Determination of quadrupole parameters with a composite pulse for spurious signal suppression

Spurious signals such as the piezoelectric signal from a ferroelectric crystal or the ringing signal from the NMR probe head tuned for low gyromagnetic ratio nuclei are often observed in pulsed NMR. Both signals are cancelled using the Hahn echo sequence with appropriate phase cyclings. The present paper applies a composite-pulse sequence to cancel the ringing signal. The main advantage of this sequence over the Hahn echo sequence is in the simplicity of optimizing the line intensity: the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. We are interested in half-integer quadrupole spins (I = 3/2, 5/2, 7/2, and 9/2), which means that we must consider the first-order quadrupole interaction during the pulses. For simplicity, we deal mainly with spin I = 3/2 nuclei. Since the central-line intensity depends on the ratio of the quadrupole coupling constant (QCC) to the amplitude of the RF pulse, we can determine the QCC from a featureless lineshape by fitting the variation of the experimental central-line intensity for increasing pulse duration with theoretical results. Contrary to the one-pulse sequence where the central-line intensity is proportional to the pulse duration if the latter is short, there is no such condition with the composite-pulse sequence. In other words, this sequence does not allow us to quantify the relative spin populations in powders. The size of the sample must be much smaller than that of the RF coil in order for the RF magnetic field to become homogeneous for the sample. We used (87)Rb (I = 3/2) in an aqueous solution of RbCl and in RbNb2O5F powder, (131)Xe (I = 3/2) of xenon gas physisorbed in Na-Y zeolite, and (23)Na (I = 3/2) in two well-known powders (NaNO3 and NaNO2) to support our theoretical result.     

Calculations of multipulse sequence in NQR of spins 32

The general formalism of the interaction representation with respect to an operator which is its own inverse is developed and applied to pure NQR of spins I = 32. Under the assumption of no relaxation and no dipolar coupling, it is shown that the calculation of the response to pure NQR multipulse sequences can be performed with the same concepts used in high field NMR, such as coherence pathways. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. It takes into account the off-resonance irradiation as well as the angular dependence of the excitation and detection for every value of the electric field gradient asymmetry parameter. Particular attention is devoted to the powder average, which is performed via a probability function derived analytically for the first time, leading to a drastic reduction of simulation times. The theory is illustrated by the study of the optimization and excitation bandwidths of one- to three-pulse sequences and compared to experimental results on Chloranil. We show that the three-pulse "stimulated echo" sequence gives a more uniform excitation profile than the traditional two-pulse echo sequence for powder samples. Thus, the "stimulated echo" sequence could be useful to cover a large spectrum when the experiment duration, or the signal to noise ratio, are not critical parameters. Analytical expressions for the nutation spectra obtained by one or two-pulse sequences are also derived for the first time.     

Comparative experimental analysis of composite pulses in 14N NQR

Experimental results of comparing composite pulses in nitrogen-14 NQR, that are analogous to common 90 degrees RF pulses in powder, are presented. All tested pulses have been taken from publications in journals. Comparative diagrams of the measurement results for induction signals and echo signals are presented. The results of the measurements demonstrate that the best outcomes are achieved when the composite pulse (45)0(95)180(164)0 is used.     

14N核四极共振的偏共振效应

用虚拟１／２自旋算符讨论了核四极共振（ＮＱＲ）中自旋Ｉ＝１的自旋系统对激发脉冲宽度和频率偏置的响应。用单脉冲和双脉冲来观测的核四极共振信号与理论预期相符合。此外还证明，若只考虑射频场在分子电场梯度（ＥＰＧ）张量主轴坐标系（ＰＡＳ）中的一个轴上的分量（即有效射频场分量）的作用，就可用ＮＭＲ矢量模型来处理Ｉ＝１的核自旋系统。 关键词：     

粉末样品中氘核NMR的回波序列

本文提出一个回波序列,它由四个90和一个45脉冲构成,具有较宽的激发带宽和较短的激发时间,可用于氘核NMR固体线型的测量之中,数值计算结果表明该回波序列的激发带宽几乎比传统的四极回波宽一倍。²D-PMMA粉末样品的实验结果证实了本文设计的回波序列的优越性。     

