Efficient Pulse Sequence Research Articles

Quantum dynamics of a fully blockaded Rydberg atom ensemble

Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension of the Hilbert space increases exponentially with the size of the system. For systems that possess a high degree of symmetry, however, classical simulation can reach much larger sizes. Here we consider an ensemble of strongly interacting atoms with permutation symmetry, enabling the computation of certain collective observables for hundreds of atoms at arbitrarily long evolution times. The system is realized by an ensemble of three-level atoms, where one of the levels corresponds to a highly excited Rydberg state. In the limit of all-to-all Rydberg blockade, the Hamiltonian is invariant under permutation of the atoms. Using techniques from representation theory, we construct a block-diagonal form of the Hamiltonian, where the size of the largest block increases only linearly with the system size. We apply this formalism to derive efficient pulse sequences to prepare arbitrary permutation-invariant quantum states. Moreover, we study the quantum dynamics following a quench, uncovering a parameter regime in which the system thermalizes slowly and exhibits pronounced revivals. Our results create opportunities for the experimental and theoretical study of large interacting and nonintegrable quantum systems. Published by the American Physical Society 2024

Multi-axis fields boost SABRE hyperpolarization

The inherently low signal-to-noise ratio of NMR and MRI is now being addressed by hyperpolarization methods. For example, iridium-based catalysts that reversibly bind both parahydrogen and ligands in solution can hyperpolarize protons (SABRE) or heteronuclei (X-SABRE) on a wide variety of ligands, using a complex interplay of spin dynamics and chemical exchange processes, with common signal enhancements between 103 and 104. This does not approach obvious theoretical limits, and further enhancement would be valuable in many applications (such as imaging mM concentration species in vivo). Most SABRE/X-SABRE implementations require far lower fields (μT-mT) than standard magnetic resonance (>1T), and this gives an additional degree of freedom: the ability to fully modulate fields in three dimensions. However, this has been underexplored because the standard simplifying theoretical assumptions in magnetic resonance need to be revisited. Here, we take a different approach, an evolutionary strategy algorithm for numerical optimization, multi-axis computer-aided heteronuclear transfer enhancement for SABRE (MACHETE-SABRE). We find nonintuitive but highly efficient multiaxial pulse sequences which experimentally can produce a sevenfold improvement in polarization over continuous excitation. This approach optimizes polarization differently than traditional methods, thus gaining extra efficiency.

Dynamic changes in lung water density and volume following supine body positioning.

Measure the changes in relative lung water density (rLWD), lung volume, and total lung water content as a function of time after supine body positioning. An efficient ultrashort-TE pulse sequence with a yarnball k-space trajectory was used to measure water density-weighted lung images for 25 min following supine body positioning (free breathing, 74-s acquisitions, 3D images at functional residual capacity, 18 time points) in 9 healthy volunteers. Global and regional (10 chest-to-back positions) rLWD, lung volume, and total lung water volume were measured in all subjects at all time points. Volume changes were validated with a nitrogen washout study in 3 participants. Global rLWD increased significantly (p = 0.001) from 31.8 ± 5.5% to 34.8 ± 6.8%, while lung volumes decreased significantly (p < 0.001) from 2390 ± 620 mL to 2130 ± 630 mL over the same 25-min interval. Total lung water volume decreased slightly from 730 ± 125 mL to 706 ± 126 mL (p = 0.028). There was a significant chest-to-back gradient in rLWD (20.7 ± 4.6% to 39.9 ± 6.1%) at all time points with absolute increases of 1.8 ± 1.2% at the chest and 5.4 ± 1.9% at the back. Nitrogen washout studies yielded a similar reduction in lung volume (12.5 ± 0.9%) and time course following supine positioning. Lung volumes during tidal breathing decrease significantly over tens of minutes following supine body positioning, with corresponding increases in lung water density (9.2 ± 4.4% relative increase). The total volume of lung water is slightly reduced over this interval (3.3 ± 4.0% relative change). Evaluation of rLWD should take time after supine positioning, and more generally, all sources of lung volume changes should be taken into consideration to avoid significant bias.

