Calculation of pulsed NMR signal in I = 3/2 quadrupolar spin system

The rf pulse response of I=3/2 spin system experiencing first order quadrupolar splitting is studied using density matrix approach. A general expression is derived in terms of spin populations, quadrupole splitting and duration and amplitude of the rf pulse for calculating the NMR signal arising due to the centre line and satellite resonances for the situation where the impressed rf pulse excites the resonances selectively as well as non-selectively. The necessary 4×4 transformation matrix obtained analytically by diagonalyzing the Hamiltonian are used to get the expression for the centre line response. The satellite signals are obtained in the same way but by using the numerical values of the roots of the related quartics. The widths of the corresponding π/2-pulses are calculated for different initial spin populations. The variations of this pulse-width and the corresponding signal amplitude as a function of satellite splitting are studied.     

Calculation of pulsed NMR signal in I=3/2 quadrupolar spin system

The rf pulse response of I=3/2 spin system experiencing first order quadrupolar splitting is studied using density matrix approach. A general expression is derived in terms of spin populations, quadrupole splitting and duration and amplitude of the rf pulse for calculating the NMR signal arising due to the centre line and satellite resonances for the situation where the impressed rf pulse excites the resonances selectively as well as non-selectively. The necessary 4×4 transformation matrix obtained analytically by diagonalyzing the Hamiltonian are used to get the expression for the centre line response. The satellite signals are obtained in the same way but by using the numerical values of the roots of the related quartics. The widths of the corresponding π/2-pulses are calculated for different initial spin populations. The variations of this pulse-width and the corresponding signal amplitude as a function of satellite splitting are studied.     

The chemical shift interaction under weak radio frequency pulses

The chemical shift anisotropy of a nuclear spin system in a strong magnetic field can be comparable to the strength of the rf pulse (weak pulse condition). In this case, the commonly used assumption that the chemical shift interaction Hamiltonian in the duration of a rf pulse can be neglected is no longer effective. The rf response characteristics of a spin-1/2 system under a weak pulse condition is studied in detail. The relationships between the distortion of the chemical shift powder spectrum and the relative rf field amplitude under various conditions are given. The suppression of sidebands of a MAS spectrum is analysed as an example of solid multiple pulse experiments. The experimental results are in good agreement with computer simulations.     

Sensitivity enhancement of NMR spectra of half-integer spin quadrupolar nuclei in solids using hyperbolic secant pulses

The experimental factors influencing the enhancements achievable for the central NMR transition, m(I)=1/2-->m(I)=-1/2, of spin-3/2 and spin-5/2 nuclei in the solid state using hyperbolic secant, HS, pulses for population transfer are investigated. In the case of powder samples spinning at the magic angle, it is found that the spinning frequency, the bandwidth and the frequency offset of the HS pulse play a crucial role in determining the maximum enhancements. Specifically, the bandwidth must be set to the spinning frequency for maximum signal enhancements. The (87)Rb NMR enhancement obtained for RbClO(4) using HS pulses was relatively insensitive to the magic angle spinning frequency; however, in the case of Al(acac)(3), the (27)Al enhancement increased with MAS frequency. In order to obtain an adiabatic HS sweep, one should optimize the rf field for a given pulse duration or optimize the pulse duration for a given rf field.     

Radio frequencies in EPR: Conventional and advanced use

This mini-review focuses on various aspects of the application of radio frequency (rf) irradiation in electron paramagnetic resonance (EPR). The development of the electron-nuclear double resonance (ENDOR) technique is briefly described, and we highlight the use of circularly polarized rf fields and pulse ENDOR methodology in one- and two-dimensional experiments. The capability of pulse ENDOR at Q-band is illustrated with interesting experimental examples. Electron spin echo envelope modulation effects induced by an rf field in liquid samples demonstrate another role which rf fields can play. Technical achievements in the design of ENDOR resonators are illustrated by the example of a bridged loop-gap resonator. Finally, the influence of longitudinal rf fields on the dynamics of EPR transitions is explained using a dressed spin resonance treatment.     

