nuclear magnetic resonance spectroscopy

Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance | J. Chem. Phys. (2014)

Posted on

Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance

Gonzalo A. Álvarez, Noam Shemesh and Lucio Frydman
J. Chem. Phys. 140, 084205 (2014); http://dx.doi.org/10.1063/1.4865335

Dynamical decoupling, a generalization of the original NMR spin-echo sequence, is becoming increasingly relevant as a tool for reducing decoherence in quantum systems. Such sequences apply non-equidistant refocusing pulses for optimizing the coupling between systems, and environmental fluctuations characterized by a given noise spectrum. One such sequence, dubbed Selective Dynamical Recoupling SDR [P. E. S. Smith, G. Bensky, G. A. Álvarez, G. Kurizki, and L. Frydman, Proc. Natl. Acad. Sci. 109, 5958 (2012)], allows one to coherently reintroduce diffusion decoherence effects driven by fluctuations arising from restricted molecular diffusion [G. A. Álvarez, N. Shemesh, and L. Frydman, Phys. Rev. Lett. 111, 080404 (2013)]. The fully-refocused, constant-time, and constant-number-of-pulses nature of SDR also allows one to filter out “intrinsic” T1 and T2 weightings, as well as pulse errors acting as additional sources of decoherence. This article explores such features when the fluctuations are now driven by unrestricted molecular diffusion. In particular, we show that diffusion-driven SDR can be exploited to investigate the decoherence arising from the frequency fluctuations imposed by internal gradients. As a result, SDR presents a unique way of probing and characterizing these internal magnetic fields, given an a priori known free diffusion coefficient. This has important implications in studies of structured systems, including porous media and live tissues, where the internal gradients may serve as fingerprints for the systems composition or structure. The principles of this method, along with full analytical solutions for the unrestricted diffusion-driven modulation of the SDR signal, are presented. The potential of this approach is demonstrated with the generation of a novel source of MRI contrast, based on the background gradients active in an ex vivo mouse brain. Additional features and limitations of this new method are discussed.

© 2014 AIP Publishing LLC

via Diffusion-assisted selective dynamical recoupling: A new approach to measure background gradients in magnetic resonance, J. Chem. Phys. 140, 084205 (2014); http://dx.doi.org/10.1063/1.4865335.

Selective dynamical recoupling (SDR) series of images and the corresponding ex-vivo mouse brain background gradients (central panel) derived from these data.
Selective dynamical recoupling (SDR) series of images and the corresponding ex-vivo mouse brain background gradients (central panel) derived from these data.

Quantum simulations of localization effects with dipolar interactions | Annalen der Physik – 2013

Posted on

Quantum simulations of localization effects with dipolar interactions

Gonzalo A. Álvarez, Robin Kaiser, Dieter Suter

Abstract:
Quantum information processing often uses systems with dipolar interactions. Here a nuclear spin-based quantum simulator is used to study the spreading of information in such a dipolar-coupled system. While the information spreads with no apparent limits in the case of ideal dipolar couplings, additional perturbations limit the spreading, leading to localization. In previous work [Phys. Rev. Lett. 104, 230403 (2010)], it was found that the system size reaches a dynamic equilibrium that decreases with the square of the perturbation strength. This work examines the impact of a disordered Hamiltonian with dipolar interactions. It shows that the expansion of the cluster of spins freezes in the presence of large disorder, reminiscent of Anderson localization of non-interacting waves in a disordered potential.

Keywords: spin dynamics;dipolar interaction;decoherence;localization;disorder;NMR;long range interactions;quantum information processing

Annalen der Physik
Special Issue on “Quantum Simulations“, featuring review papers written by last year’s Nobel Prize winners describing their foundational work (Wineland and Haroche). Issue edited by: Rainer Blatt, Immanuel Bloch, Ignacio Cirac, Peter Zoller.
Ann. Phys. 525, 833 (2013).
DOI: 10.1002/andp.201300096

© 2013 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

via Quantum simulations of localization effects with dipolar interactions – Álvarez – 2013 – Annalen der Physik – Wiley Online Library.

