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Stasiuk A, Peng P, Heller G, Cappellaro P. Frame change technique for phase transient cancellation. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2024; 362:107688. [PMID: 38678738 DOI: 10.1016/j.jmr.2024.107688] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2023] [Revised: 04/12/2024] [Accepted: 04/14/2024] [Indexed: 05/01/2024]
Abstract
The precise control of complex quantum mechanical systems can unlock applications ranging from quantum simulation to quantum computation. Controlling strongly interacting many-body systems often relies on Floquet Hamiltonian engineering that is achieved by fast switching between Hamiltonian primitives via external control. For example, in our solid-state NMR system, we perform quantum simulation by modulating the natural Hamiltonian with control pulses. As the Floquet heating errors scale with the interpulse delay, δt, it is favorable to keep δt as short as possible, forcing our control pulses to be short duration and high power. Additionally, high-power pulses help to minimize undesirable evolution from occurring during the duration of the pulse. However, such pulses introduce an appreciable phase-transient control error, a form of unitary error. In this work, we detail our ability to diagnose the error, calibrate its magnitude, and correct it for π/2-pulses of arbitrary phase. We demonstrate the improvements gained by correcting for the phase transient error, using a method which we call the "frame-change technique", in a variety of experimental settings of interest. Given that the correction mechanism adds no real control overhead, we recommend that any resonance probe be checked for these phase transient control errors, and correct them using the frame-change technique.
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Affiliation(s)
- Andrew Stasiuk
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, 02139, MA, USA; Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, 02139, MA, USA.
| | - Pai Peng
- Department of Electrical and Computer Engineering, Princeton University, Princeton, 08544, NJ, USA
| | - Garrett Heller
- Department of Physics, Massachusetts Institute of Technology, Cambridge, 02139, MA, USA
| | - Paola Cappellaro
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, 02139, MA, USA; Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, 02139, MA, USA; Department of Physics, Massachusetts Institute of Technology, Cambridge, 02139, MA, USA
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2
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Aebischer K, Ernst M. Residual proton line width under refocused frequency-switched Lee-Goldburg decoupling in MAS NMR. Phys Chem Chem Phys 2023; 25:11959-11970. [PMID: 36987593 PMCID: PMC10155489 DOI: 10.1039/d3cp00414g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 03/16/2023] [Indexed: 03/19/2023]
Abstract
Despite many decades of research, homonuclear decoupling in solid-state NMR under magic-angle spinning (MAS) has yet to reach a point where the achievable proton line widths become comparable to the resolution obtained in solution-state NMR. This makes the precise determination of isotropic chemical shifts difficult and thus presents a limiting factor in the application of proton solid-state NMR to biomolecules and small molecules. In this publication we analyze the sources of the residual line width in refocused homonuclear-decoupled spectra in detail by comparing numerical simulations and experimental data. Using a hybrid analytical/numerical approach based on Floquet theory, we find that third-order effective Hamiltonian terms are required to realistically characterize the line shape and line width under frequency-switched Lee-Goldburg (FSLG) decoupling under MAS. Increasing the radio-frequency field amplitude enhances the influence of experimental rf imperfections such as pulse transients and the MAS-modulated radial rf-field inhomogeneity. While second- and third-order terms are, as expected, reduced in size at higher rf-field amplitudes, the line width becomes dominated by first-order terms which severely limits the achievable line width. We expect, therefore, that significant improvements in the line width of FSLG-decoupled spectra can only be achieved by reducing the influence of MAS-modulated rf-field inhomogeneity and pulse transients.
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Affiliation(s)
- Kathrin Aebischer
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.
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3
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Greer M, Ariando D, Hurlimann M, Song YQ, Mandal S. Analytical models of probe dynamics effects on NMR measurements. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2021; 327:106975. [PMID: 33873092 DOI: 10.1016/j.jmr.2021.106975] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/27/2021] [Revised: 03/23/2021] [Accepted: 03/24/2021] [Indexed: 06/12/2023]
Abstract
This paper provides a detailed analysis of three common NMR probe circuits (untuned, tuned, and impedance-matched) and studies their effects on multi-pulse experiments, such as those based on the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. The magnitude of probe dynamics effects on broadband refocusing pulses are studied as a function of normalized RF bandwidth. Finally, the probe circuit models are integrated with spin dynamics simulations to design hardware-specific RF excitation and refocusing pulses for optimizing user-specified metrics such as signal-to-noise ratio (SNR) in grossly inhomogeneous fields. Preliminary experimental results on untuned probes are also presented.
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Affiliation(s)
- Mason Greer
- Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106, USA.
| | - David Ariando
- University of Florida, 1064 Center Drive, Gainesville, FL 32611, USA.
| | | | - Yi-Qiao Song
- Massachusetts General Hospital, Charlestown, MA 02129, USA.
| | - Soumyajit Mandal
- University of Florida, 1064 Center Drive, Gainesville, FL 32611, USA.
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4
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Koppe J, Knitsch R, Wegner S, Hansen MR. Sensitivity-enhanced multiple-quantum MAS NMR for half-integer spin quadrupolar nuclei using WURST-amplitude shaped pulses. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 321:106873. [PMID: 33221668 DOI: 10.1016/j.jmr.2020.106873] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Revised: 11/05/2020] [Accepted: 11/06/2020] [Indexed: 06/11/2023]
Abstract
Two-dimensional multiple-quantum MAS (MQMAS) NMR spectroscopy is one of the most widely used solid-state NMR techniques for resolving multiple overlapping central-transition lineshapes for half-integer spin quadrupolar nuclei. In particular when relying on nutation-driven MQ coherence transfers, this technique suffers from low sensitivity that can only be improved by increasing the rf-amplitude of the involved radio-frequency (rf) pulses, which are therefore typically operated at the rf-limit. In such situations, frequently encountered for the three-pulse z-filtered and split-t1 shifted-echo MQMAS NMR sequences, we introduce the advantages of rf-pulses with smoothly truncated amplitude profiles, which we have termed WURST-Amplitude Shaped Pulses (WASPs). When considering the NMR spectrometer hardware, we demonstrate that WASPs feature more suitable properties in comparison to conventional rectangular pulses, enabling a substantial reduction of voltage reflections and transient effects under identical rf-conditions. By employing extensive numerical simulations and experimental validation, we further show that WASPs intrinsically possess a higher potential for nutation-based 3Q excitation involving spin-3/2 and 3Q and 5Q excitation for spin-5/2 quadrupolar nuclei, specifically when large nutation frequencies are available. The concept of smoothly truncating rf-amplitudes is also extended to Fast Amplitude Modulation (FAM) pulses, normally incorporated for rotor-driven 1Q conversion. We additionally evaluate the potential of employing WASPs with peak rf-amplitudes beyond the rf-limit for conventional rectangular rf-pulses.