Optimization of Gradient-Echo Echo-Planar Imaging for T2* Contrast in the Brain at 0.5 T.

Gradient-recalled echo (GRE) echo-planar imaging (EPI) is an efficient MRI pulse sequence that is commonly used for several enticing applications, including functional MRI (fMRI), susceptibility-weighted imaging (SWI), and proton resonance frequency (PRF) thermometry. These applications are typically not performed in the mid-field (<1 T) as longer T2* and lower polarization present significant challenges. However, recent developments of mid-field scanners equipped with high-performance gradient sets offer the possibility to re-evaluate the feasibility of these applications. The paper introduces a metric "T2* contrast efficiency" for this evaluation, which minimizes dead time in the EPI sequence while maximizing T2* contrast so that the temporal and pseudo signal-to-noise ratios (SNRs) can be attained, which could be used to quantify experimental parameters for future fMRI experiments in the mid-field. To guide the optimization, T2* measurements of the cortical gray matter are conducted, focusing on specific regions of interest (ROIs). Temporal and pseudo SNR are calculated with the measured time-series EPI data to observe the echo times at which the maximum T2* contrast efficiency is achieved. T2* for a specific cortical ROI is reported at 0.5 T. The results suggest the optimized echo time for the EPI protocols is shorter than the effective T2* of that region. The effective reduction of dead time prior to the echo train is feasible with an optimized EPI protocol, which will increase the overall scan efficiency for several EPI-based applications at 0.5 T.

Fast, High-Fidelity Addressed Single-Qubit Gates Using Efficient Composite Pulse Sequences.

We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for ^{43}Ca^{+} hyperfine "atomic clock" qubits in a cryogenic (100K) surface trap. For a single qubit, we benchmark an error of 1.5×10^{-6} per Clifford gate (implemented using 600ns π/2 pulses). For 2 qubits in the same trap zone (ion separation 5 μm), we use a spatial microwave field gradient, combined with an efficient four-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error 3.4×10^{-5} per addressed π/2 gate. The scheme scales theoretically to larger numbers of qubits in a single register.

Simultaneous proton resonance frequency T1 - MR shear wave elastography for MR-guided focused ultrasound multiparametric treatment monitoring.

To develop an efficient MRI pulse sequence to simultaneously measure multiple parameters that have been shown to correlate with tissue nonviability following thermal therapies. A 3D segmented EPI pulse sequence was used to simultaneously measure proton resonance frequency shift (PRFS) MR thermometry (MRT), T1 relaxation time, and shear wave velocity induced by focused ultrasound (FUS) push pulses. Experiments were performed in tissue mimicking gelatin phantoms and ex vivo bovine liver. Using a carefully designed FUS triggering scheme, a heating duty cycle of approximately 65% was achieved by interleaving FUS ablation pulses with FUS push pulses to induce shear waves in the tissue. In phantom studies, temperature increases measured with PRFS MRT and increases in T1 correlated with decreased shear wave velocity, consistent with material softening with increasing temperature. During ablation in ex vivo liver, temperature increase measured with PRFS MRT initially correlated with increasing T1 and decreasing shear wave velocity, and after tissue coagulation with decreasing T1 and increasing shear wave velocity. This is consistent with a previously described hysteresis in T1 versus PRFS curves and increased tissue stiffness with tissue coagulation. An efficient approach for simultaneous and dynamic measurements of PRSF, T1 , and shear wave velocity during treatment is presented. This approach holds promise for providing co-registered dynamic measures of multiple parameters, which correlates to tissue nonviability during and following thermal therapies, such as FUS.

