Universal equations for linear adiabatic pulses and characterization of partial adiabaticity

A numerical analysis of the sech/tanh (or hyperbolic secant) and tanh/tan adiabatic inversion pulses provides a set of master equations for each type of pulse that guarantee their optimal implementation over a wide range of practical conditions without needing to further simulate the inversion profiles of the pulses. These simple equations determine the necessary maximum RF amplitude (RF(max)) required for a preselected degree of inversion across a chosen effective bandwidth (bw(eff)) and for a chosen pulse length (T(p)). The two types of pulse function differently: The sech/tanh pulse provides a rectangular inversion profile with bw(eff) being a large fraction of the adiabatic frequency sweep (bwdth), whereas for tanh/tan bw(eff) is < or =bwdth/20. If the quality of inversion is defined as the minimum allowable extent of inversion, iota(bw), at the boundaries of bw(eff), two basic linear equations are found for both types of pulse and these are of the form (RF(max)T(p))(2)=m(1)T(p)bwdth+c(1) and T(p)bwdth=m(3)T(p)bw(eff)+c(3). The different behavior of the two pulses is expressed as different dependencies of the slopes m(n) and intercepts c(n) on iota(bw) and allowances are made for second order effects within these equations. The availability of these master relationships enables a direct comparison of the two types of adiabatic pulse and it is found that tanh/tan requires about half the pulse length of an equivalent sech/tanh pulse and also has the advantage of being less sensitive to the effects of scalar coupling. In contrast sech/tanh delivers about half the total RF power of an equivalent tanh/tan pulse. It is expected that the forms of these two basic linear equations are generally applicable to adiabatic inversion pulses and thus define the concept of "linear adiabaticity." At low values of T(p)bwdth or T(p)bw(eff) the linear equations no longer apply, defining a region of "partial adiabaticity." Normal adiabatic pulses in the middle of this partial region are more efficient in terms of RF(max) or T(p) but are moderately less tolerant to RF inhomogeneity. A class of numerically optimized pulses has recently been developed that specifically trades adiabaticity in an attempt to gain RF(max) or T(p) efficiency. In comparison to normal adiabatic pulses implemented under optimal conditions, these new partially adiabatic pulses show only marginal improvements; they are restricted to single values of T(p)bw(eff), and they are vastly less tolerant to RF inhomogeneity. These comparisons, and direct comparisons between any types of inversion pulse, adiabatic or otherwise, can be made using plots of (RF(max)T(p))(2) or (Total Power) T(p) versus T(p)bw(eff).     

RF pulse concatenation for spatially selective inversion

It is shown that spatially selective inversion and saturation can be achieved by concatenation of RF pulses with lower flip angles. A concatenation rule which enables global doubling of the flip angle of any given excitation pulse applied to initial z magnetization is proposed. In this fashion, the selectivity of the single pulse is preserved, making the high selectivity achievable in the low flip-angle regime available for inversion and large flip-angle saturation purposes. The profile quality achievable with exemplary concatenated pulses is investigated in comparison with adiabatic inversion. It is verified that by using concatenated inversion in the transfer insensitive labeling technique (TILT), the MT artifact is suppressed. Copyright 2000 Academic Press.     

Efficient coherent population transfer among three states in NO molecules by Stark-Chirped rapid adiabatic passage

We present the experimental demonstration of a novel, efficient, and selective technique to prepare population inversion. The technique is an extension of Stark-chirped rapid adiabatic passage (SCRAP), i.e., SCRAP among three states. In this process a Lambda-type quantum system is driven by two laser pulses, the pump and Stokes pulses, which are appropriately detuned from transition frequencies. A third laser pulse induces a dynamic Stark shift in the upper energy level, and the timing of all three pulses is controlled in order to prepare population inversion between the two lower states in the Lambda-type level scheme. Our data on population transfer in nitric oxide (NO) molecules clearly show that SCRAP among three states provides an advantageous alternative to such techniques as stimulated Raman adiabatic passage.     

Improved Broadband Inversion Performance for NMR in Liquids

New NMR broadband inversion pulses that compensate both for resonance offset and radiofrequency (RF) inhomogeneity are described. The approach described is a straightforward computer optimization of an initial digitized waveform generated from either a constant-amplitude frequency sweep or from an existing composite inversion pulse. Problems with convergence to local minima are alleviated by the way the optimization is carried out. For a given duration and maximum allowable RF field strength B₁ (but not necessarily given RMS power deposition), the resultant broadband inversion pulse (BIP) shows superior inversion compared to inversion pulses obtained from previous methods, including adiabatic inversion pulses. Any existing BIP can be systematically elaborated to build up longer inversion pulses that perform over larger and larger bandwidths. The resulting pulse need not be adiabatic throughout its duration or across the entire operational bandwidth.     

