Adiabatic decoupling sidebands

An analytical solution is given for amplitudes and phases of adiabatic decoupling sidebands as a function of spin inversion time tau. Since all the adiabatic decoupling phases theta(t, tau) refocus at two periods (2T) of the decoupling pulse, the sidebands are located at n/2T rather than at n/T as observed in other decoupling schemes. The real (R(n)(tau)) and imaginary (I(n)(tau)) amplitudes of the sidebands have symmetry R(n)(tau) = R(-n)(tau) and I(n)(tau) = -I(-n)(tau), forming a mirror image between the counterparts of the sidebands. When frequency sweep changes direction all I(n)(tau) are inverted while all R(n)(tau) remain unchanged, leading to pure absorption sidebands with two accumulations as demonstrated by Kupce and Freeman, and to an exchange of sidebands between counterparts. The sum of the real parts for sidebands n = 1 and 2 is almost a constant near on-resonance decoupling, and it increases substantially for large decoupling offsets. The phase defocusing can be minimized for all decoupling offsets by inserting an initial decoupling period with T(ini) = T/2, eliminating all sidebands located at n/2T (n = +/-1, +/-3, +/-5, ...).     

"BEST" homonuclear adiabatic decoupling for 13C- and 15N-double-labeled proteins.

The cyclic irradiation sidebands appearing in homonuclear adiabatic decoupling are calculated in detail, which reveals the origin of the antisymmetric sidebands. The sidebands can be inverted by inserting an initial decoupling with a different period, but the same f1rms as the main decoupling that is required for Bloch-Siegert shift compensation. The sidebands can be eliminated in a broad decoupling range by adding spectra of opposite sidebands. Based on this scheme, an offset-independent double-adiabatic decoupling, named Bloch-Siegert Shift Eliminated and Cyclic Sideband Trimmed Double-Adiabatic Decoupling, or "BEST" decoupling for short, is constructed, which not only compensates the Bloch-Siegert shift as shown earlier by Zhang and Gorenstein (1998) but also eliminates residual sidebands effectively.     

“BEST” Homonuclear Adiabatic Decoupling for C- and N-Double-Labeled Proteins

The cyclic irradiation sidebands appearing in homonuclear adiabatic decoupling are calculated in detail, which reveals the origin of the antisymmetric sidebands. The sidebands can be inverted by inserting an initial decoupling with a different period, but the same f_1rms as the main decoupling that is required for Bloch–Siegert shift compensation. The sidebands can be eliminated in a broad decoupling range by adding spectra of opposite sidebands. Based on this scheme, an offset-independent double-adiabatic decoupling, named Bloch–Siegert Shift Eliminated and Cyclic Sideband Trimmed Double-Adiabatic Decoupling, or “BEST” decoupling for short, is constructed, which not only compensates the Bloch–Siegert shift as shown earlier by Zhang and Gorenstein (1998) but also eliminates residual sidebands effectively.     

Effect of Sweep Direction on Sidebands in Adiabatic Decoupling

The appearance of sidebands in adiabatic decoupling can be substantially reduced simply by matching the sweep rate and direction of adiabatic pulses with the evolution of differentJcouplings. Alternatively, a matched adiabatic defocusing pulse is applied just before the decoupling is turned on, providing an efficient means for complete suppression of sidebands.     

A Vector Model of Adiabatic Decoupling

A vector model of adiabatic decoupling is enunciated for an IS-coupled system of two spin- heteronuclei in the high-power limit of ideal adiabatic pulses. The observed S-spin magnetization evolves according to a time-dependent coupling that scales as thezcomponent of an I-spin vector which evolves due to the applied decoupling irradiation. Simple analytical expressions are derived both on and off resonance for the reduced coupling during an ideal sech/tanh inversion pulse and for the resulting signal when either in-phase or antiphase magnetization is present at the start of decoupling. The resulting model allows one to readily envision decoupling experiments, make accurate estimates of sideband intensity, and assess the relative performance of different decoupling schemes. The utility of the model is further demonstrated by applying it to several recently proposed methods for reducing sidebands. In the limit of ideal adiabatic pulses, the predictions of the vector model are almost identical to those of quantum mechanics. At the lower RF power levels used in practical adiabatic decoupling applications, where the pulses are no longer perfectly adiabatic, phase cycles are employed to achieve performance that approximates the ideal limits derived here, so the vector model is more generally applicable, as well. These limits establish standards for future determination of the most efficient parameters for practical applications of broadband adiabatic decoupling in a single transient.     

