Linear phase slope in pulse design: application to coherence transfer

Using optimal control methods, robust broadband excitation pulses can be designed with a defined linear phase dispersion. Applications include increased bandwidth for a given pulse length compared to equivalent pulses requiring no phase correction, selective pulses, and pulses that mitigate the effects of relaxation. This also makes it possible to create pulses that are equivalent to ideal hard pulses followed by an effective evolution period. For example, in applications, where the excitation pulse is followed by a constant delay, e.g. for the evolution of heteronuclear couplings, part of the pulse duration can be absorbed in existing delays, significantly reducing the time overhead of long, highly robust pulses. We refer to the class of such excitation pulses with a defined linear phase dispersion as ICEBERG pulses (Inherent Coherence Evolution optimized Broadband Excitation Resulting in constant phase Gradients). A systematic study of the dependence of the excitation efficiency on the phase dispersion of the excitation pulses is presented, which reveals surprising opportunities for improved pulse sequence performance.     

Selective excitation in Fourier transform nuclear magnetic resonance. 1978

The applications of frequency-selective excitation methods in Fourier transform NMR are discussed, and a simple technique is described for selective excitation of a narrow frequency region of a high-resolution NMR spectrum in a Fourier transform spectrometer. A regular sequence of identical radiofrequency pulses of small flip angle exerts a strong cumulative effect on magnetizations close to resonance with the transmitter frequency or one of a set of equally spaced sidebands separated by the pulse repetition rate. All other magnetizations precess through an incomplete number of full rotations between pulses, and are caught by successive pulses at an ever changing phase of their precession, which destroys the cumulative effect. The motion of the various nuclear magnetization vectors may be described pictorially according to the Bloch equations, neglecting relaxation during the pulse sequence. A general theory is presented for selective or “tailored” excitation by an arbitrary modulation of the radiofrequency transmitter signal. It confirms earlier conclusions that the frequency-domain excitation spectrum corresponds to the Fourier transform of the transmitter modulation pattern, provided that the NMR response remains linear. The excitation spectra calculated for the selective pulse sequence by these two alternative approaches show good agreement within their respective limitations. A number of practical applications of selective excitation are explored, including solvent peak suppression, the detection of partial spectra from individual chemical sites, selective studies of relaxation and slow chemical exchange, and holeburning or localized saturation.     

Fat-water selective excitation in balanced steady-state free precession using short spatial-spectral RF pulses

Fat suppression is important but challenging in balanced steady-state free precession (bSSFP) acquisitions, for a number of clinical applications. In the present work, the practicality of performing fat-water selective excitations using spatial-spectral (SPSP) RF pulses in bSSFP sequence is examined. With careful pulse design, the overall duration of these SPSP pulses was kept short to minimize detrimental effects on TR, scan time and banding artifact content. Fat-water selective excitation using SPSP pulses was demonstrated in both phantom and human bSSFP imaging at 3T, and compared to results obtained using a two-point Dixon method. The sequence with SPSP pulses performed better than the two-point Dixon method, in terms of scan time and suppression performance. Overall, it is concluded here that SPSP RF pulses do represent a viable option for fat-suppressed bSSFP imaging.     

Linear response equilibrium

A new periodic pulse sequence employing weak excitation is presented. This type of sequence drives the system into a steady-state with periodic time evolution from which the data can be reconstructed to a spectrum. It is demonstrated that the frequency response of such a sequence can be analyzed using perturbation methods and linear system analysis. A mathematical framework is proposed allowing the frequency response to be tailored by weighting a periodic flip function. The weak excitation level used implies very low specific absorption rates while generating a highly frequency selective signal in the order of 1/T2 with signal strengths comparable to those obtainable with conventional large flip angle balanced steady-state free precession techniques. The concept is illustrated with phantom experiments and in vivo feasibility of water fat separation is shown on human knee images.     

A new two-dimensional pulse sequence for T(2)* measurements of protons in (13)C isotopomers

A new two-dimensional pulse sequence for T(2)* measurement of protons directly coupled to (13)C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a "building block" into any direct or inverse detecting H,C correlation pulse sequence if proton spin-spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

The equivalence between off-resonance and on-resonance pulse sequences and its application to steady-state free precession with diffusion in inhomogeneous fields

We show that the spin dynamics of any pulse sequence with off-resonant pulses is identical to that of a modified sequence with on-resonant pulses, including relaxation and diffusion effects. This equivalence applies to pulse sequences with arbitrary offset frequency deltaomega(0) which may exceed the RF field strength omega(1). Using this approach, we examine steady-state free precession (SSFP) in grossly inhomogeneous fields. We show explicitly that the magnitude of the magnetization for each mode at an offset frequency deltaomega(0) is equal to that for SSFP with on-resonance pulses of rescaled amplitude, with the same dependence on relaxation times and diffusion coefficient. The rescaling depends on offset frequency and RF field strength. The theoretical results have been tested experimentally and excellent agreement is found.     