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Affiliation(s)
- Jonas Koppe
- Institute for Physical Chemistry, Westfälische Wilhelms-Universität, Corrensstr. 28/30, D-48149 Münster, Germany
| | - Robert Knitsch
- Institute for Physical Chemistry, Westfälische Wilhelms-Universität, Corrensstr. 28/30, D-48149 Münster, Germany
| | | | - Michael Ryan Hansen
- Institute for Physical Chemistry, Westfälische Wilhelms-Universität, Corrensstr. 28/30, D-48149 Münster, Germany; Center for Multiscale Theory and Computation (CMTC), Westfälische Wilhelms-Universität, Corrensstrasse 40, D-48149 Münster, Germany.
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5
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Hellwagner J, Grunwald L, Ochsner M, Zindel D, Meier BH, Ernst M. Origin of the residual line width under frequency-switched Lee-Goldburg decoupling in MAS solid-state NMR. MAGNETIC RESONANCE (GOTTINGEN, GERMANY) 2020; 1:13-25. [PMID: 37904890 PMCID: PMC10500695 DOI: 10.5194/mr-1-13-2020] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 01/21/2020] [Indexed: 11/01/2023]
Abstract
Homonuclear decoupling sequences in solid-state nuclear magnetic resonance (NMR) under magic-angle spinning (MAS) show experimentally significantly larger residual line width than expected from Floquet theory to second order. We present an in-depth theoretical and experimental analysis of the origin of the residual line width under decoupling based on frequency-switched Lee-Goldburg (FSLG) sequences. We analyze the effect of experimental pulse-shape errors (e.g., pulse transients and B 1 -field inhomogeneities) and use a Floquet-theory-based description of higher-order error terms that arise from the interference between the MAS rotation and the pulse sequence. It is shown that the magnitude of the third-order auto term of a single homo- or heteronuclear coupled spin pair is important and leads to significant line broadening under FSLG decoupling. Furthermore, we show the dependence of these third-order error terms on the angle of the effective field with the B 0 field. An analysis of second-order cross terms is presented that shows that the influence of three-spin terms is small since they are averaged by the pulse sequence. The importance of the inhomogeneity of the radio-frequency (rf) field is discussed and shown to be the main source of residual line broadening while pulse transients do not seem to play an important role. Experimentally, the influence of the combination of these error terms is shown by using restricted samples and pulse-transient compensation. The results show that all terms are additive but the major contribution to the residual line width comes from the rf-field inhomogeneity for the standard implementation of FSLG sequences, which is significant even for samples with a restricted volume.
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Affiliation(s)
| | - Liam Grunwald
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Manuel Ochsner
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Daniel Zindel
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Beat H. Meier
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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6
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Ranjan V, Probst S, Albanese B, Doll A, Jacquot O, Flurin E, Heeres R, Vion D, Esteve D, Morton JJL, Bertet P. Pulsed electron spin resonance spectroscopy in the Purcell regime. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2020; 310:106662. [PMID: 31837553 DOI: 10.1016/j.jmr.2019.106662] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2019] [Revised: 11/22/2019] [Accepted: 11/25/2019] [Indexed: 06/10/2023]
Abstract
In EPR, spin relaxation is typically governed by interactions with the lattice or other spins. However, it has recently been shown that given a sufficiently strong spin-resonator coupling and high resonator quality factor, the spontaneous emission of microwave photons from the spins into the resonator can become the main relaxation mechanism, as predicted by Purcell. With increasing attention on the use of microresonators for EPR to achieve high spin-number sensitivity it is important to understand how this novel regime influences measured EPR signals, for example the amplitude and temporal shape of the spin-echo. We study this regime theoretically and experimentally, using donor spins in silicon, under different conditions of spin-linewidth and coupling homogeneity. When the spin-resonator coupling is distributed inhomogeneously, we find that the effective spin-echo relaxation time measured in a saturation recovery sequence strongly depends on the parameters for the detection echo. When the spin linewidth is larger than the resonator bandwidth, the different Fourier components of the spin echo relax with different characteristic times - due to the role of the resonator in driving relaxation - which results in the temporal shape of the echo becoming dependent on the repetition time of the experiment.
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Affiliation(s)
- V Ranjan
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - S Probst
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - B Albanese
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - A Doll
- Laboratoire Nanomagnétisme et Oxydes, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - O Jacquot
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - E Flurin
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - R Heeres
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - D Vion
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - D Esteve
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France
| | - J J L Morton
- London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
| | - P Bertet
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette Cedex, France.
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7
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Amouzandeh G, Ramaswamy V, Freytag N, Edison AS, Hornak LA, Brey WW. Time and Frequency Domain Response of HTS Resonators for Use as NMR Transmit Coils. IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY : A PUBLICATION OF THE IEEE SUPERCONDUCTIVITY COMMITTEE 2019; 29:1102705. [PMID: 31857782 PMCID: PMC6921929 DOI: 10.1109/tasc.2019.2902522] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Replacing normal metal NMR coils with thin-film high-temperature superconductor (HTS) resonators can significantly improve the sensitivity of analytical NMR. To study the use of these resonators for excitation as well as detection, we investigated the radio frequency properties of the HTS NMR coils in both frequency and time domain at a variety of transmit power levels. Experiments were conducted on a double-sided, counter wound spiral resonator designed to detect NMR signals from 13C nuclei at 14.1 T. Power-dependent nonlinearity was observed in the transmission coefficient and quality factor. The ability of the HTS resonators to accurately generate short pulses was studied in the time domain over the range power levels. The results of this study show that some form of Q switching is needed to get good transmit performance from HTS coils for 13C. For that purpose, the effect of adding a shorted transmission line stub to improve the pulse shapes and reduce phase transients was studied.