Optimization of Adiabatic Selective Pulses

Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theB_effvector and the rate of motion upon it. In this paper, a method is described for optimizing adiabatic inversion pulses to achieve a frequency-selective magnetization inversion over a given bandwidth in a shorter time and to improve slice profile. An efficient adiabatic pulse is used as an initial condition. This pulse allows for flexibility in choosing its parameters; in particular, the transition sharpness may be traded off against the inverted bandwidth. The considerations for selecting the parameters of the pulse according to the requirements of the design are discussed. The optimization process then improves the slice profile by optimizing the rate of motion along the trajectory of the pulse while preserving the trajectory itself. The adiabatic behavior of the optimized pulses is fully preserved over a twofold range of variation in the RF amplitude which is sufficient for imaging applications in commercial high-field MRI machines. Design examples demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse.     

Design and optimization for variable rate selective excitation using an analytic RF scaling function

At higher B(0) fields, specific absorption rate (SAR) deposition increases. Due to maximum SAR limitation, slice coverage decreases and/or scan time increases. Conventional selective RF pulses are played out in conjunction with a time independent field gradient. Variable rate selective excitation (VERSE) is a technique that modifies the original RF and gradient waveforms such that slice profile is unchanged. The drawback is that the slice profile for off-resonance spins is distorted. A new VERSE algorithm based on modeling the scaled waveforms as a Fermi function is introduced. It ensures that system related constraints of maximum gradient amplitude and slew rate are not exceeded. The algorithm can be used to preserve the original RF pulse duration while minimizing SAR and peak b1 or to minimize the RF pulse duration. The design is general and can be applied to any symmetrical or asymmetrical RF waveform. The algorithm is demonstrated by using it to (a) minimize the SAR of a linear phase RF pulse, (b) minimize SAR of a hyperbolic secant RF pulse, and (c) minimize the duration of a linear phase RF pulse. Images with a T1-FLAIR (T1 FLuid Attenuated Inversion Recovery) sequence using a conventional and VERSE adiabatic inversion RF pulse are presented. Comparison of images and scan parameters for different anatomies and coils shows increased scan coverage and decreased SAR with the VERSE inversion RF pulse, while image quality is preserved.     

Inversion in an extended three-level medium produced by adiabatic population transfer

Features of the adiabatic population transfer are studied with the spatial evolution of interacting pulses propagating in an optically dense medium of three-level Λ-atoms taken into account. A self-consistent analytical solution describing the spatial-temporal dynamics of interacting short pulses under the conditions of adiabatic population transfer is constructed in the adiabatic approximation with consideration for the first nonadiabatic correction. Practically complete inversion on a forbidden transition determined by coherent (adiabatic) population transfer is shown to take place over a length of the medium, which may exceed the absorption length of a weak probing pulse in the absence of control radiation on the adjacent transition by several orders of magnitude.     

Compensation of refocusing inefficiency with synchronized inversion sweep (CRISIS) in multiplicity-edited HSQC

Use of adiabatic pulses in broadband inversion and decoupling is well known. Replacement of the rectangular pi pulses in the INEPT and rev-INEPT parts of the HSQC and gHSQC experiments with adiabatic pulses substantially improves the sensitivity of these experiments. However, modulation of cross peak intensity in multiplicity-edited HSQC or gHSQC experiments can be quite severe. These modulations arise during the multiplicity-editing periods due to the inefficient refocusing of the spin-echo caused by the mismatch of the echo delay with the one-bond coupling constant. These modulations (which we call echo modulations) are field strength (and hence spectral width) independent. Use of adiabatic pulses with the inversion sweep synchronized to the 1H-13C coupling constant range typically observed in a 13C spectrum will provide substantial improvement in sensitivity. The inversion profile problems associated with rectangular pi pulses can be moderately compensated by composite pulse schemes and these schemes could prove to be reasonable alternatives to adiabatic pulses. However, the adiabatic sweep provides a unique method to compensate the echo modulations for multiplicity-edited experiments. The origin and the compensation of refocusing inefficiency with synchronized inversion sweep (CRISIS) method to minimize these modulations is described.     

Population transfer between two quantum states by piecewise chirping of femtosecond pulses: theory and experiment

We propose and experimentally demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The piecewise nature of the process suggests a possibility for the selective population transfer in complex quantum systems.     