Reducing “slice cross-talk” effect in metamaterial assisted fast spin-echo MRI

Imaging of subtle changes in hand structures is challenged by the limited image quality, especially at 1.5 T. Reduction of specific absorption rate in metamaterial-assisted 1.5 T MRI provides an opportunity to utilize efficient pulse sequences and to improve the quality of acquired images. This work is devoted to the assessment of potential improvements of slice selectivity and reducing a ”slice cross-talk” artifact, using fast spin-echo (FSE) pulse sequence together with a metamaterial-based coil. The slice selection in conventional T1-weighted FSE wrist imaging pulse sequences was modeled using a ”Bloch Equations Simulator”. Two types of pulses were compared: apodized SINC pulses (reference) common for clinical FSE, and optimized selective Shinnar–Le Roux (SLR) pulses constructed in the MATPULSE program. Regular and SLR-based FSE pulse sequences were tested in a phantom experiment with different gaps between slices to investigate the “slice cross-talk” artifact presence. Combining the utilization of the metamaterial-based coil with an SLR-based FSE provided 28 times lower energy deposition in a duty cycle, as compared to the regular FSE with a conventional transmit coil. When the slice gap was decreased from 100% to 0%, the “slice cross-talk” effect reduced the signal intensity by 16%-18% in the SLR-based FSE and by 23%-32% for the regular FSE. The use of SLR pulses together with the metamaterial-based coil allowed to reduce the ”slice cross-talk” effect in contiguous FSE, while still being within the safe SAR limits.

On the use of single-frequency versus double-frequency satellite-transition pulses for MQMAS

It has been shown recently that a rotor-period long pulse applied at a frequency selective to the satellite-transitions of half-integer quadrupole nuclei can efficiently interconvert central-transition (CT) and triple-quantum (TQ) coherences for the acquisition of MQMAS spectra [I. Hung, Z. Gan, J. Magn. Reson. 324 (2021) 106913; doi: https://doi.org/10.1016/j.jmr.2021.106913]. By using a pair of such pulses and selecting opposite changes in coherence order, the anisotropic phase of the effective rf field can be refocused. Efficient multiple-quantum interconversion has led to low-power MQMAS pulse sequences capable of obtaining isotropic NMR spectra for the largest quadrupolar couplings to date. In this work, we extend the satellite-transition selective pulses from single- to double-frequency (or cosine) irradiation. By applying average Hamiltonian theory in the quadrupolar jolting frame, it is shown that the phase for TQ/CT conversion converges when the double-frequency irradiation matches the mirror-image symmetry of the satellite-transitions. The coherent conversion explains the mechanism behind the double-frequency sweep (DFS) and fast amplitude modulation (FAM) methods used for MQMAS. However, the strict matching condition limits the bandwidth of such double-frequency pulses to less than one spinning frequency. The use of a pair of identical cosine satellite-transition pulses is proposed to refocus the residual anisotropic phase spread. The refocusing leads to a more efficient MQMAS pulse sequence with a broader bandwidth suitable for large quadrupolar couplings and chemical shift ranges. Comparisons with the recently presented single-frequency lpMQMAS and other MQMAS pulse schemes show that cos-lpMQMAS is more efficient, less susceptible to fluctuations in spinning frequency, and suffers from less distortion in quadrupolar line shapes, as demonstrated with model compounds of moderate and large quadrupolar couplings, 87RbNO3 and β-71Ga2O3. In particular, the results for β-71Ga2O3 show an order of magnitude increase in MQMAS efficiency.

Efficient two-qubit pulse sequences beyond CNOT

We design efficient controlled-rotation gates with arbitrary angle acting on three-spin encoded qubits for exchange-only quantum computation. Two pulse sequence constructions are given. The first is motivated by an analytic derivation of the efficient Fong-Wandzura sequence for an exact CNOT gate. This derivation, briefly reviewed here, is based on elevating short sequences of SWAP pulses to an entangling two-qubit gate. To go beyond CNOT, we apply a similar elevation to a modified short sequence consisting of SWAPs and one pulse of arbitrary duration. This results in two-qubit sequences that carry out controlled-rotation gates of arbitrary angle. The second construction streamlines a class of arbitrary CPHASE gates established earlier. Both constructions are based on building two-qubit sequences out of subsequences with special properties that render each step of the construction analytically tractable.

Optimized quantification of spin relaxation times in the hybrid state.

