Science: Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins

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Nonequilibrium dynamics of many-body systems are important in many scientific fields. Here, we report the experimental observation of a phase transition of the quantum coherent dynamics of a three-dimensional many-spin system with dipolar interactions. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. Depending on the quench strength, we then observe either localized or extended dynamics of the system coherence. We extract the critical exponents for the localized cluster size of correlated spins and diffusion coefficient around the phase transition separating the localized from the delocalized dynamical regime. These results show that NMR techniques are well suited to studying the nonequilibrium dynamics of complex many-body systems.

 

Gonzalo A. Álvarez (1), Dieter Suter (2), Robin Kaiser (3)

(1) Department of Chemical Physics, Weizmann Institute of Science, 76100, Rehovot, Israel.
(2) Fakultät Physik, Technische Universität Dortmund, D-44221, Dortmund, Germany.
(3) Institut Non-Linéaire de Nice, CNRS, Université de Nice Sophia Antipolis, 06560, Valbonne, France.

Science 349, 846 (2015)

DOI: 10.1126/science.1261160

 

scaling_localization-delocalization_transition
Time evolution of the cluster size of correlated spins K for different quench strengths (1-p) and finite-time scaling procedure. (A) Cluster-size K as a function of the time t after the quench. The unperturbed quenched evolution (black squares) shows a cluster-size K that grows as ∼t^(4.3) at long times (dashed line is a guide to the eye). The solid symbols show the points used for a finite-time scaling analysis, while the empty symbols do not belong to the long time regime (t < 0.3 ms). For the largest perturbation strengths p to the quench, localization effects are clearly visible by the saturation of the cluster size. (B and C) In these two panels, we present the finite-time scaling procedure. In (B), the rescaled and squared correlation length l^2= K^(2/3) as a function of the evolution time 1=t^(k_2) is plotted. In (C), the curves of (B) are rescaled horizontally by the scaling factor ξ(p) to obtain a universal scaling law.

 

localization-delocalization_transition
Scaling factor and critical exponents. Normalized scaling factor ξ(p) as a function of p (blue triangles). The red solid line is a fit to the blue triangles with a expression ξ(p) proportional to|p − p_c|^nu, the critical exponent is then nu= 0,42. The two insets show the distribution of coherence orders of the density matrix as a function of the evolution time t for two perturbation strengths, which correspond to a delocalized and localized regime, respectively. The corresponding scaling factors are indicated by the arrows.

via Localization-delocalization transition in the dynamics of dipolar-coupled nuclear spins.

PLoS ONE: Size Distribution Imaging by Non-Uniform Oscillating-Gradient Spin Echo (NOGSE) MRI

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Noam Shemesh, Gonzalo A. Álvarez, Lucio Frydman

Published: July 21, 2015

DOI: 10.1371/journal.pone.0133201

Abstract

Objects making up complex porous systems in Nature usually span a range of sizes. These size distributions play fundamental roles in defining the physicochemical, biophysical and physiological properties of a wide variety of systems – ranging from advanced catalytic materials to Central Nervous System diseases. Accurate and noninvasive measurements of size distributions in opaque, three-dimensional objects, have thus remained long-standing and important challenges. Herein we describe how a recently introduced diffusion-based magnetic resonance methodology, Non-Uniform-Oscillating-Gradient-Spin-Ec​ho(NOGSE), can determine such distributions noninvasively. The method relies on its ability to probe confining lengths with a (length)^6 parametric sensitivity, in a constant-time, constant-number-of-gradients fashion; combined, these attributes provide sufficient sensitivity for characterizing the underlying distributions in μm-scaled cellular systems. Theoretical derivations and simulations are presented to verify NOGSE’s ability to faithfully reconstruct size distributions through suitable modeling of their distribution parameters. Experiments in yeast cell suspensions – where the ground truth can be determined from ancillary microscopy – corroborate these trends experimentally. Finally, by appending to the NOGSE protocol an imaging acquisition, novel MRI maps of cellular size distributions were collected from a mouse brain. The ensuing micro-architectural contrasts successfully delineated distinctive hallmark anatomical sub-structures, in both white matter and gray matter tissues, in a non-invasive manner. Such findings highlight NOGSE’s potential for characterizing aberrations in cellular size distributions upon disease, or during normal processes such as development.

Citation: Shemesh N, Álvarez GA, Frydman L (2015) Size Distribution Imaging by Non-Uniform Oscillating-Gradient Spin Echo (NOGSE) MRI. PLoS ONE 10(7): e0133201. doi:10.1371/journal.pone.0133201

Editor: Ichio Aoki, National Institute of Radiological Sciences, JAPAN

Received: November 25, 2014; Accepted: June 24, 2015; Published: July 21, 2015

Copyright: © 2015 Shemesh et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

 

via PLOS ONE: Size Distribution Imaging by Non-Uniform Oscillating-Gradient Spin Echo (NOGSE) MRI.

 

Magnetic resonance virtual histology
Magnetic resonance virtual histology based on probing molecular diffusion in tissues. Non-uniform oscillating gradient spin-echo (NOGSE) sequences are applied to generate the magnetic resonance imaging (MRI) contrast. The compartment size distributions in a mouse corpus callosum are extracted highlighting the different anatomical regions.

