the ENDOR effect was used for counting the number of equivalent phosphate oxygens and water ligands. Titration curves for determining the binding constant of Mn²⁺. ADP were obtained using the intensity of the X-band EPR spectrum and the³¹P ENDOR effect. Both curves gave the same binding constant showing that phosphate ligand counting is plausible, provided that an appropriate reference is available. The comparison of the³¹P ENDOR effect of the 1:1 ADP and ATPγS complexes shows that two phosphates are coordinated in both; while in ADP they are equivalent, in ATPγS they are slightly different. The reference system for water ligand counting was Mn(H₂O) ₆ ²⁺ in a H₂O-D₂O mixture. The results show a smaller error for the²H ENDOR effect, compared to the¹H ENDOR effect. Unlike the³¹P ENDOR effect, the¹H ENDOR effect dependence on [ADP] in the titration experiments showed that it is sensitive to variations in the zero-field splitting, which in turn alters the contributions of transitions other than the ‖?1/2>?‖1/2>. This results in a larger error in the determination of the number of water ligands.     

Electrical detection of coherent nuclear spin oscillations in phosphorus-doped silicon using pulsed ENDOR

We demonstrate the electrical detection of pulsed X-band electron nuclear double resonance (ENDOR) in phosphorus-doped silicon at 5 K. A pulse sequence analogous to Davies ENDOR in conventional electron spin resonance is used to measure the nuclear spin transition frequencies of the (31)P nuclear spins, where the (31)P electron spins are detected electrically via spin-dependent transitions through Si/SiO(2) interface states, thus not relying on a polarization of the electron spin system. In addition, the electrical detection of coherent nuclear spin oscillations is shown, demonstrating the feasibility to electrically read out the spin states of possible nuclear spin qubits.     

Absolute signs of hyperfine coupling constants as determined by pulse ENDOR of polarized radical pairs

A novel method that allows the determination of absolute signs of hyperfine coupling constants in polarized radical pair (RP) pulse electron-nuclear double resonance (ENDOR) spectra is presented, The variable mixing time (VMT) ENDOR method used here leads to a separation of ENDOR transitions originating from different electron spin manifolds by employing their dependence on the time-dependent parameters of the pulse sequence. The simple kinetic model of the RP VMT ENDOR experiment shows very good agreement with the experiments performed on the P ₇₀₀ ^.+ A ₁ ^.- RP in photosystem I. This method relies on the selective excitation of absorptive or emissive lines of one radical in the RP EPR spectrum and therefore requires high spectral resolution. This condition was fulfilled for the system studied at the low-field edge of the RP EPR spectrum obtained at Q-band. The method presented here has a very high sensitivity and does not require any equipment additional to the one used for RP pulse ENDOR. The VMT ENDOR method offers the possibility for selective suppression of signals from different electron spin manifolds.     

The Electronic State of Flavoproteins: Investigations with Proton Electron–Nuclear Double Resonance

Electron–nuclear double resonance (ENDOR) spectroscopy provides useful information on hyperfine interactions between nuclear magnetic moments and the magnetic moment of an unpaired electron spin. Because the hyperfine coupling constant reacts quite sensitively to polarity changes in the direct vicinity of the nucleus under consideration, ENDOR spectroscopy can be favorably used for the detection of subtle protein–cofactor interactions. A number of pulsed ENDOR studies on flavoproteins have been published during the past few years; most of them were designed to characterize the flavin cofactor by means of its protonation state, or to detect individual protein–cofactor interactions. The aim of this study is to compare the pulsed ENDOR spectra from different flavoproteins in terms of variations of characteristic proton hyperfine values. The general concept is to observe limits of possible influences on the cofactor’s electronic state by surrounding amino acids. Furthermore, we compare ENDOR data obtained from in vivo experiments with in vitro data to emphasize the potential of the method for gaining molecular information in complex media.     

Self-Trapped Excitons in Ionic-Covalent Silver Halide Crystals and Nanostructures: High-Frequency EPR, ESE, ENDOR and ODMR Studies

Silver halides have unique features in solid state physics because their properties are considered to be of borderline nature between ionic and covalent bonding. In AgCl, the self-trapped hole (STH) is centered and partly trapped in the cationic sublattice, forming an Ag²⁺ ion inside of a (AgCl₆)^4? complex as a result of the Jahn–Teller distortion. The STH in AgCl can capture an electron from the conduction band forming the self-trapped exciton (STE). Recent results of a study of STE by means of high-frequency electron paramagnetic resonance, electron spin echo, electron–nuclear double resonance (ENDOR) and optically detected magnetic resonance (ODMR) are reviewed. The properties of the STE in AgCl crystals, such as exchange coupling, the ordering of the triplet and singlet sublevels, the dynamical properties of the singlet and triplet states, and the hyperfine interaction with the Ag and Cl (Br) nuclei are discussed. Direct information about the spatial distribution of the wave function of STE unpaired electrons was obtained by ENDOR. From a comparison with the results of an ENDOR study of the shallow electron center and STH, it is concluded that the electron is mainly contained in a hydrogen-like 1s orbital with a Bohr radius of 15.1 ± 0.6 Å, but near its center the electron density reflects the charge distribution of the hole. The hole of the STE is virtually identical to an isolated STH center. For AgCl nanocrystals embedded into the KCl crystalline matrix, the anisotropy of the g-factor of STE and STH was found to be substantially reduced compared with that of bulk AgCl crystals, which can be explained by a considerable suppression of the Jahn–Teller effect in nanoparticles. A study of ODMR in AgBr nanocrystals in KBr revealed spatial confinement effects and allowed estimating the nanocrystal size from the shape of the ODMR spectra.     