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Affiliation(s)
- Ghoncheh Amouzandeh
- National High Magnetic Laboratory and the Department of Physics, Florida State University, Tallahassee, FL 32310 USA
| | | | | | | | | | - William W Brey
- National High Magnetic Laboratory, Florida State University, Tallahassee, FL 32310 USA
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8
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Probst S, Ranjan V, Ansel Q, Heeres R, Albanese B, Albertinale E, Vion D, Esteve D, Glaser SJ, Sugny D, Bertet P. Shaped pulses for transient compensation in quantum-limited electron spin resonance spectroscopy. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2019; 303:42-47. [PMID: 31003062 DOI: 10.1016/j.jmr.2019.04.008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2019] [Revised: 04/08/2019] [Accepted: 04/09/2019] [Indexed: 06/09/2023]
Abstract
In high sensitivity inductive electron spin resonance spectroscopy, superconducting microwave resonators with large quality factors are employed. While they enhance the sensitivity, they also distort considerably the shape of the applied rectangular microwave control pulses, which limits the degree of control over the spin ensemble. Here, we employ shaped microwave pulses compensating the signal distortion to drive the spins faster than the resonator bandwidth. This translates into a shorter echo, with enhanced signal-to-noise ratio. The shaped pulses are also useful to minimize the dead-time of our spectrometer, which allows to reduce the wait time between successive drive pulses.
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Affiliation(s)
- Sebastian Probst
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191, Gif-sur-Yvette Cedex, France
| | - Vishal Ranjan
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191, Gif-sur-Yvette Cedex, France
| | - Quentin Ansel
- Université de Bourgogne Franche-Comté, Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS UMR 6303, 21078 Dijon Cedex, France
| | - Reinier Heeres
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191, Gif-sur-Yvette Cedex, France
| | - Bartolo Albanese
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191, Gif-sur-Yvette Cedex, France
| | - Emanuele Albertinale
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191, Gif-sur-Yvette Cedex, France
| | - Denis Vion
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191, Gif-sur-Yvette Cedex, France
| | - Daniel Esteve
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191, Gif-sur-Yvette Cedex, France
| | - Steffen J Glaser
- Department of Chemistry, Technische Universität München, Lichtenbergstraße 4, D-85747 Garching, Germany; Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 Munchen, Germany
| | - Dominique Sugny
- Université de Bourgogne Franche-Comté, Laboratoire Interdisciplinaire Carnot de Bourgogne, CNRS UMR 6303, 21078 Dijon Cedex, France
| | - Patrice Bertet
- Quantronics Group, SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191, Gif-sur-Yvette Cedex, France.
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9
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Eisenach ER, Barry JF, Pham LM, Rojas RG, Englund DR, Braje DA. Broadband loop gap resonator for nitrogen vacancy centers in diamond. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:094705. [PMID: 30278724 DOI: 10.1063/1.5037465] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Accepted: 08/31/2018] [Indexed: 06/08/2023]
Abstract
We present an S-band tunable loop gap resonator (LGR), which provides strong, homogeneous, and directionally uniform broadband microwave (MW) drive for nitrogen-vacancy (NV) ensembles. With 42 dBm of input power, the composite device provides drive field amplitudes approaching 5 G over a circular area ≳50 mm2 or cylindrical volume ≳250 mm3. The wide 80 MHz device bandwidth allows driving all NV Zeeman resonances for bias magnetic fields below 20 G. The device realizes percent-scale MW drive inhomogeneity; we measure a fractional root-mean-square inhomogeneity σ rms = 1.6% and a peak-to-peak variation σ pp = 3% over a circular area of 11 mm2 and σ rms = 3.2% and σ pp = 10.5% over a larger 32 mm2 circular area. We demonstrate incident MW power coupling to the LGR using two methodologies: a printed circuit board-fabricated exciter antenna for deployed compact bulk sensors and an inductive coupling coil suitable for microscope-style imaging. The inductive coupling coil allows for approximately 2π steradian combined optical access above and below the device, ideal for envisioned and existing NV imaging and bulk sensing applications.
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Affiliation(s)
- E R Eisenach
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - J F Barry
- MIT Lincoln Laboratory, Lexington, Massachusetts 02421, USA
| | - L M Pham
- MIT Lincoln Laboratory, Lexington, Massachusetts 02421, USA
| | - R G Rojas
- MIT Lincoln Laboratory, Lexington, Massachusetts 02421, USA
| | - D R Englund
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - D A Braje
- MIT Lincoln Laboratory, Lexington, Massachusetts 02421, USA
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10
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Hellwagner J, Wili N, Ibáñez LF, Wittmann JJ, Meier BH, Ernst M. Transient effects in π-pulse sequences in MAS solid-state NMR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2018; 287:65-73. [PMID: 29289819 DOI: 10.1016/j.jmr.2017.12.015] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2017] [Revised: 12/12/2017] [Accepted: 12/19/2017] [Indexed: 06/07/2023]
Abstract
Dipolar recoupling techniques that use isolated rotor-synchronized π pulses are commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological molecules. These sequences excel through their simplicity, stability towards radio-frequency (rf) inhomogeneity, and low rf requirements. For a theoretical understanding of such sequences, we present a Floquet treatment based on an interaction-frame transformation including the chemical-shift offset dependence. This approach is applied to the homonuclear dipolar-recoupling sequence Radio-Frequency Driven Recoupling (RFDR) and the heteronuclear recoupling sequence Rotational Echo Double Resonance (REDOR). Based on the Floquet approach, we show the influence of effective fields caused by pulse transients and discuss the advantages of pulse-transient compensation. We demonstrate experimentally that the transfer efficiency for homonuclear recoupling can be doubled in some cases in model compounds as well as in simple peptides if pulse-transient compensation is applied to the π pulses. Additionally, we discuss the influence of various phase cycles on the recoupling efficiency in order to reduce the magnitude of effective fields. Based on the findings from RFDR, we are able to explain why the REDOR sequence does not suffer in the recoupling efficiency despite the presence of effective fields.
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Affiliation(s)
- Johannes Hellwagner
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Nino Wili
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | | | - Johannes J Wittmann
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Beat H Meier
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Matthias Ernst
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
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11
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Koos MRM, Feyrer H, Luy B. Broadband RF-amplitude-dependent flip angle pulses with linear phase slope. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2017; 55:797-803. [PMID: 28321918 DOI: 10.1002/mrc.4593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2016] [Revised: 03/08/2017] [Accepted: 03/11/2017] [Indexed: 06/06/2023]
Abstract
Pulse sequences in NMR spectroscopy sometimes require the application of pulses with effective flip angles different from 90° and 180°. Previously (Magn. Reson. Chem. 2015, 53, 886-893), offset-compensated broadband excitation pulses with RF-amplitude-dependent effective flip angles (RADFA) were introduced that are applicable in such cases. However, especially RF-amplitude-restricted RADFA pulses turned out to perform not as good as desired in terms of achievable bandwidths. Here, a class of RF-amplitude-restricted RADFA pulses with linear phase slope is introduced that allows excitation over much larger bandwidths with better performance. In this theoretical work, the basic principle of the pulse class is explained, their physical limits explored, and their properties, also compared with other pulse classes, discussed in detail. Copyright © 2017 John Wiley & Sons, Ltd.