C–H dipolar recoupling under very fast magic-angle spinning using virtual pulses

A new solid-state NMR pulse sequence for recoupling ¹³C–¹H dipolar interactions under magic-angle spinning is proposed, which works under a spinning speed of a few to several tens kilohertz. The sequence is composed of two different frequency switched Lee–Goldburg sequences, and the modulation of the spin part of the ¹³C–¹H dipolar interaction is introduced by a virtual pulse sequence consisting of unitary operators connecting the rotating frame and the tilted rotating frame. When the cycle time of the spinning is equal to or twice the cycle time of the sequence, the ¹³C–¹H dipolar interactions can be recoupled. The sequence is insensitive to experimental imperfections such as rf inhomogeneity or frequency offset, and the resulting lineshape can be represented by a simple analytical equation based on the zeroth-order average Hamiltonian. Experimental results for [2-¹³C] -valine·HCl are reported.     

Cross polarization, radio frequency field homogeneity, and circuit balancing in high field solid state NMR probes

Homogeneous radio frequency (RF) fields are important for sensitivity and efficiency of magnetization transfer in solid state NMR experiments. If the fields are inhomogeneous the cross polarization (CP) experiment transfers magnetization in only a thin slice of sample rather than throughout the entire volume. Asymmetric patterns have been observed in plots of the CP signal versus RF field mismatch for an 800 MHz solid-state NMR probe where each channel is resonated in a single-ended mode. A simple model of CP shows these patterns can be reproduced if the RF fields for the two nuclei are centered at different places in the coil. Experimental measurements using B1 field imaging, nutation arrays on extremely short NMR samples, and de-tuning experiments involving disks of copper incrementally moved through the coil support this model of spatially offset RF fields. We have found that resonating the high frequency channel in a double-ended or "balanced" mode can alleviate this field offset problem, and have implemented this in a three-channel solid state NMR probe of our own design.     

Plasma-induced spatiotemporal modulation of propagating femtosecond pulses

The dynamics of the femtosecond pulse propagation in a plasma channel is investigated by the pumpprobe longitudinal diffractometry and second harmonic generation frequency-resolved optical gating (SHGFROG) technique. The spatial characteristics, corresponding to the electronic density and the size of the channel, can be observed by the recorded ring pattern, and the spectral and temporal characteristics are recorded by the SHG-FROG traces. The spatiotemporal characteristics will help us to better understand the dynamics of the plasma induced by the femtosecond pulse and the femtosecond pulse propagating in the plasma channel.     

Coherence selection in double CP MAS NMR spectroscopy

Applications of double cross-polarization (CP) magic-angle spinning (MAS) NMR spectroscopy, via (1)H/(15)N and then (15)N/(13)C coherence transfers, for (13)C coherence selection are demonstrated on a (15)N/(13)C-labeled N-acetyl-glucosamine (GlcNAc) compound. The (15)N/(13)C coherence transfer is very sensitive to the settings of the experimental parameters. To resolve explicitly these parameter dependences, we have systematically monitored the (13)C{(15)N/(1)H} signal as a function of the rf field strength and the MAS frequency. The data reveal that the zero-quantum coherence transfer, with which the (13)C effective rf field is larger than that of the (15)N by the spinning frequency, would give better signal sensitivity. We demonstrate in one- and two-dimensional double CP experiments that spectral editing can be achieved by tailoring the experimental parameters, such as the rf field strengths and/or the MAS frequency.     

Cross- and axial-peak intensities in 2D-SLF experiments based on cross-polarization--the role of the initial density matrix

Simulations and experiments on simple oriented systems have been used to estimate the relative ratio of cross-peak to axial-peak intensities in 2D-SLF experiments based on dipolar oscillations during cross-polarization (CP). The density matrix prior to dipolar evolution is considered and for an isolated spin pair, it is shown that direct calculations of the ratios match well with simulations and experimental results. Along with the standard CP pulse sequence, two other pulse sequences namely CP with polarization inversion (PI-CP) and another novel variation of the standard CP experiment (EXE-CP) reported recently have been considered. Inclusion of homonuclear dipolar coupling has been observed to increase the axial-peak intensities. In combination with Lee-Goldburg (LG) decoupling, experiments on an oriented liquid crystalline sample have been carried out and the performance of the pulse schemes have been compared. The applicability of the new pulse sequence for different samples and different nuclei is discussed. Such studies are expected to lead to a better understanding of the experiments and to the design of useful pulse sequences.     

Photocurrent and spin manipulation in quantum dots

In this paper we use a density matrix formalism to model the spin photocurrent obtained from a single self-assembled quantum dot photodiode under the influence of an applied strong polarized electromagnetic pulse and a gate voltage. We show that the degree of polarization of the output photocurrent generated by a circularly polarized pulse in a strongly anisotropic quantum dot can be switched as we increase the pulse intensity. A similar effect is observed in a quantum dot with weak anisotropic electron–hole exchange interaction by using an elliptically polarized pulse. In the latter, a shorter pulse is needed, which creates an effective exchange channel through the biexciton. This phenomenon can be used as a dynamical switch to invert the spin-polarization of the extracted current.     