The optimization and analysis of spin ensemble trajectories in the hybrid state-a state in which the direction of the magnetization adiabatically follows the steady state while the magnitude remains in a transient state. Numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for -encoding, -encoding, and their weighted sum, respectively, followed by a comparison between the Cramér-Rao bounds obtained with our optimized spin-trajectories, Look-Locker sequences, and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. After a nonrecurring inversion segment on the southern half of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern hemisphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance - and -encoding still result in near optimal signal-to-noise efficiency for each relaxation time. Thus, the second parameter can be encoded at virtually no extra cost. We provided new insights into the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We found that joint acquisitions of and in the hybrid state are substantially more efficient than sequential encoding techniques.

Parameter map error due to normal noise and aliasing artifacts in MR fingerprinting.

To introduce a quantitative tool that enables rapid forecasting of T1 and T2 parameter map errors due to normal and aliasing noise as a function of the MR fingerprinting (MRF) sequence, which can be used in sequence optimization. The variances of normal noise and aliasing artifacts in the collected signal are related to the variances in T1 and T2 maps through derived quality factors. This analytical result is tested against the results of a Monte-Carlo approach for analyzing MRF sequence encoding capability in the presence of aliasing noise, and verified with phantom experiments at 3T. To further show the utility of our approach, our quality factors are used to find efficient MRF sequences for fewer repetitions. Experimental results verify the ability of our quality factors to rapidly assess the efficiency of an MRF sequence in the presence of both normal and aliasing noise. Quality factor assessment of MRF sequences is in agreement with the results of a Monte-Carlo approach. Analysis of MRF parameter map errors from phantom experiments is consistent with the derived quality factors, with T1 (T2 ) data yielding goodness of fit R2 ≥ 0.92 (0.80). In phantom and in vivo experiments, the efficient pulse sequence, determined through quality factor maximization, led to comparable or improved accuracy and precision relative to a longer sequence, demonstrating quality factor utility in MRF sequence design. The here introduced quality factor framework allows for rapid analysis and optimization of MRF sequence design through T1 and T2 error forecasting.

Linking the rotation of a rigid body to the Schr\xf6dinger equation: The quantum tennis racket effect and beyond

The design of efficient and robust pulse sequences is a fundamental requirement in quantum control. Numerical methods can be used for this purpose, but with relatively little insight into the control mechanism. Here, we show that the free rotation of a classical rigid body plays a fundamental role in the control of two-level quantum systems by means of external electromagnetic pulses. For a state to state transfer, we derive a family of control fields depending upon two free parameters, which allow us to adjust the efficiency, the time and the robustness of the control process. As an illustrative example, we consider the quantum analog of the tennis racket effect, which is a geometric property of any classical rigid body. This effect is demonstrated experimentally for the control of a spin 1/2 particle by using techniques of Nuclear Magnetic Resonance. We also show that the dynamics of a rigid body can be used to implement one-qubit quantum gates. In particular, non-adiabatic geometric quantum phase gates can be realized based on the Montgomery phase of a rigid body. The robustness issue of the gates is discussed.

Breath-hold black blood quantitative T1rho imaging of liver using single shot fast spin echo acquisition.

Liver fibrosis is a key feature in most chronic liver diseases. T1rho magnetic resonance imaging is a potentially important technique for noninvasive diagnosis, severity grading, and therapy monitoring of liver fibrosis. However, it remains challenging to perform robust T1rho quantification of liver on human subjects. One major reason is that the presence of rich blood signal in liver can cause artificially high T1rho measurement and makes T1rho quantification susceptible to motion. A pulse sequence based on single shot fast/turbo spin echo (SSFSE/SSTSE) acquisition, with theoretical analysis and simulation based on the extended phase graph (EPG) algorithm, was presented for breath-hold single slice quantitative T1rho imaging of liver with suppression of blood signal. The pulse sequence was evaluated in human subjects at 3.0 T with 500 Hz spinlock frequency and time-of-spinlock (TSL) 0, 10, 30 and 50 ms. Human scan demonstrated that the entire T1rho data sets with four spinlock time can be acquired within a single breath-hold of 10 seconds with black blood effect. T1rho quantification with suppression of blood signal results in significantly reduced T1rho value of liver compared to the results without blood suppression. A signal-to-noise ratio (SNR) efficient pulse sequence was reported for T1rho quantification of liver. The black blood effect, together with a short breath-hold, mitigates the risk of quantification errors as would occur in the conventional methods.