Efficient population transfer by delayed pulses despite coupling ambiguity

In traditional schemes of multilevel multilaser excitation, each laser pulse interacts with only one pair of states, and the rotating wave approximation (RWA) is applicable. Here we study the population transfer process in a three-state system when each of the two lasers interacts with each of the pair of states and when the Rabi frequencies characterizing the interaction strengths of the system are comparable to or larger than the difference of the transition frequencies. We show that complete and robust population transfer is possible under conditions more general than those hitherto considered necessary for stimulated Raman adiabatic passage (STIRAP) or for successive π pulses. Using adiabatic Floquet theory we show that successful population transfer can be interpreted as adiabatic passage by means of a transfer state which connects the initial and final states. The Floquet picture offers a convenient interpretation of the population transfer as accompanied by multiple absorption of photons from or emission into the laser fields.     

Asymmetric adiabatic pulses for NH selection.

Many types of NMR experiments demand the use of frequency-selective pulses to invert magnetization within discrete frequency limits. For certain experiments, only one side of the inversion band must be sharply demarcated, in which case this transition bandwidth can be narrowed when using an asymmetric adiabatic full passage. In the present study, a highly efficient asymmetric adiabatic full passage was created from a combination of two adiabatic half passages which used different modulation functions (HS12 and tanh/tan). Each adiabatic half passage occupied a different amount of time in the total pulse and performed one-half of the inversion. On one side, HS12 produced a sharp transition between inverted and noninverted states which was approximately 2.5 times narrower than the transition bandwidth afforded by a symmetric hyperbolic secant pulse of equal length. On the other side of the narrow transition band, the tanh/tan pulse achieved broadband inversion. These asymmetric pulses were applied to select NH groups immediately adjacent to the water signal in water-flip-back HSQC experiments using a double spin echo for the reverse INEPT step.     

Stimulated Raman adiabatic passage in fields with stochastic amplitudes

A theoretical analysis is presented of the effect of correlation between fluctuations of laser pulse amplitudes on population transfer between the states of a three-level atom coupled by the laser field. The carrier frequencies of the pulses are tuned to resonance with the transitions between the ground and excited states, |〈 and | 2〈, and the excited and metastable states, |2〈 and |3〈, in a lambda-type configuration. The laser pulses are timed so that population transfer between states |1〈 and | 3〈 is made possible by stimulated Raman adiabatic passage (STIRAP) in the absence of fluctuations. STIRAP does not occur when the laser fields are not correlated. When the fluctuations of one pulse amplitude duplicate those of the other, STIRAP can be observed for pulse amplitudes larger than those required in the absence of fluctuations.     

Intermolecular multiple-quantum coherence NMR signals modulated by double distant dipolar fields

A modified CRAZED pulse sequence was applied to obtain the intermolecular multiple-quantum coherence NMR signals from double distant dipolar fields in highly polarized spin systems. Complete theoretical analyses were explicitly derived from the dipolar field treatment combined with product operator formalism. Two typical samples containing several different components were chosen for the experimental verifications. The computer simulations and experimental observations are consistent with the theoretical predictions. The results presented herein provide a convenient way to understand the combined effects of multiple distant dipolar fields from the different components in complicated chemical or biological solutions. When experimental conditions such as selective radio-frequency pulses are not optimal, it may be helpful to identify possible unexpected signals or artefacts of high-resolution NMR spectroscopy in inhomogeneous fields.     

Velocity selective radiofrequency pulse trains

The incorporation of velocity-encoding gradient pulses in RF-pulse trains is proposed and examined. Velocity selective perturbation is shown to be analogous in many respects to the well established use of trains of short RF-pulses for chemical shift selective perturbation. Velocity selective perturbation is viable in a biomedical setting only if additional RF refocusing pulses are inserted between the individual RF-pulse elements. Aspects of velocity selective excitation saturation and inversion are examined, and new inversion pulse trains proposed. The selective perturbation of both flowing and stationary spins is demonstrated in phantoms and possible biomedical applications of these pulse trains are discussed.     

General theory of population transfer by adiabatic rapid passage with intense, chirped laser pulses

We present a general theory of adiabatic rapid passage (ARP) with intense, linearly chirped laser pulses. For pulses with a Gaussian profile and a fixed bandwidth, we derive a rigorous formula for the maximum temporal chirp rate that can be sustained by the pulse. A modified Landau-Zener formula displays clearly the relationships among the pulse parameters. This formula is used to derive the optimal conditions for efficient, robust population transfer. As illustrations of the theory, we present results for two- and four-level systems, and selective vibronic excitation in the I₂ molecule. We demonstrate that population transfer with chirped pulses is more robust and more selective than population transfer with transform-limited pulses. Received 6 September 2000 and Received in final form 25 September 2000     