Quantum simulations of localization effects with dipolar interactions - Álvarez - 2013 - Annalen der Physik - Wiley Online Library
Time evolution of the cluster-size of correlated spins starting from different initial sates. The experimental data is shown for two different perturbation strengths given in the legend. The solid black squares, red triangles and green rhombuses are evolutions from an uncorrelated initial state. Empty symbols start from an initial state with K0 correlated spins. The insets show the Multiple Quantum Coherence spectrum starting from K0 = 141 as a functions of time for a perturbation strength.

Measuring small compartment dimensions by probing diffusion dynamics via Non-uniform Oscillating-Gradient Spin-Echo NOGSE NMR | J. Magn. Reson. (2013)

Posted on

Measuring small compartment dimensions by probing diffusion dynamics via Non-uniform Oscillating-Gradient Spin-Echo NOGSE NMR

Noam Shemesh, Gonzalo A. Álvarez, Lucio Frydman.
Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.

J. Magn. Reson. 237, 49–62 (2013).

 

Highlights:
•NOGSE, a novel diffusion MR approach for measuring pore sizes, is presented and analyzed.
•NOGSE is based on a constant time and a constant number of oscillating gradients.
•Experiments on microstructural phantoms, spinal cords and brains, validate NOGSE.

Abstract:
Noninvasive measurements of microstructure in materials, cells, and in biological tissues, constitute a unique capability of gradient-assisted NMR. Diffusion–diffraction MR approaches pioneered by Callaghan demonstrated this ability; Oscillating-Gradient Spin-Echo OGSE methodologies tackle the demanding gradient amplitudes required for observing diffraction patterns by utilizing constant-frequency oscillating gradient pairs that probe the diffusion spectrum, Dω. Here we present a new class of diffusion MR experiments, termed Non-uniform Oscillating-Gradient Spin-Echo NOGSE, which dynamically probe multiple frequencies of the diffusion spectral density at once, thus affording direct microstructural information on the compartment’s dimension. The NOGSE methodology applies N constant-amplitude gradient oscillations; N − 1 of these oscillations are spaced by a characteristic time x, followed by a single gradient oscillation characterized by a time y, such that the diffusion dynamics is probed while keeping N − 1x + y ≡ TNOGSE constant. These constant-time, fixed-gradient-amplitude, multi-frequency attributes render NOGSE particularly useful for probing small compartment dimensions with relatively weak gradients – alleviating difficulties associated with probing Dω frequency-by-frequency or with varying relaxation weightings, as in other diffusion-monitoring experiments. Analytical descriptions of the NOGSE signal are given, and the sequence’s ability to extract small compartment sizes with a sensitivity towards length to the sixth power, is demonstrated using a microstructural phantom. Excellent agreement between theory and experiments was evidenced even upon applying weak gradient amplitudes. An MR imaging version of NOGSE was also implemented in ex vivo pig spinal cords and mouse brains, affording maps based on compartment sizes. The effects of size distributions on NOGSE are also briefly analyzed.

Keywords:
Restricted diffusion; Oscillating gradients; OGSE; Microstructure; Magnetic resonance imaging; CNS; Gradient echoes; Selective dynamical recoupling

Graphical abstract:

Measuring small compartment dimensions by probing diffusion dynamics via Non-uniform Oscillating-Gradient Spin-Echo NOGSE NMR

via Measuring small compartment dimensions by probing diffusion dynamics via Non-uniform Oscillating-Gradient Spin-Echo NOGSE NMR.

