Ensemble of single quadrupolar nuclei in rotating solids: sidebands in NMR spectrum

A novel way is proposed to describe the evolution of nuclear magnetic polarization and the induced NMR spectrum. In this method, the effect of a high-intensity external static magnetic field and the effects of proper Hamiltonian left over interaction components, which commute with the first, are taken into account simultaneously and equivalently. The method suits any concrete NMR problem. This brings forth the really existing details in the registered spectra, evoked by Hamiltonian secular terms, which may be otherwise smoothed due to approximate treatment of the effects of the secular terms. Complete analytical expressions are obtained describing the NMR spectra including the rotational sideband sets of single quadrupolar nuclei in rotating solids.     

超强磁场中核磁共振信号与屏蔽效应的理论研究

研究了超强磁场对于核磁共振样品中双原子分子中电子系统的哈密顿量的影响,并且给出了磁共振信号中由于外磁场与氢原子电子系统相互作用所产生的含有B02的修正项.基于核磁共振原理,获得了利用氢的NMR谱对超强磁场进行精确测量的理论依据,推导出了一种基于核磁共振技术的超强磁场测量公式,从而在理论上证明了对超强磁场进行精确测量是可行的.     

Geometry of kinked protein helices from NMR data

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.     

Hardware modification of a 7 mm MAS NMR probe to a single-crystal goniometer

Tensorial terms of the Hamiltonian can be measured by solid-state single-crystal nuclear magnetic resonance (NMR) spectroscopy which requires a goniometer NMR probehead. Goniometer probes; however, are not standard parts of solid NMR spectrometers and are available only at a much higher price than magic-angle spinning (MAS) probeheads widely used in research. Due to requirements of MAS experiments, modern probeheads are designed for small ceramic rotors, which are 1-4 mm in diameter, to reach very high angular frequencies, so there are several older 7 mm MAS probeheads used rarely todays in NMR laboratories. In this paper, a simple method is presented how to rebuild step-by-step a 7 mm Bruker MAS probehead to be suitable for single-crystal spectroscopy. In the second part (31)P chemical shift tensors of Na(4)P(2)O(7) x 10H(2)O are determined to demonstrate the functionality of the rebuilt probehead.     

Nuclear quadrupole effects in orientation-modulated NMR

A quantum-statistical method is used to study the structure of the NMR spectrum under adiabatic orientation-modulated (OM) magnetically anisotropic Hamiltonian of a nuclear system by rotational oscillation of a crystal about a fixed axis. A general expression is obtained for an NMR absorption signal, in phase with the OM, which reflects the main anomalies of such a spectrum. The results are used to interpret the OM NMR spectrum in spin systems with weak axisymmetric nuclear quadrupole interactions.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 4, pp. 48–52, April, 1990.     

Effects of vibrational intercentre interaction in a trigonal two-centre system with twofold electronic degeneracy at each centre

The effect of intercentre interaction (via vibrations and electron-electron coupling) on the magnetic and magnetic resonance characteristics of a pair of Jahn-Teller centres is investigated. In the limiting case of strong vibronic coupling when the splitting of degenerate electronic terms is sufficiently large the exchange Hamiltonian for the pair has the Heisenberg form. The energy spectrum of spin states of the pair system is obtained and the temperature dependence of the effective magnetic moment is investigated. It is shown that under some conditions this temperature dependence has an anomalous nonmonotonic character. The g factors of the two-centre Jahn-Teller system are obtained and the changes of the EPR spectrum with the exchange and vibrational coupling constants is analysed. With inclusion of only the exchange interaction, the pair spectrum possesses an additional isotropic resonance placed in the middle of the known broadened EPR spectrum of single centres with the Jahn-Teller effect for an orbital E term. The vibrational interaction between the centres results in a radical transformation of the spectrum, which in this case contains only an isotropic resonance line.     

The Schrödinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

We investigate the non-relativistic Schrödinger and Pauli-Dirac oscillators in noncommutative phase space using the five-dimensional Galilean covariant framework. The Schrödinger oscillator presented the correct energy spectrum whose non isotropy is caused by the noncommutativity with an expected similarity between this system and the particle in a magnetic field. A general Hamiltonian for the 3-dimensional Galilean covariant Pauli-Dirac oscillator was obtained and it presents the usual terms that appears in commutative space, like Zeeman effect and spin-orbit terms. We find that the Hamiltonian also possesses terms involving the noncommutative parameters that are related to a type of magnetic moment and an electric dipole moment.     