Efficiency of heteronuclear broadband decoupling and homonuclear J cross polarization analyzed on two time scales

Decoupling sequences can be evaluated, as shown in Waugh's theory, with a J scaling factor on a long time scale. The efficiency of low-power decoupling, however, must be determined by cycling sidebands, as well as by the J scaling factor, when the sampling is not synchronized with the decoupling cycle. We introduced, therefore, another scaling factor which characterizes the decoupling on a short time scale. It is also shown that these scaling factors are useful for evaluating the efficiency of homonuclear J cross polarization. We clarified criteria of the factors suitable for various J coupling constants and chemical-shift ranges. Typical decoupling sequences were analyzed using the two scaling factors.     

A two-dimensional experiment that separates decoupling sidebands from the main peaks.

Broadband decoupling techniques generate undesirable cycling sidebands. The new two-dimensional technique described here allows separation of these sidebands from the main peaks by spreading the sideband responses in the indirectly detected dimension (F(1)) according to their frequency separations from the parent peaks, leaving the main resonances at zero frequency in F(1). This trace at zero frequency shows a thousandfold suppression of the residual sidebands, making possible the detection of very weak signals from dilute constituents of the sample. The experimental results can be displayed as one-dimensional "quiet decoupling" spectra without any significant loss of sensitivity. The new technique (DESIRE-decoupling sideband resolved spectroscopy) is simple, robust, and straightforward to implement.     

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.     

Floquet-van Vleck analysis of heteronuclear spin decoupling in solids: the effect of spinning and decoupling sidebands on the spectrum

We investigate the effect of magic angle spinning on heteronuclear spin decoupling in solids. We use an analytical Floquet-van Vleck formalism to derive expressions for the powder-averaged signal as a function of time. These expressions show that the spectrum consists of a centerband at the isotropic frequency of the observed spin, omega(0), and rotational decoupling sidebands at omega(0)+/-omega(1)+/-momega(r), where omega(1) is the decoupling field strength and omega(r) is the rotation frequency. Rotary resonance occurs when the rotational decoupling sidebands overlap with the centerband. Away from the rotary resonance conditions, the intensity of the centerband as a function of omega(r)/omega(1) is simply related to the total intensity of the rotational decoupling sidebands. Notably, in the absence of offset terms it is shown that as omega(1) decreases, the centerband intensity can decrease without any associated broadening. Furthermore, the centerband width is shown to be independent of spinning speed, to second order for the effects we consider. The effects of I spin chemical shift anisotropy and homonuclear dipolar couplings are also investigated. The analytical results are compared to simulations and experiments.     

A two-dimensional artifact from asynchronous decoupling

Many heteronuclear NMR experiments employ decoupling to collapse the heteronuclear multiplet, using decoupling schemes with a periodic phase modulation like WALTZ, MLEV, or GARP. Because of the periodic nature of these schemes, cycling sidebands are generated, whose intensity can be strongly reduced by decoupling asynchronously. We show that the most common implementation of asynchronous decoupling on modern spectrometers is such that the cycling sidebands are subjected to a periodic modulation. For multidimensional experiments, this results in ridges that can seriously compromise the quality of the spectrum. Based on our model, the artifact in a 2D [(1)H]-(15)N NOE equilibrium experiment is simulated and it is shown that the artifact can be prevented by using synchronous decoupling.     

Single-cycle optical pulses synchronized with molecular oscillations

Molecular modulation can produce an ultra-broad spectrum of infrared, visible, and ultraviolet light. This technique relies on the adiabatic preparation of highly coherent molecular vibrations or rotations in large ensembles of molecules. Coherent molecular motion leads to laser frequency modulation, and results in an efficient collinear generation of equidistant mutually coherent sidebands. In this paper I discuss perspectives for using this light source to synthesize sub-cycle and non-sinusoidal light pulses that are perfectly synchronized with the molecular oscillations in the given molecular system. These pulses provide a unique tool for studying ultra-fast atomic and molecular dynamics. PACS 42.50.Gy; 42.50.Hz; 42.65.Dr; 42.65.Re     