Nonresonant interaction of femtosecond laser pulse with centrosymmetric molecules

We have derived a system of equations that describes the evolution of the density matrix of a centrosymmetric molecule interacting with a single nonresonant femtosecond laser pulse. The dynamics of the ground electronic state is expressed in terms of the effective Hamiltonian and the coherences between the ground an excited electronic states are functionals of the ground state density matrix. Using the time-dependent perturbation theory, we have calculated the energy deposited in the molecule as a result of rotational stimulated Raman scattering. The effective absorption coefficient is found to be proportional to the fourth power of the pulse amplitude and has a resonance-like dependence with respect to the pulse duration.     

Powder MAS NMR lineshapes of quadrupolar nuclei in the presence of second-order quadrupole interaction

We derive a complete analytical solution for the powder magic angle spinning (MAS) nuclear magnetic resonance (NMR) lineshape in the presence of second-order quadrupole interaction, considering a radiofrequency (rf) pulse of finite width, a finite MAS frequency, and a non-zero asymmetry parameter. I_x is calculated using two approaches. The first applies time-dependent perturbation theory in the presence of the rf pulse and stationary perturbation theory (SPT) in its absence. The second is based on the Magnus expansion of the density matrix in the interaction representation during the pulse and SPT in its absence. We solve the problem in the laboratory frame using the properties of the Fourier transform and spin operators. Diagonalisation is not required. Both approaches agree well with each other under all conditions and also with the transition probability approach for the central transition. The Magnus expansion exists at all times and the effect of the non-secular terms is negligible. We describe an analytical method of averaging I_x over the Euler angles and simulate the ¹¹B MAS NMR lineshapes for crystalline and vitreous B₂O₃. A critical analysis is given of all earlier calculations of the MAS NMR lineshape.     

The influence of the skin effect on gamma detected pulsed NMRON signals

The influence of the skin effect on single and triple (spin echo) gamma detected pulsed NMRON signals is calculated using a density matrix approach within a pure Zeeman manifold. For single pulse NMRON the turn angle dependences of the signals for uniform and exponential profiles of the resonant nuclei are presented for a typical inhomogeneous broadening applicable to intermediate mass impurities in ferromagnetic hosts. For triple pulse NMRON the baseline and principal spin echo amplitudes for equal resonant rf pulses are presented for the same inhomogeneous broadening. It is found that the skin effect leads to the form of pulsed NMRON signals that are in accord with experiment.     

Transverse Ising model: Markovian evolution of classical and quantum correlations under decoherence

The transverse Ising Model (TIM) in one dimension is the simplest model which exhibits a quantum phase transition (QPT). Quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity are known to provide signatures of QPTs. The issue is less well explored when the quantum system is subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. In this paper we study the dynamics of the mutual information I(ρ _AB ), the classical correlations C(ρ _AB ) and the quantum correlations Q(ρ _AB ), as measured by the QD, in a two-qubit state the density matrix of which is the reduced density matrix obtained from the ground state of the TIM in 1d. The time evolution brought about by system-environment interactions is assumed to be Markovian in nature and the quantum channels considered are amplitude damping, bit-flip, phase-flip and bit-phase-flip. Each quantum channel is shown to be distinguished by a specific type of dynamics. In the case of the phase-flip channel, there is a finite time interval in which the quantum correlations are larger in magnitude than the classical correlations. For this channel as well as the bit-phase-flip channel, appropriate quantities associated with the dynamics of the correlations can be derived which signal the occurrence of a QPT.     