Electronic properties of a Penrose tiling lattice in a magnetic field

The one-electron energy spectrum of a two-dimensional Penrose tiling lattice in a uniform magnetic field is calculated as a function of magnetic fields with a tight-binding Hamiltonian. The calculated results show the following remarkable features characteristic of the Penrose lattice. (1) The density of states in a magnetic field has a central peak with zero width at the zero energy. It is shown that the zero-energy states correspond to the ring states in which the wavefunction has a non-vanishing amplitudes only at the sites on a ring-like region around the origin. (2) The energy levels coalesce into Landau type levels and the boundary states due to the finite size effects based on a fixed boundary condition appear in the gap region between Landau levels. (3) The magnetic field dependence of the energy spectrum has a repeated pattern of self-similarity with the golden mean ratio of two successive periods.     

Entanglement assisted metrology

We propose a new approach to the measurement of a single spin state, based on nuclear magnetic resonance (NMR) techniques and inspired by the coherent control over many-body systems envisaged by quantum information processing. A single target spin is coupled via the magnetic dipolar interaction to a large ensemble of spins. Applying radio frequency pulses, we can control the evolution so that the spin ensemble reaches one of two orthogonal states whose collective properties differ depending on the state of the target spin and are easily measured. We first describe this measurement process using quantum gates; then we show how equivalent schemes can be defined in terms of the Hamiltonian and thus implemented under conditions of real control, using well established NMR techniques. We demonstrate this method with a proof of principle experiment in ensemble liquid state NMR and simulations for small spin systems.     

ARPES measurements of SnAs electronic band structure

A change in the time dependence of the second moment of the distribution of intensities of coherences with various orders in the spectrum of multiple-quantum NMR in a solid at the inclusion of an inhomogeneous magnetic field in the effective interaction is studied. Both the secular dipole–dipole and nonspecular twoquantum interactions are considered as nucleus–nucleus interactions, which correspond to traditional experimental realizations. It is shown that, with an increase in the magnitude of the inhomogeneous field, an exponential increase in the second moment of multiple-quantum NMR with time changes to a power-law increase. The results obtained in this work indicate that this second moment, which determines the average number of dynamically correlated spins, can be used as a convenient characteristic for studying a transition to a many-body localized state.     

The lamb shift in helium from a self-consistent field theory of electrodynamics

In this paper we present the results of an investigation of the finite self-consistent field theory of electrodynamics applied earlier to the calculation of the Lamb shift in hydrogen (Sachs & Schwebel, 1961; Sachs, 1972), now applied to the problem of the Lamb shift in the low-lying states of Helium. We construct the covariant nonlinear field equations of this theory for Helium, from the Lagrangian formalism. In the linear approximation, the Hamiltonian associated with this field theory for the two-electron atom is set up. It is equivalent to the Breit Hamiltonian plus two extra terms. This generalization is a direct consequence of the two-component spinor formalism of the factorization of the Maxwell theory of electromagnetism that is contained in this theory of electrodynamics (Sachs, 1971). Thus, the energy spectrum predicted for the Helium atom is the spectrum predicted by the Breit Hamiltonian, shifted by amounts in the different energy states according to the effects of the extra terms in the Hamiltonian. The latter can be associated with the corrections to the Helium spectrum that are conventionally attributed to the Lamb shift. The level shifts for the 1¹ S and 2³ S states are calculated using the Foldy-Wouthuysen transformation, with the generalization of Charplvy for the two-electron atom. The results are found to be in close agreement with the experimental values for the energy shifts not predicted by the Dirac theory, and with the theoretical values predicted by quantum electrodynamics.     

A quasi-energy operator in the Jaynes-Cummings model in a polychromatic classical field

A perturbation theory is developed for constructing the quasi-energy operator Q of the Tavis-Cummings Hamiltonian, which includes the interaction of atoms with a classical quasi-monochromatic field. The operator Q of the first order in the interaction δ of an atom with a resonator mode has a form of the generalized Tavis-Cummings Hamiltonian (in the interaction representation) to which the oppositely rotating terms with a changed interaction constant are added. Such a Hamiltonian has a singularity in the dimensionless amplitude σ of a classical field. In the vicinity of this singularity, the Hamiltonian spectrum tends to a continuous one, while the degree of squeezing of field quadratures (in its eigenstates) increases infinitely. In the case of one atom and the biharmonic perturbation, the operator Q is obtained up to the third order of the perturbation theory. The spectral problem for Q is studied. The features of the dependence of the quasi-energy spectrum on σ are explained by the presence of an efficient barrier between the regions of the “coordinate” space. It is found that the above-mentioned singularity corresponds to the beginning of the parametric resonance zone. Analytic expressions for the top and bottom of this zone in the δσ plane are presented.     

Controlling coherence using the internal structure of hard pi pulses

The tiny difference between hard pi pulses and their delta-function approximation can be exploited to control coherence. Variants on the magic echo that work despite a large spread in resonance offsets are demonstrated using the zeroth- and first-order average Hamiltonian terms, for 13C NMR in 60C. The 29Si NMR linewidth of silicon has been reduced by a factor of about 70,00 using this approach, which also has potential applications in magnetic resonance microscopy and imaging of solids.     