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Affiliation(s)
- Martin R M Koos
- Institut für Biologische Grenzflächen 4 - Magnetische Resonanz, Karlsruher Institut für Technologie (KIT), Postfach 3640, 76021, Karlsruhe, Germany
| | - Hannes Feyrer
- Institut für Organische Chemie, Karlsruher Institut für Technologie (KIT), Fritz-Haber-Weg 6, 76131, Karlsruhe, Germany
- Department of Medical Biochemistry and Biophysics (MBB), Karolinska Institutet, Scheeles Väg 2, 171 77, Stockholm, Sweden
| | - Burkhard Luy
- Institut für Biologische Grenzflächen 4 - Magnetische Resonanz, Karlsruher Institut für Technologie (KIT), Postfach 3640, 76021, Karlsruhe, Germany
- Institut für Organische Chemie, Karlsruher Institut für Technologie (KIT), Fritz-Haber-Weg 6, 76131, Karlsruhe, Germany
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12
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Doll A, Jeschke G. Wideband frequency-swept excitation in pulsed EPR spectroscopy. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 280:46-62. [PMID: 28579102 DOI: 10.1016/j.jmr.2017.01.004] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2016] [Revised: 12/31/2016] [Accepted: 01/03/2017] [Indexed: 06/07/2023]
Abstract
Excitation of electron spins with monochromatic rectangular pulses is limited to bandwidths that are smaller than the spectral widths of most organic radicals and much smaller than the spectral widths of transition and rare earth metal ions. With frequency-swept pulses, bandwidths of up to 800MHz have previously been attained for excitation and detection of spin packets at frequencies of about 9.6GHz and bandwidths of up to 2.5GHz in a polarization transfer experiment at frequencies of about 34GHz. The remaining limitations, mainly due to resonator bandwidth and due to pulse length restrictions are discussed. Flip angles for state-space rotations on passage of a transition can generally be computed from the critical adiabaticity by the Landau-Zener-Stückelberg-Majorana expression. For hyperbolic secant pulses, the Demkov-Kunike model describes excitation for spin packets within and outside the sweep range. Well within the sweep range, the Bloch-Siegert phase shift is proportional to critical adiabaticity to a very good approximation. Because of the dependence of both flip angle and coherence phase on critical adiabaticity, it is advantageous to use pairs of amplitude and frequency modulation functions that provide such offset-independent adiabaticity. Compensation for the resonator response function should restore offset-independent adiabaticity. Whereas resonance offsets and Bloch-Siegert phase can be refocused at certain pulse length ratios, phase dispersion in coupled spin systems cannot generally be refocused. Based on the bandwidth limitations that arise from spin dynamics, requirements are derived for a spectrometer that achieves precise spin control over wide bands. The design of such a spectrometer and hardware characterization by EPR experiments are discussed.
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Affiliation(s)
- Andrin Doll
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, CH-8093 Zurich, Switzerland
| | - Gunnar Jeschke
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, CH-8093 Zurich, Switzerland.
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13
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Spindler PE, Schöps P, Kallies W, Glaser SJ, Prisner TF. Perspectives of shaped pulses for EPR spectroscopy. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2017; 280:30-45. [PMID: 28579101 DOI: 10.1016/j.jmr.2017.02.023] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2016] [Revised: 02/27/2017] [Accepted: 02/28/2017] [Indexed: 06/07/2023]
Abstract
This article describes current uses of shaped pulses, generated by an arbitrary waveform generator, in the field of EPR spectroscopy. We show applications of sech/tanh and WURST pulses to dipolar spectroscopy, including new pulse schemes and procedures, and discuss the more general concept of optimum-control-based pulses for applications in EPR spectroscopy. The article also describes a procedure to correct for experimental imperfections, mostly introduced by the microwave resonator, and discusses further potential applications and limitations of such pulses.
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Affiliation(s)
- Philipp E Spindler
- Institute of Physical and Theoretical Chemistry and Center of Biomolecular Magnetic Resonance, Goethe University Frankfurt, Germany
| | - Philipp Schöps
- Institute of Physical and Theoretical Chemistry and Center of Biomolecular Magnetic Resonance, Goethe University Frankfurt, Germany
| | - Wolfgang Kallies
- Department of Chemistry, Technical University of Munich, Germany
| | - Steffen J Glaser
- Department of Chemistry, Technical University of Munich, Germany
| | - Thomas F Prisner
- Institute of Physical and Theoretical Chemistry and Center of Biomolecular Magnetic Resonance, Goethe University Frankfurt, Germany.
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14
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Hellwagner J, Sharma K, Tan KO, Wittmann JJ, Meier BH, Madhu PK, Ernst M. Optimizing symmetry-based recoupling sequences in solid-state NMR by pulse-transient compensation and asynchronous implementation. J Chem Phys 2017; 146:244202. [PMID: 28668064 DOI: 10.1063/1.4989542] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Pulse imperfections like pulse transients and radio-frequency field maladjustment or inhomogeneity are the main sources of performance degradation and limited reproducibility in solid-state nuclear magnetic resonance experiments. We quantitatively analyze the influence of such imperfections on the performance of symmetry-based pulse sequences and describe how they can be compensated. Based on a triple-mode Floquet analysis, we develop a theoretical description of symmetry-based dipolar recoupling sequences, in particular, R26411, calculating first- and second-order effective Hamiltonians using real pulse shapes. We discuss the various origins of effective fields, namely, pulse transients, deviation from the ideal flip angle, and fictitious fields, and develop strategies to counteract them for the restoration of full transfer efficiency. We compare experimental applications of transient-compensated pulses and an asynchronous implementation of the sequence to a supercycle, SR26, which is known to be efficient in compensating higher-order error terms. We are able to show the superiority of R26 compared to the supercycle, SR26, given the ability to reduce experimental error on the pulse sequence by pulse-transient compensation and a complete theoretical understanding of the sequence.