The application of steady-state free precession in rapid 2DFT NMR imaging: FAST and CE-FAST sequences

In the classic spectroscopic steady-state free precession (SSFP) experiment, a regular sequence of phase-coherent radio frequency pulses is applied with constant flip angle and a repetition time shorter than the NMR relaxation times of the sample. As the steady state is reached, an NMR signal appears between pulses that consists of two distinct components: a free induction signal following the RF pulses and decaying during the repetition interval and a spin-echo-like signal forming at its end prior to the subsequent RF pulse. Both signals may be exploited for NMR imaging if the gradient schemes fulfill the phase coherence requirements of SSFP. This article describes two Fourier acquired steady-state sequences dubbed FAST and CE-FAST, which may be used for the rapid acquisition of NMR images from the SSFP signals.     

Gapped pulses for frequency-swept MRI

A recently introduced method called SWIFT (SWeep Imaging with Fourier Transform) is a fundamentally different approach to MRI which is particularly well suited to imaging objects with extremely fast spin–spin relaxation rates. The method exploits a frequency-swept excitation pulse and virtually simultaneous signal acquisition in a time-shared mode. Correlation of the spin system response with the excitation pulse function is used to extract the signals of interest. With SWIFT, image quality is highly dependent on producing uniform and broadband spin excitation. These requirements are satisfied by using frequency-modulated pulses belonging to the hyperbolic secant family (HSn pulses). This article describes the experimental steps needed to properly implement HSn pulses in SWIFT. In addition, properties of HSn pulses in the rapid passage, linear region are investigated, followed by an analysis of the pulses after inserting the “gaps” needed for time-shared excitation and acquisition. Finally, compact expressions are presented to estimate the amplitude and flip angle of the HSn pulses, as well as the relative energy deposited by the SWIFT sequence.     

Cooling overall spin temperature: protein NMR experiments optimized for longitudinal relaxation effects

In experiments performed on protonated proteins at high fields, 80% of the NMR spectrometer time is spent waiting for the ¹H atoms to recover their polarization after recording the free induction decay. Selective excitation of a fraction of the protons in a large molecule has previously been shown to lead to faster longitudinal relaxation for the selected protons [K. Pervushin, B. Vögeli, A. Eletsky, Longitudinal ¹H relaxation optimization in TROSY NMR spectroscopy, J. Am. Chem. Soc. 124 (2002) 12898–12902; P. Schanda, B. Brutscher, Very fast two-dimensional NMR spectroscopy for real-time investigation of dynamic events in proteins on the time scale of seconds, J. Am. Chem. Soc. 127 (2005) 8014–8015; H.S. Attreya, T. Szyperski, G-matrix Fourier transform NMR spectroscopy for complete protein resonance assignment, Proc. Natl. Acad. Sci. USA 101 (2004) 9642–9647]. The pool of non-selected protons acts as a “thermal bath” and spin-diffusion processes (“flip-flop” transitions) channel the excess energy from the excited pool to the non-selected protons in regions of the molecule where other relaxation processes can dissipate the excess energy. We present here a sensitivity enhanced HSQC sequence (COST-HSQC), based on one selective E-BURP pulse, which can be used on protonated ¹⁵N enriched proteins (with or without ¹³C isotopic enrichment). This experiment is compared to a gradient sensitivity enhanced HSQC with a water flip-back pulse (the water flip-back pulse quenches the spin diffusion between ¹H^N and ¹H^α spins). This experiment is shown to have significant advantages in some circumstances. Some observed limitations, namely sample overheating with short recovery delays and complex longitudinal relaxation behaviour are discussed and analysed.     

Use of Carr-Purcell pulse sequence with low refocusing flip angle to measure T₁ and T₂ in a single experiment

The Carr-Purcell pulse sequence, with low refocusing flip angle, produces echoes midway between refocusing pulses that decay to a minimum value dependent on T(2). When the refocusing flip angle was π/2 (CP(90)) and τ>T(2), the signal after the minimum value, increased to reach a steady-state free precession regime (SSFP), composed of a free induction decay signal after each pulse and an echo, before the next pulse. When τ相似文献   

Formation and erasure of population difference gratings in the coherent interaction of a resonant medium with extremely short optical pulses

In the regime of coherent interaction of short optical pulses with a resonant medium, which is implemented with a pulse duration shorter than the relaxation times in the medium, the formation of population gratings can occur without overlapping the pulses therein. In this case, there are new possibilities for controlling optical pulses, which are especially pronounced for extremely short pulses. It is shown that, with the proper choice of the parameters of a sequence of extremely short optical pulses, not only the formation of population gratings, but also their erasure are possible. It is demonstrated that this effect can be used for the creation of an ultrahigh-speed optical deflector.     