Exact Solvability and Quantum Integrability of a Derivative Nonlinear Schrödinger Model

Using a variant of quantum inverse scattering method (QISM) which is directly applicable to field theoretical systems, we derive all possible commutation relations among the operator valued elements of the monodromy matrix associated with an integrable derivative nonlinear Schrödinger (DNLS) model. From these commutation relations we obtain the exact Bethe eigenstates for the quantum conserved quantities of DNLS model. We also explicitly construct the first few quantum conserved quantities including the Hamiltonian in terms of the basic field operators of this model. It turns out that this quantum Hamiltonian has a new kind of coupling constant which is quite different from the classical one. This fact allows us to apply QISM to generate the spectrum of quantum DNLS Hamiltonian for the full range of its coupling constant.     

A renormalization scheme for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators

An iteration scheme which makes use of a numerical renormalization group approach is used to calculate the spectrum of vibronic levels. This spectrum resulted from dynamic effects occurring in certain molecules or impurities in insulators.The Hamiltonian of these systems is expressed in the matrix form, using products of suitable electron-phonon states as a basis. In applying this method to multimode electron-phonon systems, phonon modes are coupled in a chain-like fashion. Then a finite chain calculation in terms of Hubbard X-operators is explored by setting up the vibronic Hamiltonian.Calculations are based on Lanczos algorithm, in which only the nearest neighbor matrix elements along the chain need to be taken into account. The iterative scheme is then applied to a two-level electronic system coupled to phonons. A single-particle Green's function corresponding to a two-level system is applied to calculate the spectral density of states, which, coupled to single mode is carried out. The strength of lines in density of states is affected by the coupling constant as well as the temperature dependence of some measurable quantities.     

QHE and far infra-red properties of bilayer graphene in a strong magnetic field

We describe the quantum Hall effect (QHE) and far infra-red (FIR) absorption properties of bilayer graphene in a strong magnetic field and contrast them with the weak field regime. This includes a derivation of the effective low energy Hamiltonian for this system and the consequences of this Hamiltonian for the sequencing of the Landau levels in the material: The form of this effective Hamiltonian gives rise to the presence of a level with doubled degeneracy at zero energy. The effect of a potential difference between the layer of a bilayer is also investigated. It is found that there is a density-dependent gap near the K points in the band structure. The consequences of this gap on the QHE are then described. Also, the magneto-absorption spectrum is investigated and an experiment proposed to distinguish between model ground states of the bilayer quantum Hall effect system based on the different absorption characteristics of right-handed and left-handed polarisation of FIR light. Finally, the effects of trigonal warping are taken into account in the absorption picture.     

非厄米哈密顿量的物理意义

分析了一个脉冲激光与原子相互作用的四能级系统，并考虑最上层能级的自电离过程，从而引入非厄米哈密顿量.在缀饰原子模型下，通过直接求解此哈密顿量的本征值与本征函数，得到系统布居的演化函数.与数值方法所得演化函数的对比表明二者相当符合，从而肯定了非厄米哈密顿量在量子力学框架中的地位，并得到其本征值虚部的物理意义.这将使传统量子力学中力学量的定义得以拓展. 关键词： 非厄米哈密顿量 缀饰原子模型     

The multiple quantum NMR dynamics in systems of equivalent spins with a dipolar ordered initial state

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the Hamiltonian responsible for the MQ NMR dynamics (the MQ Hamiltonian) is used to develop analytic and numerical methods for the investigation of the MQ NMR dynamics in systems consisting of hundreds of spins from the “first principles.” We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for systems of 200–600 spins. It is shown that these profiles may be well approximated by exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, the dipolar ordered state and the thermal equilibrium state in a strong external magnetic field.     

1-D and 2-D NMR of broad-line solids: an application to quasicrystals

Nuclear magnetic resonance (NMR) techniques for measuring one-dimensional absorption spectra and two-dimensional exchange spectra of solids with extremely inhomogeneously broadened lines are discussed. Among various “broad-line” solids, quasicrystals represent alloys of metallic elements, the structures of which include “forbidden” symmetry elements. NMR absorption lines of quasicrystals exhibit a strong electric-quadrupole-induced inhomogeneous broadening that originates from the lack of translational periodicity of the otherwise perfectly long-range-ordered quasiperiodic lattice. Recording an NMR spectrum of a quasicrystalline sample requires a magnetic field-sweep technique. The two-dimensional exchange experiment on quasicrystals can be performed on selectively excited portions of the NMR spectrum only. Due to the off-resonance effects in a selective excitation, the use of a simple three-pulse stimulated-echo exchange sequence is preferred. The²⁷Al spectra of the Al-Pd-Mn and Al-Pd-Re families show interesting features like temperature-dependent frequency shifts and exchange effects due to atomic motion.