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Affiliation(s)
- Johannes Hellwagner
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Kshama Sharma
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| | - Kong Ooi Tan
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Johannes J Wittmann
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Beat H Meier
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - P K Madhu
- TIFR Centre for Interdisciplinary Sciences, 21 Brundavan Colony, Narsingi, Hyderabad 500075, India
| | - Matthias Ernst
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
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15
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Damme LV, Leiner D, Mardešić P, Glaser SJ, Sugny D. Linking the rotation of a rigid body to the Schrödinger equation: The quantum tennis racket effect and beyond. Sci Rep 2017. [PMID: 28638097 PMCID: PMC5479806 DOI: 10.1038/s41598-017-04174-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
Abstract
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.
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Affiliation(s)
- L Van Damme
- Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 5209 CNRS-Université Bourgogne Franche Comté, 9 Av. A. Savary, BP 47 870, F-21078, Dijon Cedex, France
| | - D Leiner
- Department of Chemistry, Technical University of Munich, Lichtenbergstrasse 4, D-85747, Garching, Germany
| | - P Mardešić
- Institut de Mathématiques de Bourgogne, UMR 5584 CNRS-Université de Bourgogne Franche-Comté, 9 Av. A. Savary, BP 47870, 21078, Dijon Cedex, France
| | - S J Glaser
- Department of Chemistry, Technical University of Munich, Lichtenbergstrasse 4, D-85747, Garching, Germany.
| | - D Sugny
- Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 5209 CNRS-Université Bourgogne Franche Comté, 9 Av. A. Savary, BP 47 870, F-21078, Dijon Cedex, France. .,Institute for Advanced Study, Technical University of Munich, Lichtenbergstrasse 2 a, D-85748, Garching, Germany.
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16
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Frantsuzov I, Vasa SK, Ernst M, Brown SP, Zorin V, Kentgens APM, Hodgkinson P. Rationalising Heteronuclear Decoupling in Refocussing Applications of Solid-State NMR Spectroscopy. Chemphyschem 2017; 18:394-405. [PMID: 28111874 PMCID: PMC5396389 DOI: 10.1002/cphc.201601003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2016] [Revised: 11/07/2016] [Indexed: 12/16/2022]
Abstract
Factors affecting the performance of 1 H heteronuclear decoupling sequences for magic-angle spinning (MAS) NMR spectroscopy of organic solids are explored, as observed by time constants for the decay of nuclear magnetisation under a spin-echo (T2' ). By using a common protocol over a wide range of experimental conditions, including very high magnetic fields and very high radio-frequency (RF) nutation rates, decoupling performance is observed to degrade consistently with increasing magnetic field. Inhomogeneity of the RF field is found to have a significant impact on T2' values, with differences of about 20 % observed between probes with different coil geometries. Increasing RF nutation rates dramatically improve robustness with respect to RF offset, but the performance of phase-modulated sequences degrades at the very high nutation rates achievable in microcoils as a result of RF transients. The insights gained provide better understanding of the factors limiting decoupling performance under different conditions, and the high values of T2' observed (which generally exceed previous literature values) provide reference points for experiments involving spin magnetisation refocussing, such as 2D correlation spectra and measuring small spin couplings.
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Affiliation(s)
- Ilya Frantsuzov
- Department of ChemistryDurham UniversitySouth RoadDurhamDH1 3LEUnited Kingdom
| | - Suresh K. Vasa
- Institute for Molecules and MaterialsRadboud UniversityHeyendaalseweg 1356525 EDNijmegenThe Netherlands
| | - Matthias Ernst
- Laboratory of Physical ChemistryETH ZürichVladimir-Prelog-Weg 28093ZürichSwitzerland
| | - Steven P. Brown
- Department of PhysicsUniversity of WarwickCoventryCV4 7ALUnited Kingdom
| | - Vadim Zorin
- Agilent Technologies (UK) Ltd.6 Mead RoadYarntonOxfordshireOX5 1QUUnited Kingdom
- Mestrelab ResearchS.L Feliciano Barrera 9B—Bajo15706Santiago de CompostelaSpain
| | - Arno P. M. Kentgens
- Institute for Molecules and MaterialsRadboud UniversityHeyendaalseweg 1356525 EDNijmegenThe Netherlands
| | - Paul Hodgkinson
- Department of ChemistryDurham UniversitySouth RoadDurhamDH1 3LEUnited Kingdom
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17
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Franssen WMJ, Rezus YLA, Kentgens APM. High radio-frequency field strength nutation NMR of quadrupolar nuclei. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2016; 273:33-39. [PMID: 27741438 DOI: 10.1016/j.jmr.2016.09.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2016] [Revised: 09/07/2016] [Accepted: 09/25/2016] [Indexed: 06/06/2023]
Abstract
Owing to the introduction of microcoils, high RF field strength nutation NMR is a viable candidate for the study of quadrupolar nuclei with strong quadrupolar couplings, not accessible using contemporary NMR techniques. We show powder 23Na nutation spectra on sodium nitrite for RF field strengths of up to 1170kHz, that conform to theoretical predictions. For lanthanum fluoride powder, 139La nutation spectra taken at elevated RF field amplitudes show clear discrepancies when compared to the theory. These errors are shown to be mainly caused by pulse transients at the end of the pulse, which proved to be detrimental to the shape of the nutation spectra. Using a nutation pulse which ends in a sudden frequency jump, we show that these errors can be reduced, and nutation spectra that conform to theory can be readily acquired. This enables nutation NMR for the study of quadrupolar nuclei with a strong quadrupolar coupling, bridging the gap between NMR, which can only analyse nuclei with a weak to medium quadrupolar coupling, and NQR, were extensive searching for the right quadrupolar frequency is the limiting factor.