Nonselective excitation of pulsed ELDOR using multi-frequency microwaves

The use of a polychromatic microwave pulse to expand the pumping bandwidth in pulsed electron-electron double resonance (PELDOR) was investigated. The pumping pulse was applied in resonance with the broad (～100 mT) electron paramagnetic resonance (EPR) signal of the manganese cluster of photosystem II in the S2 state. The observation pulses were in resonance with the narrow EPR signal of the tyrosine radical, YD·. It was found that in the case of the polychromatic pumping pulse containing five harmonics with the microwave frequencies between 8.5 and 10.5 GHz the PELDOR effect corresponding to the dipole interaction between the Mn cluster and YD· was about 2.9 times larger than that achieved with a monochromatic pulse. In addition to the dipolar modulation, the nuclear modulation effects were observed. The effects could be suppressed by averaging the PELDOR trace over the time interval between the observation microwave pulses. The polychromatic excitation technique described will be useful for improving the PELDOR sensitivity in the measurements of long distances in biological samples, where the pair consists of a radical with a narrow EPR spectrum and slow phase relaxation, and a metal center that has a broad EPR spectrum and a short phase relaxation time.     

Photon Echo from Localized Excitons in Semiconductor Nanostructures

An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.     

Anwendung von Doppelresonanzmethoden in der Fourier-Transformationsspektroskopie der hochauflösenden NMR

The influence of a second radio-frequency-field on the free induction decay is investigated theoretically for an AX-System with intramolecular dipol-dipol-interaction as relaxation mechanism. When the second rf-field is irradiated only during the detection of the free induction signal the Fourier-transformation of this signal yields spin-decoupled-or spin-tickling-spectra without the influence of Overhauser-effects. In the other case when the second rf-field is shut off just before the short π/2-pulse is applied the Fourier Transform of the free precession signal consists of lines at the single-resonance positions, the intensities of which are changed through the generalized Overhauser-effect. The line intensity changes are different whether a selective or a nonselective pulse is applied.     

Quasiballistic magnetization reversal

We demonstrate a quasiballistic switching of the magnetization in a microscopic magnetoresistive memory cell. By means of time resolved magnetotransport, we follow the large angle precession of the free layer magnetization of a spin valve cell upon application of transverse magnetic field pulses. Stopping the field pulse after a 180 degrees precession rotation leads to magnetization reversal with reversal times as short as 165 ps. This switching mode represents the fundamental ultrafast limit of field induced magnetization reversal.     

Separation and characterization of different signals from intermolecular three-spin orders in solution NMR

In this paper, signals originating from a pure specific coherence of intermolecular three-spin orders were separated and characterized experimentally in highly polarized two-component spin systems. A modified CRAZED sequence with selective radio-frequency excitation was designed to separate the small signals from the strong conventional single-spin single-quantum signals. General theoretical expressions of the pulse sequence with arbitrary flip angle pulses were derived using dipolar field treatment. The expressions were used to predict the relaxation and diffusion properties and optimal experimental parameters such as flip angles. For the first time, relaxation and diffusion properties of pure intermolecular single-quantum, double-quantum, and triple-quantum coherences of three-spin orders were characterized and analyzed in one-dimensional experiments. All experimental observations are in excellent agreement with the theoretical predictions. The theoretical results show that the quantum-mechanical treatment leads to exactly the same predictions as the dipolar field treatment. The quantitative study of intermolecular multiple-quantum coherences of three-spin orders presented herein provides a better understanding of their mechanisms.     

Creation of cluster state of four ions in ion-trap system by individual addressing

The cluster state is a special, highly entangled quantum state that forms the universal resource, on which measurement-based quantum computation can be performed. In this study, a new scheme is presented for creating four-ions cluster state in ion-trap system. This scheme is based on resonant sideband excitation in which the population is transferred to target states by precise control of pulse area. Meanwhile, the scheme is consist of combination of elementary stages belonging to a universal set whereby cluster state has been created in five interaction stages by individually addressed ions with red- or blue-sideband resonance laser pulses. The paper studies the population transfer of the system by numerical solutions of the master equation, considering the effect of decoherence channels due to dissipation in the phonon modes. The presented scheme does not require control of the turn-off ratio and time delay among pulses.