NMR spectroscopy in inhomogeneous B0 and B1 fields with non-linear correlation

Resolved NMR spectra from samples in inhomogeneous B0 and B1 fields can be obtained with the so-called "ex situ" methodology, employing a train of composite or adiabatic z-rotation RF pulses to periodically refocus the inhomogeneous broadening during the detection of the time-domain signal. Earlier schemes relied on a linear correlation between the inhomogeneous B0 and B1 fields. Here the pulse length, bandwidth, and amplitude of the adiabatic pulses of the hyperbolic secant type are adjusted to improve the refocusing for a setup with non-linear correlation. The field correlation is measured using a two-dimensional nutation experiment augmented with a third dimension with varying RF carrier frequency accounting for off-resonance effects. The pulse optimization is performed with a computer algorithm using the experimentally determined field correlation and a standard adiabatic z-rotation pulse as a starting point for the iterative optimization procedure. The shape of the z-rotation RF pulse is manipulated to provide refocusing for the conditions given by the sample-, magnet-, and RF-coil geometry.     

Selective polarization inversion of protons in rotating solids

The selective inversion of lines under phase modulated Lee-Goldburg (PMLG) decoupling in MAS proton spectroscopy is demonstrated. Short pulses inserted between consecutive PMLG irradiation intervals selectively invert the polarization of an on-resonance line while sustaining a high resolution proton evolution. The pulse scheme is combined with windowed-PMLG detection to obtain a one-dimensional high resolution spectrum with one of the proton lines inverted. Initial preparation of the protons in selectively inverted states can be used to follow the flow of polarization during spin diffusion. Examples of proton-proton spin exchange in alanine and histidine are demonstrated. Selective inversion is also used in conjunction with proton carbon LG-cross-polarization to achieve carbon spectra with lines characterized by different polarization states.     

Adjustable, broadband, selective excitation with uniform phase

An advance in the problem of achieving broadband, selective, and uniform-phase excitation in NMR spectroscopy of liquids is outlined. Broadband means that, neglecting relaxation, any frequency bandwidth may be excited even when the available radiofrequency (RF) field strength is strictly limited. Selective means that sharp transition edges can be created between pure-phase excitation and no excitation at all. Uniform phase means that, neglecting spin-spin coupling, all resonance lines have nearly the same phase. Conventional uniform-phase excitation pulses (e.g., E-BURP), mostly based on amplitude modulation of the RF field, are not broadband: they have an achievable bandwidth that is strictly limited by the peak power available. Other compensated pulses based on adiabatic half-passage, like BIR-4, are not selective. By contrast, inversion pulses based on adiabatic fast passage can be broadband (and selective) in the sense above. The advance outlined is a way to reformulate these frequency modulated (FM) pulses for excitation, rather than just inversion.     

Quantum correlations of pulses of optical parametric oscillator synchronously pumped above threshold

The quantum analysis of radiation from a degenerate optical parametric oscillator synchronously pumped above its oscillation threshold is presented. It is shown that pulses of signal and pump fields at the output of the oscillator have the following properties: quantum fluctuations of the fields are independent in each individual pulse, but correlated in pulses of the pulse train with a temporal step multiple of the pulse period. The number of essentially correlated pulses is on the order of the oscillator cavity finesse. Cross-correlations between the pump and signal pulses are established above the oscillation threshold. These correlations lead to a significant quantum effect in the integral characteristics of the fields. A theoretical analysis revealed that the spectrum of field fluctuations measured using a balanced homodyne detection technique of phase quadratures of the fields with a pulsed local oscillator reveals quantum noise suppression in the vicinity of frequencies that are multiples of the pulse repetition rate.     

Stimulated Raman adiabatic passage with temporal pulselets

Stimulated Raman adiabatic passage (STIRAP) is a well established technique whereby two pulses, S preceding P, induce complete population transfer between states 1 and 3 of a three-state chain, 1-2-3. Traditionally, the S and P pulse envelopes are taken as positive (often with Gaussian form of time dependence). However, when the envelope undergoes a sign change during the pulse, as occurs with pulses in which an abrupt phase change of π occurs and whose temporal area (time-integrated Rabi frequency) is zero, then the simple population transfer need not occur. Instead there may occur multiple adiabatic passages, in which the population may ultimately be left in either state 1 (a double STIRAP) or state 3 (a triple STIRAP) or, with suitable pulse delay, in a superposition of these two states. These adiabatic changes offer possibilities to produce final-state probability amplitudes with either positive or negative signs. We here show simulated examples of such behavior, and discuss the adiabatic conditions needed for such excitation to occur.