Physiological and Functional Magnetic Resonance Imaging Using Balanced Steady-state Free Precession.

Balanced steady-state free precession (bSSFP) is a highly efficient pulse sequence that is known to provide the highest signal-to-noise ratio per unit time. Recently, bSSFP is getting increasingly popular in both the research and clinical communities. This review will be focusing on the application of the bSSFP technique in the context of probing the physiological and functional information. In the first part of this review, the basic principles of bSSFP are briefly covered. Afterwards, recent developments related to the application of bSSFP, in terms of physiological and functional imaging, are introduced and reviewed. Despite its long development history, bSSFP is still a promising technique that has many potential benefits for obtaining high-resolution physiological and functional images.

Self-navigated low-rank MRI for MPIO-labeled immune cell imaging of the heart.

Super-paramagnetic iron oxide (SPIO) particles can magnetically label immune cells in circulation; the accumulation of labeled cells can then be detected by magnetic resonance imaging (MRI). This has enormous potential for imaging inflammatory responses in the heart, but it has been difficult to do in vivo using conventional free-breathing, ungated cardiac imaging. Subspace imaging with temporal navigation and sparse sampling of (k, t)-space has previously been used to accelerate several cardiac imaging applications, conventionally alternating between acquiring navigator data and sparse data every other TR. Here we describe a more efficient self-navigated pulse sequence to acquire both navigator and sparse (k, t)-space data in the space of a single TR, doubling imaging speed to approach 100 frames per second (fps). We show the feasibility of using the resulting method to assess myocardial inflammation in a pre-clinical rodent ischemic reperfusion injury (IRI) model using micron-sized paramagnetic iron oxide (MPIO) particles to label immune cells in situ.

Collaborative development for setup, execution, sharing and analytics of complex NMR experiments

Factory settings of NMR pulse sequences are rarely ideal for every scenario in which they are utilised. The optimisation of NMR experiments has for many years been performed locally, with implementations often specific to an individual spectrometer. Furthermore, these optimised experiments are normally retained solely for the use of an individual laboratory, spectrometer or even single user. Here we introduce a web-based service that provides a database for the deposition, annotation and optimisation of NMR experiments. The application uses a Wiki environment to enable the collaborative development of pulse sequences. It also provides a flexible mechanism to automatically generate NMR experiments from deposited sequences.Multidimensional NMR experiments of proteins and other macromolecules consume significant resources, in terms of both spectrometer time and effort required to analyse the results. Systematic analysis of simulated experiments can enable optimal allocation of NMR resources for structural analysis of proteins. Our web-based application (http://nmrplus.org) provides all the necessary information, includes the auxiliaries (waveforms, decoupling sequences etc.), for analysis of experiments by accurate numerical simulation of multidimensional NMR experiments. The online database of the NMR experiments, together with a systematic evaluation of their sensitivity, provides a framework for selection of the most efficient pulse sequences. The development of such a framework provides a basis for the collaborative optimisation of pulse sequences by the NMR community, with the benefits of this collective effort being available to the whole community.