Coherent dynamical recoupling of diffusion-driven decoherence in magnetic resonance | Phys. Rev. Lett. 111, 080404 (2013)

Posted on Updated on

Coherent dynamical recoupling of diffusion-driven decoherence in magnetic resonance

Gonzalo A. Álvarez, Noam Shemesh, and Lucio Frydman
Department of Chemical Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
Received 13 May 2013; published 20 August 2013

During recent years, dynamical decoupling (DD) has gained relevance as a tool for manipulating and interrogating quantum systems. This is particularly relevant for spins involved in nuclear magnetic resonance (NMR), where DD sequences can be used to prolong quantum coherences, or to selectively couple or decouple the effects imposed by random environmental fluctuations. In this Letter, we show that these concepts can be exploited to selectively recouple diffusion processes in restricted spaces. The ensuing method provides a novel tool to measure restriction lengths in confined systems such as capillaries, pores or cells. The principles of this method for selectively recoupling diffusion-driven decoherence, its standing within the context of diffusion NMR, extensions to the characterization of other kinds of quantum fluctuations, and corroborating experiments, are presented.

© 2013 American Physical Society

via Phys. Rev. Lett. 111, 080404 (2013): Coherent Dynamical Recoupling of Diffusion-Driven Decoherence in Magnetic Resonance.

arXiv: [1305.2794] Coherent dynamical recoupling of diffusion-driven decoherence in magnetic resonance.

Time evolution of the spin magnetization under CPMG (N = 8 pulses) and Hahn-echo sequences for spins diffusing in a restricted space (circles, triangles), and under free diffusion (crosses, dashes). The solid black lines show the time range where the restricted diffusion effects dominate; the difference ∆M_SDR between these lines gives a contrast, over which signals can be coherently modulated by a suitable Selective Dynamical Decoupling (SDR) filter function.
Time evolution of the spin magnetization under CPMG (N = 8 pulses) and Hahn-echo sequences for spins diffusing in a restricted space (circles, triangles), and under free diffusion (crosses, dashes). The solid black lines show the time range where the restricted diffusion effects dominate; the difference ∆M_SDR between these lines gives a contrast, over which signals can be coherently modulated by a suitable Selective Dynamical Decoupling (SDR) filter function.
Experimental SDR signals normalized with the first data point (symbols) as a function of the x delays of the SDR sequence. The solid lines are analytical fittings of our model to the experimental curve. By using the measured diffusion coefficient D0 ∼ 2.3 × 10−5 cm^2/s, the fitted diameter d given in the plots is in agreement with the nominal value d = 5 ± 1μm.
Experimental SDR signals normalized with the first data point (symbols) as a function of the x delays of the SDR sequence. The solid lines are analytical fittings of our model to the experimental curve. By using the measured diffusion coefficient D0 ∼ 2.3 × 10−5 cm^2/s, the fitted diameter d given in the plots is in agreement with the nominal value d = 5 ± 1μm. The behavior of the SDR curves resemble the root mean square displacement of the diffusing spins in a restricted space: in both cases curves plateu for times x larger than the correlation time characteristic of achieving a restricted diffusion regime, evidence a full sampling of the restricting space.

Robustness of dynamical decoupling sequences | Phys. Rev. A 87, 042309 (2013)

Posted on

Robustness of dynamical decoupling sequences

Mustafa Ahmed Ali Ahmed [1,2], Gonzalo A. Álvarez [1,3], and Dieter Suter [1]
1Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
2Department of Physics, International University of Africa, Khartoum, Sudan
3Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel

Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences can equally suppress its effect on the system. Under these conditions, the remaining decay of the qubits under DD allows us to compare very precisely the robustness of the different DD sequences with respect to imperfections of the control pulses.

©2013 American Physical Society

via Phys. Rev. A 87, 042309 (2013): Robustness of dynamical decoupling sequences.