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Affiliation(s)
- W M J Franssen
- Radboud University, Institute for Molecules and Materials (IMM), Solid State NMR, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - Y L A Rezus
- Radboud University, Institute for Molecules and Materials (IMM), Solid State NMR, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - A P M Kentgens
- Radboud University, Institute for Molecules and Materials (IMM), Solid State NMR, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
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18
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Schanda P, Ernst M. Studying Dynamics by Magic-Angle Spinning Solid-State NMR Spectroscopy: Principles and Applications to Biomolecules. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2016; 96:1-46. [PMID: 27110043 PMCID: PMC4836562 DOI: 10.1016/j.pnmrs.2016.02.001] [Citation(s) in RCA: 143] [Impact Index Per Article: 17.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Magic-angle spinning solid-state NMR spectroscopy is an important technique to study molecular structure, dynamics and interactions, and is rapidly gaining importance in biomolecular sciences. Here we provide an overview of experimental approaches to study molecular dynamics by MAS solid-state NMR, with an emphasis on the underlying theoretical concepts and differences of MAS solid-state NMR compared to solution-state NMR. The theoretical foundations of nuclear spin relaxation are revisited, focusing on the particularities of spin relaxation in solid samples under magic-angle spinning. We discuss the range of validity of Redfield theory, as well as the inherent multi-exponential behavior of relaxation in solids. Experimental challenges for measuring relaxation parameters in MAS solid-state NMR and a few recently proposed relaxation approaches are discussed, which provide information about time scales and amplitudes of motions ranging from picoseconds to milliseconds. We also discuss the theoretical basis and experimental measurements of anisotropic interactions (chemical-shift anisotropies, dipolar and quadrupolar couplings), which give direct information about the amplitude of motions. The potential of combining relaxation data with such measurements of dynamically-averaged anisotropic interactions is discussed. Although the focus of this review is on the theoretical foundations of dynamics studies rather than their application, we close by discussing a small number of recent dynamics studies, where the dynamic properties of proteins in crystals are compared to those in solution.
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Affiliation(s)
- Paul Schanda
- CEA, Institut de Biologie Structurale (IBS), 38027 Grenoble, France ; CNRS, Institut de Biologie Structurale (IBS), 38027 Grenoble, France ; Université Grenoble Alpes, IBS, 38027 Grenoble, France
| | - Matthias Ernst
- ETH Zürich, Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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19
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Wittmann JJ, Mertens V, Takeda K, Meier BH, Ernst M. Quantification and compensation of the influence of pulse transients on symmetry-based recoupling sequences. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2016; 263:7-18. [PMID: 26766289 DOI: 10.1016/j.jmr.2015.12.011] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2015] [Revised: 12/08/2015] [Accepted: 12/16/2015] [Indexed: 06/05/2023]
Abstract
Deviations of amplitude and phase of radio-frequency pulses from the desired values, can have a severe impact on the performance of multiple-pulse sequences in NMR spectroscopy. A particular problem are pulse transients that appear every time there is a discontinuity in amplitude or phase. Based on a Floquet description using pulses with arbitrarily shaped amplitudes and phases we present a systematic study of the influence of pulse transients on symmetry-based pulse sequences in solid-state NMR under magic-angle spinning. This treatment explains the dependence of the experimentally observed transfer efficiency on the details of experimental setups. In addition, three approaches are compared which have the aim to re-establish highly efficient recoupling. We demonstrate that the application of transient-compensated pulses as basic elements of symmetry-based sequences leads to a significantly improved robustness of the experiments with respect to variations in the experimental setup.
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Affiliation(s)
- Johannes J Wittmann
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Valerie Mertens
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Kazuyuki Takeda
- Division of Chemistry, Graduate School of Science, Kyoto University, 606-8502 Kyoto, Japan
| | - Beat H Meier
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Matthias Ernst
- Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
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20
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Mandal S, Oh S, Hürlimann MD. Absolute phase effects on CPMG-type pulse sequences. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2015; 261:121-132. [PMID: 26575106 DOI: 10.1016/j.jmr.2015.10.014] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2015] [Revised: 10/21/2015] [Accepted: 10/23/2015] [Indexed: 06/05/2023]
Abstract
We describe and analyze the effects of transients within radio-frequency (RF) pulses on multiple-pulse NMR measurements such as the well-known Carr-Purcell-Meiboom-Gill (CPMG) sequence. These transients are functions of the absolute RF phases at the beginning and end of the pulse, and are thus affected by the timing of the pulse sequence with respect to the period of the RF waveform. Changes in transients between refocusing pulses in CPMG-type sequences can result in signal decay, persistent oscillations, changes in echo shape, and other effects. We have explored such effects by performing experiments in two different low-frequency NMR systems. The first uses a conventional tuned-and-matched probe circuit, while the second uses an ultra-broadband un-tuned or non-resonant probe circuit. We show that there are distinct differences between the absolute phase effects in these two systems, and present simple models that explain these differences.
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Affiliation(s)
- Soumyajit Mandal
- Case Western Reserve University, Cleveland, OH 44106, USA; Schlumberger-Doll Research, Cambridge, MA 02139, USA.
| | - Sangwon Oh
- Yale University, New Haven, CT 06520, USA; Schlumberger-Doll Research, Cambridge, MA 02139, USA.
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21
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Wittmann JJ, Takeda K, Meier BH, Ernst M. Kompensation von Pulsimperfektionen in der Festkörper-NMR- Spektroskopie: ein Schlüssel zu verbesserter Reproduzierbarkeit und Effizienz. Angew Chem Int Ed Engl 2015. [DOI: 10.1002/ange.201504782] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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22
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Wittmann JJ, Takeda K, Meier BH, Ernst M. Compensating Pulse Imperfections in Solid-State NMR Spectroscopy: A Key to Better Reproducibility and Performance. Angew Chem Int Ed Engl 2015; 54:12592-6. [DOI: 10.1002/anie.201504782] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2015] [Revised: 07/03/2015] [Indexed: 11/11/2022]
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23
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Yap YS, Tabuchi Y, Negoro M, Kagawa A, Kitagawa M. A Ku band pulsed electron paramagnetic resonance spectrometer using an arbitrary waveform generator for quantum control experiments at millikelvin temperatures. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2015; 86:063110. [PMID: 26133831 DOI: 10.1063/1.4922791] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a 17 GHz (Ku band) arbitrary waveform pulsed electron paramagnetic resonance spectrometer for experiments down to millikelvin temperatures. The spectrometer is located at room temperature, while the resonator is placed either in a room temperature magnet or inside a cryogen-free dilution refrigerator; the operating temperature range of the dilution unit is from ca. 10 mK to 8 K. This combination provides the opportunity to perform quantum control experiments on electron spins in the pure-state regime. At 0.6 T, spin echo experiments were carried out using γ-irradiated quartz glass from 1 K to 12.3 mK. With decreasing temperatures, we observed an increase in spin echo signal intensities due to increasing spin polarizations, in accordance with theoretical predictions. Through experimental data fitting, thermal spin polarization at 100 mK was estimated to be at least 99%, which was almost pure state. Next, to demonstrate the ability to create arbitrary waveform pulses, we generate a shaped pulse by superposing three Gaussian pulses of different frequencies. The resulting pulse was able to selectively and coherently excite three different spin packets simultaneously-a useful ability for analyzing multi-spin system and for controlling a multi-qubit quantum computer. By applying this pulse to the inhomogeneously broadened sample, we obtain three well-resolved excitations at 8 K, 1 K, and 14 mK.