Multiple-pulse coherence enhancement of solid state spin qubits

We describe how the spin coherence time of a localized electron spin in solids, i.e., a solid state spin qubit, can be prolonged by applying designed electron spin resonance pulse sequences. In particular, the spin echo decay due to the spectral diffusion of the electron spin resonance frequency induced by the non-Markovian temporal fluctuations of the nuclear spin flip-flop dynamics can be strongly suppressed using multiple-pulse sequences akin to the Carr-Purcell-Meiboom-Gill pulse sequence in nuclear magnetic resonance. Spin coherence time can be enhanced by factors of 4-10 in GaAs quantum-dot and Si:P quantum computer architectures using composite sequences with an even number of pulses.     

Carr-Purcell sequences with composite pulses

We present novel Carr-Purcell-like sequences using composite pulses that exhibit improved performance in strongly inhomogeneous fields. The sequences are designed to retain the intrinsic error correction of the standard Carr-Purcell-Meiboom-Gill (CPMG) sequence. This is achieved by matching the excitation pulse with the refocusing cycle such that the initial transverse magnetization lies along the axis n(Beta) characterizing the overall rotation of the refocusing cycle. Such sequences are suitable for relaxation measurements. It is shown that in sufficiently inhomogeneous fields, the echo amplitudes have an initial transient modulation that is limited to the first few echoes and then decay with the intrinsic relaxation time of the sample. We show different examples of such sequences that are constructed from simple composite pulses. Sequences of the form 90 degrees (0)-(90 degrees (90-theta/2)-theta(180-theta/2)-90 degrees (90-theta/2))(n) with theta approximately 90 degrees and 270 degrees generate signal over a bandwidth larger than that of the conventional CPMG sequence, resulting in an improved signal-to-noise ratio in inhomogeneous fields. The new sequence 127 degrees (x,y)-(127 degrees (x)-127 degrees (-x))(n) only excites signal off-resonance with a spectrum that is bimodal, peaking at Delta omega(0)=+/-omega(1). Depending on the phase and exact timing of the first pulse, symmetric or antisymmetric excitation is obtained. We also demonstrate several new sequences with improved dependence on the RF field strength. The sequence (22.5 degrees (67.5)-90 degrees (-22.5))-(90 degrees (67.5)-45 degrees (157.5)-90 degrees (67.5))(n) has the property that the phase of the signal depends on B(1), allowing coarse B(1) imaging in a one-dimensional experiment.     

Coherent excitation with phase-incremented pulses

An outline is given for calculating the evolution of a spin system by a pulse sequence with phase-incremented pulses (PIPs). It is done in a frame with a speed of 2pideltaf=deltaphi/deltatau relative to the rotating frame, where deltaphi and deltatau are the phase- and time-increment of the PIP. This particular frame is defined as the eigenframe, in which the phase of the PIP for the center band is stationary and is subjected to a universal phase shift (UPS=-deltaphi/2), and the strength of the PIP is scaled by a factor of lambda=2[1-cos(deltaphi)]/(deltaphi). The phase differences between different eigenframes can be attributed to the initial phases of the PIPs, making it possible to use the Bloch vector model even in different eigenframes. A new way is provided to construct composite pulses with not only amplitude and phase modulations but also offset modulation. Several examples, including a broadband inversion pulse, a Hahn spin echo, and a selective inversion and null pulse, all composed of PIPs, are discussed in detail.     

On the Use of the Phase Memory TimeT2for the Quantitative Characterization of the Rotational Motions of Proteins in Lipid Bilayer Systems

Numerical simulations of the echo responses from a nitroxide label rigidly attached to a large protein undergoing ultraslow rotational motions in a lipid bilayer are presented. The echoes are formed by the application of Hahn, COSY, and 2D-ELDOR sequences utilizing both soft and hard microwave pulses. The simulations address the question of whether the echo responses elicited by these sequences are affected by restricted angular excursions of the long axis of the protein relative to the normal to the bilayer plane. The results indicate that all three pulse sequences yield the same quantitative motional information regardless of the nature of the microwave pulses and there is no theoretical reason for preferring one sequence above the others.     