Average error per pulse for different DD sequences with delay τ =100μs. The average decay per pulse for different sequences is plotted against the number of pulses. The most conspicuous feature is that CP performs very badly and CPMG very well. The compensated sequences lie between these two extremes, and we find that the higher order sequences (XY8, KDD perform better than the lower order sequences (XY4). For unknown initial conditions, KDD shows the best performance. Under the present conditions, sequences that differ only with respect to time reversal symmetry perform quite similarly.
Average error per pulse for different DD sequences with delay τ =100μs.
The average decay per pulse for different sequences is plotted against the number of pulses. The most conspicuous feature is that CP performs very badly and CPMG very well. The compensated sequences lie between these two extremes, and we find that the higher order sequences (XY8, KDD perform better than the lower order sequences (XY4). For unknown initial conditions, KDD shows the best performance. Under the present conditions, sequences that differ only with respect to time reversal symmetry perform quite similarly.

Experimental protection of quantum gates against decoherence and control errors | Phys. Rev. A 86, 050301(R) 2012

Posted on

 Experimental protection of quantum gates against decoherence and control errors

Alexandre M. Souza, Gonzalo A. Álvarez, and Dieter Suter
Fakultät Physik, Technische Universität Dortmund, D-44221, Dortmund, Germany

One of the biggest challenges for implementing quantum devices is the requirement to perform accurate quantum gates. The destructive effects of interactions with the environment present some of the most difficult obstacles that must be overcome for precise quantum control. In this work we implement a proof of principle experiment of quantum gates protected against a fluctuating environment and control pulse errors using dynamical decoupling techniques. We show that decoherence can be reduced during the application of quantum gates. High-fidelity quantum gates can be achieved even if the gate time exceeds the free evolution decoherence time by one order of magnitude and for protected operations consisting of up to 330 individual control pulses.

©2012 American Physical Society

via Phys. Rev. A 86, 050301 2012: Experimental protection of quantum gates against decoherence and control errors.

Gate fidelity as a function of gate time for different gate operations protected by different dynamical decoupling (DD) sequences. “Simple” indicates gates that were implemented by unprotected rotations. BB1 means that the gates are only protected by BB1 composite pulses which does not protect against decoherence. The delay between the pulses for the NOOP was ≈ 3μs.
Gate fidelity as a function of gate time for different gate operations protected by different dynamical decoupling (DD) sequences. “Simple” indicates gates that were implemented by unprotected rotations. BB1 means that the gates are only protected by BB1 composite pulses which does not protect against decoherence. The delay between the pulses for the NOOP was ≈ 3μs.

Iterative rotation scheme for robust dynamical decoupling | Phys. Rev. A 85, 052324 (2012)

Posted on

Gonzalo A. Álvarez, Alexandre M. Souza, and Dieter Suter

Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
Received 1 March 2012; published 29 May 2012

The loss of quantum information due to interactions with external degrees of freedom, which is known as decoherence, remains one of the main obstacles for large-scale implementations of quantum computing. Accordingly, different measures are being explored for reducing its effect. One of them is dynamical decoupling DD which offers a practical solution because it only requires the application of control pulses to the system qubits. Starting from basic DD sequences, more sophisticated schemes were developed that eliminate higher-order terms of the system-environment interaction and are also more robust against experimental imperfections. A particularly successful scheme, called concatenated DD CDD, gives a recipe for generating higher-order sequences by inserting lower-order sequences into the delays of a generating sequence. Here, we show how this scheme can be improved further by converting some of the pulses to virtual and thus ideal pulses. The resulting scheme, called (XY4)^n, results in lower power deposition and is more robust against pulse imperfections than the original CDD scheme.

©2012 American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevA.85.052324
DOI: 10.1103/PhysRevA.85.052324

via Phys. Rev. A 85, 052324 2012: Iterative rotation scheme for robust dynamical decoupling.