A new decoupling method for accurate quantification of polyethylene copolymer composition and triad sequence distribution with 13C NMR

(13)C NMR is a powerful analytical tool for characterizing polyethylene copolymer composition and sequence distribution. Accurate characterization of the composition and sequence distribution is critical for researchers in industry and academia. Some common composite pulse decoupling (CPD) sequences used in polyethylene copolymer (13)C NMR can lead to artifacts such as modulations of the decoupled (13)C NMR signals (decoupling sidebands) resulting in systematic errors in quantitative analysis. A new CPD method was developed, which suppresses decoupling sidebands below the limit of detection (less than 1:40,000 compared to the intensity of the decoupled signal). This new CPD sequence consists of an improved Waltz-16 CPD, implemented as a bilevel method. Compared with other conventional CPD programs this new decoupling method produced the cleanest (13)C NMR spectra for polyethylene copolymer composition and triad sequence distribution analyses.     

Wavelength-tunable multicolored femtosecond laser pulse generation in a fused silica glass plate

We obtained an array of multicolored femtosecond laser pulses with as many as 17 different colors that are spatially isolated. The mechanism of generation was proved to be cascaded four-wave mixing and with the following procedure. The output beam from a femtosecond laser was split into two. One of the two beams was pulse-compressed with a hollow core fiber and the intensity of the other was reduced. The two beams were synchronized and combined with a small crossing angle in a plate of fused silica glass plate. The wavelengths of the sidebands are continuously tunable from near-ultraviolet to near-infrared. The pulse duration, spatial mode, spectrum, and energy stability of the sidebands were studied. As many as fifteen spectral up-shifted pulses and two spectral downshifted pulses were obtained with spectral bandwidths broader than 1.8 octaves. Properties such as pulse energy as high as 1 μmJ, 45 fs pulse duration, smaller than 1.1 times of the diffraction limit Gaussian spatial profile, and better than 2% RMS power stability of the generated sidebands make it can be used in various experiments. The characterization showed that the sidebands have sufficiently good qualities to enable application to for various multicolor femtosecond laser experiments, for example, a multicolor pump-probe experiment.     

Multicolor femtosecond laser with μJ level by cascaded four-wave mixing

We obtained an array of multicolored femtosecond laser pulses with as many as 17 different colors that are spatially isolated. The mechanism of generation was proved to be cascaded four-wave mixing and with the following procedure. The output beam from a femtosecond laser was split into two. One of the two beams was pulse-compressed with a hollow core fiber and the intensity of the other was reduced. The two beams were synchronized and combined with a small crossing angle in a plate of fused silica glass plate. The wavelengths of the sidebands are continuously tunable from near-ultraviolet to near-infrared. The pulse duration, spatial mode, spectrum, and energy stability of the sidebands were studied. As many as fifteen spectral up-shifted pulses and two spectral downshifted pulses were obtained with spectral bandwidths broader than 1.8 octaves. Properties such as pulse energy as high as 1 μmJ, 45 fs pulse duration, smaller than 1.1 times of the diffraction limit Gaussian spatial profile, and better than 2% RMS power stability of the generated sidebands make it can be used in various experiments. The characterization showed that the sidebands have sufficiently good qualities to enable application to for various multicolor femtosecond laser experiments, for example, a multicolor pump-probe experiment.     

Chemical shift imaging without water suppression at 3 T

Purpose

Proton magnetic resonance spectroscopy without water suppression is possible but is hampered by the presence of sideband artifacts. The aim of this study was to develop a chemical shift imaging method without water suppression for clinical routine with reduced sideband artifacts.

Materials and Methods

Spectra from ten healthy volunteers were acquired using a 3T (TimTrio, Siemens, Erlagen, Germany) scanner with a Point RESolved Spectroscopy sequence for volume selection. Postprocessing was performed in three steps: correcting the water peak position in all spectra (chemical shift correction), subtracting the Gaussian convolution of all free induction decay signals (FIDs) (water signal reduction), and subtracting the FID of a water phantom from the volunteer's FID signal (reduction of sidebands). For the postprocessing customized software was developed with Matlab 2007b.

Results

The described technique provides spectra with reduced water signal and sidebands. Quantitative analysis showed that there is a good agreement between spectra obtained with water suppressing radiofrequency pulses and the new method. Moreover, spectra obtained with the new method do not need phase correction.