The use of ENDOR to identify the atomic structure of defects in diamond

Although nearly 100 paramagnetic defects have been catalogued in diamond by spin Hamiltonian parameters measured by electron paramagnetic resonance (EPR), very few of these have been unambiguously associated with an atomic model. It has been necessary to use electron nuclear double resonance (ENDOR) to obtain enough information to make proper assignment of such models. The reason for the limitation of EPR, and the way in which ENDOR overcomes these limitations are discussed. The interpretation of hyperfine structure in terms of unpaired electrons in molecular orbitals, and of quadrupole interactions in terms of all electrons, paired and unpaired, as a source of information about molecular structure in diamond, is evaluated by reference to some well documented examples. The measurements so far made by ENDOR on defects in diamond are reviewed, and the salient contribution for the assignment of a model for each defect is explained. The details revealed by ENDOR considerably increase knowledge about defects, particularly those involving substitutional nitrogen atoms. This in turn helps in understanding the complex electron and atom, migration processes which go on under appropriate conditions of temperature and pressure, or optical excitation. The possibilities are discussed for using ENDOR to increase the number of well characterized centres.     

Pulse EPR, ENDOR, and ELDOR Study of Anionic Flavin Radicals in Na+-Translocating NADH:Quinone Oxidoreductase

The Na⁺-translocating nicotinamide adenine dinucleotide (NADH):quinine oxidoreductase (Na⁺–NQR) is a component of respiratory chain of various bacteria and it generates a redox-driven transmembrane electrochemical Na⁺ potential. It contains four different flavin prosthetic groups, including two flavin mononucleotide (FMN) residues covalently bound to the subunits NqrB and NqrC. Na⁺–NQR from Vibrio harveyi was poised at different redox potentials to prepare two samples, containing either both FMN_NqrB and FMN_NqrC or only FMN_NqrB in a paramagnetic state. These two samples were comparatively studied using pulse electron paramagnetic resonance (EPR), electron-nuclear double resonance (ENDOR), and electron-electron double resonance (ELDOR) spectroscopy. The echo-detected EPR spectra and electron spin relaxation properties were very similar for flavin radicals in both samples. The splitting of the outer peaks in the proton ENDOR spectra, assigned to the C(8α) methyl protons, allows to identify both radicals as anionic flavosemiquinones. The mean interspin distance of 20.7 Å between these radicals was determined by pulse ELDOR experiment, which allows to estimate the edge-to-edge distance (r _e) between these flavin centers as: 11.7 Å < r _e < 20.7 Å. The direct electron transfer between FMN_NqrB and FMN_NqrC during the physiological turnover of the Na⁺–NQR complex is suggested.     

Spin dynamics in continuous wave and pulsed ENDOR spectroscopy of coals

ENDOR experiments on coals recorded using continuous wave (CW) and pulsed techniques appear to give qualitatively different spectra. A matrix proton signal dominates the ENDOR spectrum of coals recorded in the CW ENDOR experiment while both a matrix and local proton ENDOR signals with huperfine couplings of up to 20 MHz are observed in spectra recorded using pulsed excitation techniques. Analysis of these spectra lead to different implications for the structure of the molecules that host the unpaired electron. Using a combination of pulsed EPR (Electron Spin Echo, FID detected hole burning) and pulsed Electron Nuclear Multiple Resonance (Sub-level relaxation, hyperfine selective ENDOR, EPR sub-spectra) experiments, we investigate the electron and nuclear spin dynamics in order to reconcile the different signal amplitudes observed in the CW and pulsed ENDOR spectra. In the CW ENDOR experiment, the results of the FID detected hole burning experiments prove that the low ENDOR signal intensity can not be attributed to spectral diffusion mechanisms competing with ENDOR mechanisms. Instead, we find that an unfavorable ratio of the electron and nuclear spin relaxation rates results in small local ENDOR signals. The matrix line dominates the spectrum because of the large number of matrix protons. In the pulsed ENDOR experiment, the hyperfine contrast selectivity mechanism suppresses the intensity of the matrix ENDOR signal and enhances the amplitudes of the local ENDOR signals. In addition, the ENDOR signal is not a function of the ratio of the electron and nuclear relaxation rates.