Saturation‐recovery metabolic‐exchange rate imaging with hyperpolarized [1‐13C] pyruvate using spectral‐spatial excitation

Within the last decade hyperpolarized [1-13C] pyruvate chemical-shift imaging has demonstrated impressive potential for metabolic MR imaging for a wide range of applications in oncology, cardiology, and neurology. In this work, a highly efficient pulse sequence is described for time-resolved, multislice chemical shift imaging of the injected substrate and obtained downstream metabolites. Using spectral-spatial excitation in combination with single-shot spiral data acquisition, the overall encoding is evenly distributed between excitation and signal reception, allowing the encoding of one full two-dimensional metabolite image per excitation. The signal-to-noise ratio can be flexibly adjusted and optimized using lower flip angles for the pyruvate substrate and larger ones for the downstream metabolites. Selectively adjusting the excitation of the down-stream metabolites to 90° leads to a so-called "saturation-recovery" scheme with the detected signal content being determined by forward conversion of the available pyruvate. In case of repetitive excitations, the polarization is preserved using smaller flip angles for pyruvate. Metabolic exchange rates are determined spatially resolved from the metabolite images using a simplified two-site exchange model. This novel contrast is an important step toward more quantitative metabolic imaging. Goal of this work was to derive, analyze, and implement this "saturation-recovery metabolic exchange rate imaging" and demonstrate its capabilities in four rats bearing subcutaneous tumors.

Tunable coupling between three qubits as a building block for a superconducting quantum computer

Large-scale quantum computers will consist of many interacting qubits. In this paper we expand the two flux qubit coupling scheme first devised by P. Plourde et al. [Phys. Rev. B 70, 140501 (2004)] and realized by T. Hime et al. [Science 314, 1427 (2006)] to a three-qubit, two-coupler scenario. We study L-shaped and line-shaped coupler geometries, and show how the interaction strength between qubits changes in terms of the couplers' dimensions. We explore two cases: the ``on-state'' where the interaction energy between two nearest-neighbor qubits is high, and the ``off-state'' where it is turned off. In both situations we study the undesirable crosstalk with the third qubit. Finally, we use the grape algorithm to find efficient pulse sequences for two-qubit gates subject to our calculated physical constraints on the coupling strength.

Selective J‐resolved‐HMQC‐1 and ‐2, new methods for measuring proton–proton coupling constants in strongly coupled spin systems

Efficient pulse sequences for measuring (1)H-(1)H coupling constants (JHH) in strongly coupled spin systems, named selective J-resolved-HMQC-1 and -2, have been developed. In the strongly coupled spin systems such as -CH2-CHA(OH)-CHB(OH)-CH2-, measurements of (3)JHAHB are generally difficult owing to the complicated splitting caused by the adjacent CH2 protons. For easier and accurate measurements of (3)JHAHB in such a spin system, a selective excitation pulse is incorporated into the J-resolved HMQC pulse sequence. In the proposed methods, only two strongly coupled protons, HA and HB which are excited by a selective pulse, are observed as J-resolved HMQC signals. The cross peaks of HA and HB appear as doublets owing to (3)JHAHB along the F1 dimension in the selective J-resolved HMQC-1 and -2 experiments. The efficiency of the proposed pulse sequences has been demonstrated in application to the stereochemical studies of the complicated natural product, monazomycin.

BIRD‐J‐resolved HMBC and BIRD‐high‐resolution HMBC pulse sequences for measuring heteronuclear long‐range coupling constants and proton–proton spin coupling constants in complicated spin systems

Efficient pulse sequences for measuring long-range C-H coupling constants (J(C-H)) and proton-proton spin coupling constants (J(H-H)), named BIRD-J-resolved HMBC and BIRD-high-resolution HMBC, respectively, have been developed. In spin systems possessing a secondary methyl group positioned between protonated carbons (e.g. -CH(2)-CH(CH(3))-CH(2)-), the methine proton splits in a complicated fashion, resulting in difficulty in the determination of its spin coupling constants. For easy and accurate measurements of the long-range J(C-H) and J(H-H) in such a spin system, the BIRD pulse [90°x(H)-180°x (H/C)- 90° (-x)(H)] or [90°x(H)-180°x(H/C)-90° (-x)(H)180°x(C)] is incorporated into the J-resolved portion of the pulse sequence. As a result, the above secondary methyl group can be selectively decoupled, providing simplified cross-peak patterns, which are suitable for the accurate measurements of the long-range J(C-H) and J(H-H).