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Affiliation(s)
- Yung Szen Yap
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka-shi, Osaka 560-8531, Japan
| | - Yutaka Tabuchi
- Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Meguro-ku, Tokyo 153-8904, Japan
| | - Makoto Negoro
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka-shi, Osaka 560-8531, Japan
| | - Akinori Kagawa
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka-shi, Osaka 560-8531, Japan
| | - Masahiro Kitagawa
- Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka-shi, Osaka 560-8531, Japan
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24
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Doll A, Qi M, Pribitzer S, Wili N, Yulikov M, Godt A, Jeschke G. Sensitivity enhancement by population transfer in Gd(iii) spin labels. Phys Chem Chem Phys 2015; 17:7334-44. [DOI: 10.1039/c4cp05893c] [Citation(s) in RCA: 49] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Frequency-swept chirp pulses with bandwidths > 1 GHz rearrange electron spin populations in the S = 7/2 spin of Gd(iii) ions for better sensitivity, as demonstrated with distance measurements between Gd(iii) ions.
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Affiliation(s)
- Andrin Doll
- Laboratory of Physical Chemistry
- ETH Zurich
- 8093 Zurich
- Switzerland
| | - Mian Qi
- Faculty of Chemistry and Center for Molecular Materials
- Bielefeld University
- 33615 Bielefeld
- Germany
| | | | - Nino Wili
- Laboratory of Physical Chemistry
- ETH Zurich
- 8093 Zurich
- Switzerland
| | - Maxim Yulikov
- Laboratory of Physical Chemistry
- ETH Zurich
- 8093 Zurich
- Switzerland
| | - Adelheid Godt
- Faculty of Chemistry and Center for Molecular Materials
- Bielefeld University
- 33615 Bielefeld
- Germany
| | - Gunnar Jeschke
- Laboratory of Physical Chemistry
- ETH Zurich
- 8093 Zurich
- Switzerland
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25
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Köcher SS, Heydenreich T, Glaser SJ. Visualization and analysis of modulated pulses in magnetic resonance by joint time-frequency representations. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2014; 249:63-71. [PMID: 25462948 DOI: 10.1016/j.jmr.2014.10.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2014] [Revised: 09/27/2014] [Accepted: 10/05/2014] [Indexed: 06/04/2023]
Abstract
We study the utility of joint time-frequency representations for the analysis of shaped or composite pulses for magnetic resonance. Such spectrograms are commonly used for the visualization of shaped laser pulses in optical spectroscopy. This intuitive representation provides additional insight compared to conventional approaches, which exclusively show either temporal or spectral information. We focus on the short-time Fourier transform, which provides not only amplitude but also phase information. The approach is illustrated for broadband inversion pulses, multiple quantum excitation and broadband heteronuclear decoupling. The physical interpretation and validity of the approach is discussed.
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Affiliation(s)
- S S Köcher
- Department of Chemistry, Technische Universität München, Lichtenbergstrasse 4, D-85747 Garching, Germany
| | - T Heydenreich
- Department of Chemistry, Technische Universität München, Lichtenbergstrasse 4, D-85747 Garching, Germany
| | - S J Glaser
- Department of Chemistry, Technische Universität München, Lichtenbergstrasse 4, D-85747 Garching, Germany.
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26
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Yap YS, Yamamoto H, Tabuchi Y, Negoro M, Kagawa A, Kitagawa M. Strongly driven electron spins using a K(u) band stripline electron paramagnetic resonance resonator. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2013; 232:62-67. [PMID: 23703225 DOI: 10.1016/j.jmr.2013.04.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2013] [Revised: 04/23/2013] [Accepted: 04/26/2013] [Indexed: 06/02/2023]
Abstract
This article details our work to obtain strong excitation for electron paramagnetic resonance (EPR) experiments by improving the resonator's efficiency. The advantages and application of strong excitation are discussed. Two 17 GHz transmission-type, stripline resonators were designed, simulated and fabricated. Scattering parameter measurements were carried out and quality factor were measured to be around 160 and 85. Simulation results of the microwave's magnetic field distribution are also presented. To determine the excitation field at the sample, nutation experiments were carried out and power dependence were measured using two organic samples at room temperature. The highest recorded Rabi frequency was rated at 210 MHz with an input power of about 1 W, which corresponds to a π/2 pulse of about 1.2 ns.
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Affiliation(s)
- Yung Szen Yap
- Graduate School of Engineering Science, Osaka University, Japan.
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27
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Doll A, Pribitzer S, Tschaggelar R, Jeschke G. Adiabatic and fast passage ultra-wideband inversion in pulsed EPR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2013; 230:27-39. [PMID: 23434533 DOI: 10.1016/j.jmr.2013.01.002] [Citation(s) in RCA: 95] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2012] [Revised: 01/04/2013] [Accepted: 01/09/2013] [Indexed: 05/12/2023]
Abstract
We demonstrate that adiabatic and fast passage ultra-wideband (UWB) pulses can achieve inversion over several hundreds of MHz and thus enhance the measurement sensitivity, as shown by two selected experiments. Technically, frequency-swept pulses are generated by a 12 GS/s arbitrary waveform generator and upconverted to X-band frequencies. This pulsed UWB source is utilized as an incoherent channel in an ordinary pulsed EPR spectrometer. We discuss experimental methodologies and modeling techniques to account for the response of the resonator, which can strongly limit the excitation bandwidth of the entire non-linear excitation chain. Aided by these procedures, pulses compensated for bandwidth or variations in group delay reveal enhanced inversion efficiency. The degree of bandwidth compensation is shown to depend critically on the time available for excitation. As a result, we demonstrate optimized inversion recovery and double electron electron resonance (DEER) experiments. First, virtually complete inversion of the nitroxide spectrum with an adiabatic pulse of 128ns length is achieved. Consequently, spectral diffusion between inverted and non-inverted spins is largely suppressed and the observation bandwidth can be increased to increase measurement sensitivity. Second, DEER is performed on a terpyridine-based copper (II) complex with a nitroxide-copper distance of 2.5nm. As previously demonstrated on this complex, when pumping copper spins and observing nitroxide spins, the modulation depth is severely limited by the excitation bandwidth of the pump pulse. By using fast passage UWB pulses with a maximum length of 64ns, we achieve up to threefold enhancement of the modulation depth. Associated artifacts in distance distributions when increasing the bandwidth of the pump pulse are shown to be small.