 

Normalized spin-signal after about 100 pulses for different DD sequences as a function of the RF frequency of the DD pulses and the delay between them. All sequences have 100 pulses except (XY4)^2, which contains 96. The labels (a) and (s) refers the the asymmetric and symmetric version of the sequences. The plot shows that our concatenation scheme with virtual pulses (XY4)^2 outperforms the concatenation scheme with real pulses CDD_2. Following a similar procedure we introduce a new sequence KDD^2 that outperforms the other DD sequences shown in the plot. This new sequence is based on the KDD sequence [PRL 106, 240501 (2011)].
Normalized spin-signal after about 100 pulses for different DD sequences as a function of the RF frequency of the DD pulses and the delay between them. All sequences have 100 pulses except (XY4)^2, which contains 96. The labels (a) and (s) refers the the asymmetric and symmetric version of the sequences. The plot shows that our concatenation scheme with virtual pulses (XY4)^2 outperforms the concatenation scheme with real pulses CDD_2. Following a similar procedure we introduce a new sequence KDD^2 that outperforms the other DD sequences shown in the plot. This new sequence is based on the KDD sequence [PRL 106, 240501 (2011)].

Shift-driven modulations of spin-echo signals | Proc. Natl. Acad. Sci. U. S. A. 109, 5958 (2012).

Posted on Updated on

Pieter E. S. Smith, Guy Bensky, Gonzalo A. Álvarez, Gershon Kurizki, and Lucio Frydman

Abstract:

Since the pioneering works of Carr-Purcell and Meiboom-Gill [Carr HY, Purcell EM (1954) Phys Rev 94:630; Meiboom S, Gill D (1985) Rev Sci Instrum 29:688], trains of π-pulses have featured amongst the main tools of quantum control. Echo trains find widespread use in nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI), thanks to their ability to free the evolution of a spin-1/2 from several sources of decoherence. Spin echoes have also been researched in dynamic decoupling scenarios, for prolonging the lifetimes of quantum states or coherences. Inspired by this search we introduce a family of spin-echo sequences, which can still detect site-specific interactions like the chemical shift. This is achieved thanks to the presence of weak environmental fluctuations of common occurrence in high-field NMR—such as homonuclear spin-spin couplings or chemical/biochemical exchanges. Both intuitive and rigorous derivations of the resulting “selective dynamical recoupling” sequences are provided. Applications of these novel experiments are given for a variety of NMR scenarios including determinations of shift effects under inhomogeneities overwhelming individual chemical identities, and model-free characterizations of chemically exchanging partners.chemical exchange dynamic decoupling magnetic field inhomogeneity magnetic resonance quantum control

via Proc. Natl. Acad. Sci. U. S. A. 109, 5958 (2012): Shift-driven modulations of spin-echo signals.

Behavior observed for the illustrated compound (Cynnamic acid) upon implementing the proposed selective dynamical recoupling (SDR) sequence, as mediated by homonuclear 1H-1H couplings, for the indicated parameters. Experiments (black traces) are compared against simulations (red) using the indicated parameters, and analytical curves (blue) arise from the two-site modulation predicted by our results. (A) x-dependence observed for the isolated olefinic proton pair of Cynnamic acid at high-resolution. (B) Idem but for the Cynnamic acid placed in a grossly inhomogeneous magnetic field (shimming coils off), illustrating SDR’s ability to retrieve high resolution shift modulations. While it relies on fully refocused π-pulse trains that normally cancel also the shift modulations, by the assistance of slowly fluctuations due to the homonuclear 1H-1H couplings the shift modulation are selectively reintroduced.
Behavior observed for the illustrated compound (Cynnamic acid) upon implementing the proposed selective dynamical recoupling (SDR) sequence, as mediated by homonuclear 1H-1H couplings, for the indicated parameters. Experiments (black traces) are compared against simulations (red) using the indicated parameters, and analytical curves (blue) arise from the two-site modulation predicted by our results. (A) x-dependence observed for the isolated olefinic proton pair of Cynnamic acid at high-resolution. (B) Idem but for the Cynnamic acid placed in a grossly inhomogeneous magnetic field (shimming coils off), illustrating SDR’s ability to retrieve high resolution shift modulations. While it relies on fully refocused π-pulse trains that normally cancel also the shift modulations, by the assistance of slowly fluctuations due to the homonuclear 1H-1H couplings the shift modulation are selectively reintroduced.

Copyright ©2012 by the National Academy of Sciences