Conclusion

The new method offers sufficient reduction of the water peak and sidebands. Its simplicity allows its use in clinical applications.     

An analytical formulation of CPMAS

An exact expression for the cross polarization between two spin-1/2 particles is derived from the quantum Liouville equation. This is given in the form of two integrodifferential equations. These can be solved exactly in the static case (no sample spinning) and a powder average easily performed numerically. With magic-angle spinning, the neglect of certain interference terms simplifies the numerical calculation. A further assumption decoupling the calculation of the sidebands gives a very simple formula that is capable of giving a qualitative interpretation of all experimental observations. Examples are given illustrating typical buildup curves and CPMAS matching profiles.     

Adiabatic Decoupling and Time-Dependent Born–Oppenheimer Theory

We reconsider the time-dependent Born–Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the first time when a band crossing is encountered. The adiabatic decoupling leads to an effective Schr?dinger equation for the nuclei, including contributions from the Berry connection. Received: 10 July 2000 / Accepted: 30 July 2001     

THE APPLICATION OF ADIABATIC THEOREM TO THE BEAA DYNAMICS IN ACCELERATORS

In this paper, the adiabatic criterion and the formulae for calculating the increment of adiabatic invariant due to the nonadiabatic change of paramters in Hamiltonian are derived and we have found that this increment is quite small, even in the case where the Landau's adiabatic criterion^[1] is violated.     

To what extent does the centerband and each spinning sideband contain contributions from different crystallites of the powder sample?

It is shown that due to the destructive interference of the magnetization paths of crystallites taking place during the rotor period at slow spinning regime, the contribution of different crystallites to the centerband and to each spinning sideband is strongly weighted. For this, a separated-local-field experiment is used to tag the crystallites contributing to a given spinning sideband at different spinning speeds. The orientation dependence of spinning sidebands is also responsible for different lineshapes of the centerband and of each spinning sidebands observed under conditions of off-magic angle spinning.     

Calibration of STUD+ Parameters to Achieve Optimally Efficient Broadband Adiabatic Decoupling in a Single Transient

To provide the most efficient conditions for spin decoupling with least RF power, master calibration curves are provided for the maximum centerband amplitude, and the minimum amplitude for the largest cycling sideband, resulting from STUD+ adiabatic decoupling applied during a single free induction decay. The principal curve is defined as a function of the four most critical experimental input parameters: the maximum amplitude of the RF field,RF_max, the length of the sech/tanh pulse,T_p, the extent of the frequency sweep,bwdth,and the coupling constant,J_o. Less critical parameters, the effective (or actual) decoupled bandwidth,bw_eff, and the sech/tanh truncation factor, β, which become more important asbwdthis decreased, are calibrated in separate curves. The relative importance of nine additional factors in determining optimal decoupling performance in a single transient are considered. Specific parameters for efficient adiabatic decoupling can be determined via a set of four equations which will be most useful for¹³C decoupling, covering the range of one-bond¹³C¹H coupling constants from 125 to 225 Hz, and decoupled bandwidths of 7 to 100 kHz, with a bandwidth of 100 kHz being the requirement for a 2 GHz spectrometer. The four equations are derived from a recent vector model of adiabatic decoupling, and experiment, supported by computer simulations. The vector model predicts an inverse linear relation between the centerband and maximum sideband amplitudes, and it predicts a simple parabolic relationship between maximum sideband amplitude and the productJ_oT_p. The ratiobwdth/(RF_max)²can be viewed as a characteristic time scale, τ_c, affecting sideband levels, with τ_c≈T_pgiving the most efficient STUD+ decoupling, as suggested by the adiabatic condition. Functional relationships betweenbwdthand less critical parameters,bw_effand β, for efficient decoupling can be derived from Bloch-equation calculations of the inversion profile for a single sech/tanh pulse. Residual splitting of the centerband, normally associated with incomplete or inefficient decoupling, is not seen in sech/tanh decoupling and therefore cannot be used as a measure of adiabatic decoupling efficiency. The calibrated experimental performance levels achieved in this study are within 20% of theoretical performance levels derived previously for ideal sech/tanh decoupling at high power, indicating a small scope for further improvement at practical RF power levels. The optimization procedures employed here will be generally applicable to any good combination of adiabatic inversion pulse and phase cycle.