Velocity sensitivity of slice-selective excitation

The purpose of this study was to investigate how flow affects slice-selective excitation, particularly for radiofrequency (rf) pulses optimized for slice-selective excitation of stationary material. Simulation methods were used to calculate the slice profiles for material flowing at different velocities, using optimal flow compensation when appropriate. Four rf pulses of very different shapes were used in the simulation study: a 90° linear-phase Shinnar-LeRoux pulse; a 90° self-refocusing pulse; a minimum-phase Shinnar-LeRoux inversion pulse; and a SPINCALC inversion pulse. Slice profiles from simulations with a laminar flow model were compared with experimental studies for two different rf pulses using a clinical magnetic resonance imaging (MRI) system. We found that, for a given rf pulse, the effect of flow on slice-selective excitation depends on the product of the selection gradient amplitude, the component of velocity in the slice selection direction, and the square of the rf pulse duration. The shapes of the slice profiles from the Shinnar-LeRoux pulses were relatively insensitive to velocity. However, the slice profiles from the self-refocusing pulse and the SPINCALC pulse were significantly degraded by velocity. Experimental slice profiles showed excellent agreement with simulation. In conclusion, our study demonstrates that slice-selective excitation can be significantly degraded by flow depending on the velocity, the gradient amplitude, and characteristics of the rf excitation pulse used. The results can aid in the design of rf pulses for slice-selective excitation of flowing material.     

Coherent Interband and Intersubband Dynamics in Terahertz-Driven GaAs Quantum Wells

We theoretically investigate the optical absorption spectra and charge density by subjecting a GaAs quantum well to both an intense terahertz (THz)-frequency driving field and an optical pulse within the theory of density matrix. In presence of a strong THz field, the optical transitions in quantum well subbands are altered by the THz field. The alteration has a direct impact on the optical absorption and the charge density. The excitonic peak splitting and THz optical sideband in the absorption spectra show up when changing the THz field intensity and/or frequency. The Autler-Towns splitting is a result from the THz nonlinear dynamics of confined excitons. On the other hand, the carrier charge density is created as wave packets formed by coherent superposition of several eigenstates. The charge density exhibitsquantum beats for short pulses and/or wider wells and is modulated by the THz field.     

Improved selective 180° radiofrequency pulses for magnetization inversion and phase reversal

Many efforts have been made to find a good selective 180° rf pulse, which include using amplitude and phase modulations, applying optimization techniques, and employing double-pulse techniques. While adequate selective magnetization inversion pulses have been designed, problems remain in the design of selective phase reversal pulses. In this paper we describe a novel approach which achieves large nutation angle selective rf pulses by using a series of small nutation angle pulse twins with alternated gradients (SNAPTAG). The design scheme takes into account the special properties of the rotation matrix appropriate for describing an rf pulse in the presence of a static field gradient. These pulses are suitable not only for selective magnetization inversion but also for selective phase reversal.     

激光脉冲和电子束对撞准确度的测量方法

超强激光脉冲与相对论电子束相互对撞是当前主要的强场量子电动力学（QED）实验手段。如何测量超强激光脉冲和电子束对撞的准确度,进而实现微米精度的准确对撞,是目前限制实验发展的重要因素。利用蒙特卡罗数值模拟方法,系统研究了超强激光脉冲和相对论电子束相互对撞过程,重点关注了电子和辐射光子动力学信息与激光脉冲和电子束对撞偏移量之间的对应关系。研究发现:辐射光子的空间分布信息,可以有效反映出激光脉冲和电子束的对撞偏移量。基于该研究结果,实验中可利用光子空间分布的信息,实现对激光脉冲和电子束对撞准确度的调节,从而有望促进强场QED实验技术的发展。     

Repetitive cross-polarization contacts via equilibration-re-equilibration of the proton bath: Sensitivity enhancement for NMR of membrane proteins reconstituted in magnetically aligned bicelles

Thermodynamic limit of magnetization corresponding to the intact proton bath usually cannot be transferred in a single cross-polarization contact. This is mainly due to the finite ratio between the number densities of the high- and low-gamma nuclei, quantum-mechanical bounds on spin dynamics, and Hartmann-Hahn mismatches due to rf field inhomogeneity. Moreover, for fully hydrated membrane proteins refolded in magnetically oriented bicelles, short spin-lock relaxation times (T1ρ) and rf heating can further decrease cross polarization efficiency. Here we show that multiple equilibrations-re-equilibrations of the high- and low-spin reservoirs during the preparation period yield an over twofold gain in the magnetization transfer as compared to a single-contact cross polarization (CP), and up to 45% enhancement as compared to the mismatch-optimized CP-MOIST scheme for bicelle-reconstituted membrane proteins. This enhancement is achieved by employing the differences between the spin-lattice relaxation times for the high- and low-gamma spins. The new technique is applicable to systems with short T1ρ's, and speeds up acquisition of the multidimensional solid-state NMR spectra of oriented membrane proteins for their subsequent structural and dynamic studies.