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Affiliation(s)
- Andrin Doll
- ETH Zurich, Laboratory of Physical Chemistry, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland
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28
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Borneman TW, Cory DG. Bandwidth-limited control and ringdown suppression in high-Q resonators. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2012; 225:120-9. [PMID: 23165232 DOI: 10.1016/j.jmr.2012.10.011] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2012] [Revised: 10/18/2012] [Accepted: 10/21/2012] [Indexed: 05/12/2023]
Abstract
We describe how the transient behavior of a tuned and matched resonator circuit and a ringdown suppression pulse may be integrated into an optimal control theory (OCT) pulse-design algorithm to derive control sequences with limited ringdown that perform a desired quantum operation in the presence of resonator distortions of the ideal waveform. Inclusion of ringdown suppression in numerical pulse optimizations significantly reduces spectrometer deadtime when using high quality factor (high-Q) resonators, leading to increased signal-to-noise ratio (SNR) and sensitivity of inductive measurements. To demonstrate the method, we experimentally measure the free-induction decay of an inhomogeneously broadened solid-state free radical spin system at high Q. The measurement is enabled by using a numerically optimized bandwidth-limited OCT pulse, including ringdown suppression, robust to variations in static and microwave field strengths. We also discuss the applications of pulse design in high-Q resonators to universal control of anisotropic-hyperfine coupled electron-nuclear spin systems via electron-only modulation even when the bandwidth of the resonator is significantly smaller than the hyperfine coupling strength. These results demonstrate how limitations imposed by linear response theory may be vastly exceeded when using a sufficiently accurate system model to optimize pulses of high complexity.
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Affiliation(s)
- Troy W Borneman
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
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Takeda K. Microcoils and microsamples in solid-state NMR. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2012; 47-48:1-9. [PMID: 23083521 DOI: 10.1016/j.ssnmr.2012.09.002] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2012] [Revised: 09/13/2012] [Accepted: 09/14/2012] [Indexed: 06/01/2023]
Abstract
Recent reports on microcoils are reviewed. The first part of the review includes a discussion of how the geometries of the sample and coil affect the NMR signal intensity. In addition to derivation of the well-known result that the signal intensity increases as the coil size decreases, the prediction that dilution of a small sample with magnetically inert matter leads to better sensitivity if a tiny coil is not available is given. The second part of the review focuses on the issues specific to solid-state NMR. They include realization of magic-angle spinning (MAS) using a microcoil and harnessing of such strong pulses that are feasible only with a microcoil. Two strategies for microcoil MAS, the piggyback method and magic-angle coil spinning (MACS), are reviewed. In addition, MAS of flat, disk-shaped samples is discussed in the context of solid-state NMR of small-volume samples. Strong RF irradiation, which has been exploited in wide-line spectral excitation, multiple-quantum MAS (MQMAS), and dipolar decoupling experiments, has been accompanied by new challenges regarding the Bloch-Siegert effect, the minimum time resolution of the spectrometer, and the time scale of pulse transient effects. For a possible solution to the latter problem, recent reports on active compensation of pulse transients are described.
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Affiliation(s)
- Kazuyuki Takeda
- Division of Chemistry, Graduate School of Science, Kyoto University, 606-8502 Kyoto, Japan.
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Spindler PE, Zhang Y, Endeward B, Gershernzon N, Skinner TE, Glaser SJ, Prisner TF. Shaped optimal control pulses for increased excitation bandwidth in EPR. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2012; 218:49-58. [PMID: 22578555 DOI: 10.1016/j.jmr.2012.02.013] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2011] [Revised: 02/16/2012] [Accepted: 02/18/2012] [Indexed: 05/12/2023]
Abstract
A 1 ns resolution pulse shaping unit has been developed for pulsed EPR spectroscopy to enable 14-bit amplitude and phase modulation. Shaped broadband excitation pulses designed using optimal control theory (OCT) have been tested with this device at X-band frequency (9 GHz). FT-EPR experiments on organic radicals in solution have been performed with the new pulses, designed for uniform excitation over a significantly increased bandwidth compared to a classical rectangular π/2 pulse of the same B(1) amplitude. The concept of a dead-time compensated prefocused pulse has been introduced to EPR with a self-refocusing of 200 ns after the end of the pulse. Echo-like refocused signals have been recorded and compared to the performance of a classical Hahn-echo sequence. The impulse response function of the microwave setup has been measured and incorporated into the algorithm for designing OCT pulses, resulting in further significant improvements in performance. Experimental limitations and potential new applications of OCT pulses in EPR spectroscopy will be discussed.
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Affiliation(s)
- Philipp E Spindler
- Institut für physikalische und theoretische Chemie, Goethe Universität Frankfurt, Max von Laue Strasse 7, 60438 Frankfurt am Main, Germany.
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Weber J, Seemann M, Schmedt auf der Günne J. Pulse-transient adapted C-symmetry pulse sequences. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2012; 43-44:42-50. [PMID: 22445515 DOI: 10.1016/j.ssnmr.2012.02.009] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2012] [Revised: 02/28/2012] [Accepted: 02/29/2012] [Indexed: 05/31/2023]
Abstract
In solid-state NMR, pulse sequences make often use of pulses which are short compared to the recovery time of the probe head. Especially, rotorsynchronized dipolar recoupling experiments under magic-angle-spinning conditions can profit from the use of very high pulse amplitudes which in turn will reduce the length of the individual pulses. In this contribution we show that C-symmetry based pulse sequences used for double-quantum filtering experiments can strongly be influenced by pulse transients. We analyze the origin of pulse transients and show that the quadrature component can be minimized by cable-length variation which causes a mutual cancellation of probe-external and internal contributions. We implement and test a model to investigate the influence of pulse-transients by numerically exact calculations of the spin-density matrix allowing for composite pulses consisting of slices which are short compared to the circuit recovery time-constant. Moreover we introduce a phase-tuned C-element, which can be applied to γ-encoded experiments from the C-symmetry class, to reconstitute an almost ideal performance of the sequence. We have validated the modified transient-adapted pulse sequences theoretically on the basis of numerically exact calculations of the spin-dynamics. While comparably easy to apply the scheme proved also robust in practical application to (15)N, (13)C and (31)P double-quantum filtered experiments and leads to a significantly increased conversion efficiency.
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Affiliation(s)
- Johannes Weber
- Ludwig-Maximilians-Universität, Department Chemie, Butenandtstr. 5-13 (Haus D), 81377 München, Germany
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