14N Pulsed nuclear quadrupole resonance. 4. Two-pulse sequences for the determination of T1 and T2 relaxation times

A general theory, based on density matrix calculations, has been developed for the special case of a two-pulse sequence applied to spin 1 (¹⁴N) nuclear quadrupole resonance (NQR) of a powder sample. It is shown that the homolog of the NMR inversion-recovery experiment leads easily to the spin-lattice relaxation time T ₁ (associated with the diagonal elements of the density matrix) provided that an appropriate phase cycling is used. Conversely, in spite of two-step phase cycling schemes adapted to spin-spin relaxation measurements, the homolog of the NMR Hahn spin-echo sequence may pose some problems if the results are displayed in the magnitude mode. First, at short decay times, the echo may be corrupted by unwanted signals. Secondly, in that case, the amplitude of the resulting signal can evolve unexpectedly and differently as a function of the phase of the second pulse. Thirdly, at long decay times, the echo maximum occurs earlier than expected. All these problems in principle disappear with a complete four-step phase cycling scheme and the echo decay curve yields reliably the spin-spin relaxation time T ₂ (associated with off-diagonal elements). This theory allowed the exploitation of many test experiments performed at different frequencies on hexamethylenetetramine (HMT) and sodium nitrite.     

相位可控的核四极矩共振激励脉冲发生器设计

在核四极矩共振（NQR）领域,射频激励脉冲信号的优劣对NQR响应信号有重要影响.针对常规方法中射频激励脉冲参数不可控的问题,本文基于32位闪存微型控制器STM32和直接数字频率合成（DDS）芯片AD9910设计了一种相位可控激励脉冲发生器.采用STM32控制AD9910产生波形参数（脉冲宽度、脉冲间隔、脉冲个数和共振频率等）可控的射频激励脉冲,利用LabVIEW软件平台设计脉冲参数设置界面,并建立计算机与微控制器通信,实现波形参数的精确优化控制.实验结果表明,该方法实现了相位可控的NQR激励脉冲序列,可为后续NQR信号检测提供有效激励源.     

Calculations of Multipulse Sequence in NQR of Spins

The general formalism of the interaction representation with respect to an operator which is its own inverse is developed and applied to pure NQR of spins I = . Under the assumption of no relaxation and no dipolar coupling, it is shown that the calculation of the response to pure NQR multipulse sequences can be performed with the same concepts used in high field NMR, such as coherence pathways. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. It takes into account the off-resonance irradiation as well as the angular dependence of the excitation and detection for every value of the electric field gradient asymmetry parameter. Particular attention is devoted to the powder average, which is performed via a probability function derived analytically for the first time, leading to a drastic reduction of simulation times. The theory is illustrated by the study of the optimization and excitation bandwidths of one- to three-pulse sequences and compared to experimental results on Chloranil. We show that the three-pulse “stimulated echo” sequence gives a more uniform excitation profile than the traditional two-pulse echo sequence for powder samples. Thus, the “stimulated echo” sequence could be useful to cover a large spectrum when the experiment duration, or the signal to noise ratio, are not critical parameters. Analytical expressions for the nutation spectra obtained by one or two-pulse sequences are also derived for the first time.     

Three-Frequency Composite Multipulse Nuclear Quadrupole Resonance Technique for Explosive Detection

New method of multifrequency nuclear quadrupole resonance (NQR) for the explosive detection has been proposed. This technique consists of application of the series of composite excitation circles, each consisting of two or three successive pulses of different frequencies. In this work, we study in detail the multipulse sequence consisting of n excitation sets, each set consists of three pulses. The first pulse is applied with frequency ?? _?, the second pulse with frequency ?? ₀, and the third pulse with frequency ?? _?C, but with a shifted phase. The NQR signal is detected at the frequency ?? ₊. The maximal amplitude of the detected signal is obtained by tuning the pulse parameters at frequencies ?? _? and ?? ₀. We have shown that the phase of the NQR signal at the frequency ?? ₊ second part of the composite pulse with the frequency ?? ₀ the signals with different phases to suppress the spurious signals. The method could be used for increasing the NQR signal, avoiding the spurious signals and improving the reliability of NQR detection. Possible applications of the method for the explosive detection are also discussed.     

Non-cyclic geometric phase of nuclear quadrupole resonance signals of powdered samples

The non-cyclic geometric phase of ¹⁴N and ³⁵Cl NQR signals induced by the character of trajectory of nuclear magnetization motion upon pulse r.f. excitation of powdered samples is studied. Analytical expressions for the geometric phases of NQR signals of the nuclei of spins I=1 and 3/2 upon nuclear magnetization rotation induced by means of r.f. pulses with frequency detuned from the resonance and for any impulse duration for a separate crystallite are obtained. It is shown that the geometric phase recorded for the signal from a powdered sample at Δω=0 can be different from zero and can oscillate upon changes in duration of the r.f. excitation pulse. An alternative variant of the nutation experiment aimed at obtaining the asymmetry parameter η from locations of frequency singularities in the nutation phase spectrum for nuclei of spin I=3/2 in powder substances is proposed.     

Band-Selective HSQC and HMBC Experiments Using Excitation Sculpting and PFGSE

Variants of the HSQC and HMBC experiments are described. They allow the restriction of the heteronuclear chemical shift domain without causing spectral folding. Selectivity is introduced in the HSQC experiment by means of excitation sculpting. The selective element of the pulse sequence is a double pulsed field gradient spin echo. It may be used either split by the t(1) evolution period, or not. The selectivity profile depends on the scheme used as well as on the number of protons attached to the heteronucleus. The selective HMBC experiment requires only a single echo sequence as no strict control of the signal phase is required. A complex glycoconjugate is used as a test compound for the new pulse sequences.     

Performance of frequency-modulated pulses in NQR

This paper presents an analysis of the performance of frequency-modulated pulses and of pulses modulated simultaneously in amplitude and frequency in the pure nuclear quadrupolar resonance (NQR) spectroscopy of spin 3/2 nuclei. Computer simulations are given of the offset compensation efficiency of such pulses as applied to single crystals. Spin evolution equations were solved numerically. Experimental measurements, using FM pulses, of the³⁵Cl NQR of sodium chlorate (NaClO₃) single crystal and of mercuric chloride (HgCl₂) powder are reported. The results suggest that frequency modulated pulses are alternative pulses to composite pulses in NQR.     

Influence of molecular motions on NQR echoes

The influence of thermal molecular motions on spin echo decay in pure nuclear quadrupole resonance (NQR) is considered. Our calculations show that the Hahn echo decay is caused by dipole-dipole interaction of the nuclear spins and is strongly affected by molecular mobility that can lead to the shortening of the echo decay with increased temperature. Slow molecular motion yields an exponential τ₃ time dependence, while fast motion yields an exponential decay. The outlined theory allows us to explain an unusual shortening of the³⁵Cl NQR echo decay on heating in thiourea-C₂Cl₆ inclusion compound.     

Electron spin-echo experiments in photo-excited triplet states in an external magnetic field

Electron spin-echo experiments in the photo-excited triplet states of quinoxaline-d₆ and naphthalene-d₈ at 1·2 K in an external magnetic field are presented. These include two-pulse Hahn echoes, three-pulse stimulated echoes and Carr-Purcell pulse-echo trains. The decay of the Hahn and stimulated echoes as a function of pulse interval yields measures of the spin relaxation times. Furthermore, the Hahn echo is used to obtain E.P.R. line shapes and the dynamics of the triplet sublevel populations. The angular dependence of the Hahn echo is also investigated. The Hahn echo decay time and decay modulation suggest the kind of role played by nuclear spins in the loss of electron spin phase coherence. Some promising characteristics of the pulse method are discussed.     

The transient processes in multi-pulse nitrogen-14 NQR

It has been demonstrated that transient processes, observed in a single crystal of NaNO₂ acted upon by pulse sequences MW-2 and MW-4 and their modifications with 180° flip angle of the pulses (Solid State Nucl. Magn. Resonance 10 (1997) 63; Sov. Phys.—JETP 88(5) (1999) 1580), which manifest themselves in the oscillating form of the NQR signals envelope, can be explained in the frames of a two-particle model. It has been proved that the nature of echo signals in the effective field of multi-pulse sequences received by the inversion of the phase of the sequence pulses or by introducing an additional 180° pulse is connected with re-focusing of accumulated digressions of the flip angle from the ideal 180° pulse. Experimental results of observing single and multiple echoes in a number of powdered nitrogenated substances in the effective field of various sequences at room temperature have been presented.