Quantum state transfer in disordered spin chains: How much engineering is reasonable? | Quant. Inf. Comm. (2015)

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Analia Zwick, Gonzalo A. Álvarez, Joachim Stolze, and Omar Osenda

Quant. Inf. Comput. 15, 582-600 (2015).

The transmission of quantum states through spin chains is an important element in the im- plementation of quantum information technologies. Speed and fidelity of transfer are the main objectives which have to be achieved by the devices even in the presence of imperfections which are unavoidable in any manufacturing process. To reach these goals, several kinds of spin chains have been suggested, which differ in the degree of fine-tuning, or engineering, of the system parameters. In this work we present a systematic study of two important classes of such chains. In one class only the spin couplings at the ends of the chain have to be adjusted to a value different from the bulk coupling constant, while in the other class every coupling has to have a specific value. We demonstrate that configurations from the two different classes may perform similarly when subjected to the same kind of disorder in spite of the large difference in the engineering effort necessary to prepare the system. We identify the system features responsible for these similarities and we perform a detailed study of the transfer fidelity as a function of chain length and disorder strength, yielding empirical scaling laws for the fidelity which are similar for all kinds of chain and all dis- order models. These results are helpful in identifying the optimal spin chain for a given quantum information transfer task. In particular, they help in judging whether it is worthwhile to engineer all couplings in the chain as compared to adjusting only the boundary couplings.

via [1306.1695] Quantum state transfer in disordered spin chains: How much engineering is reasonable?.

Comparison of the averaged state transfer fidelity for different quantum state transfer channels. The left hand side panels are boundary controlled spin-chain channels and the right hand side panels are fully engineered perfect state transfer channels. Two kinds of disorder are considered in the plot: Absolute disorder with a perturbation strength proportional to the maximum coupling strength of the spin-chain or relative disorder when the perturbation strength in each spin-spin coupling is relative to its optimal value. For the boundary controlled spin channels, both types of disorder are equivalent since the bulk of the chains contains homogeneous couplings, while for the fully engineered spin-channels they provide different effects on the transfer fidelity. The average is calculated over 1000 disorder realizations. The black contour lines belong to fidelities F = 0.99, 0.95, 0.9, 0.8, 0.7, respectively. The colored symbols show the crossovers between the different systems.
Comparison of the averaged state transfer fidelity for different quantum state transfer channels. The left hand side panels are boundary controlled spin-chain channels and the right hand side panels are fully engineered perfect state transfer channels. Two kinds of disorder are considered in the plot: Absolute disorder with a perturbation strength proportional to the maximum coupling strength of the spin-chain or relative disorder when the perturbation strength in each spin-spin coupling is relative to its optimal value. For the boundary controlled spin channels, both types of disorder are equivalent since the bulk of the chains contains homogeneous couplings, while for the fully engineered spin-channels they provide different effects on the transfer fidelity. The average is calculated over 1000 disorder realizations. The black contour lines belong to fidelities F = 0.99, 0.95, 0.9, 0.8, 0.7, respectively. The colored symbols show the crossovers between the different systems.

Optimized dynamical control of state transfer through noisy spin chains | New Journal of Physics

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Optimized dynamical control of state transfer through noisy spin chains

Analia Zwick, Gonzalo A Álvarez, Guy Bensky and Gershon Kurizki
Focus on Coherent Control of Complex Quantum Systems:
New J. Phys. 16, 065021 (2014).

We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel spin-chain. This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channelʼs spin–spin couplings. It may also facilitate transfer in the presence of diagonal disorder on site energy noise in the channel.

via Optimized dynamical control of state transfer through noisy spin chains – Abstract – New Journal of Physics – IOPscience.

Top inset: Spin-channel for state transfer with boundary-controlled couplings. Boundary-controlled spin chain mapped to a non-interacting spinless fermions system. The two boundary spins 0 and N+1 are resonantly coupled to the chain by the fermionic-mode z with a coupling strength J_z*α(t). (a) Spectrum of the effective fermionic system (rectangular bars) which interacts with the bath-modes k (red-even k and blue-odd k vertical lines) with strengths J ̃_k* α(t). Dashed contour: noise spectrum described by the Wigner-semicircle (maximal-disorder) lineshape with a central gap around ω_z. In the central gap, the optimal spectral-filters F_T(ω) generated by dynamical boundary-control with α_p(t) (p = 0 (black dotted), p = 2 (orange thin)) are shown. Bottom inset: a zoom of the tails of the filter spectrum that protect the state transfer against a general noisy bath with a central gap. (b) Infidelity as a function of transfer time T under optimal control (filter) with p = 0 (black dotted) and p = 2 (orange thin).
Top inset: Spin-channel for state transfer with boundary-controlled couplings. Boundary-controlled spin chain mapped to a non-interacting spinless fermions system. The two boundary spins 0 and N+1 are resonantly coupled to the chain by the fermionic-mode z with a coupling strength J_z*α(t). (a) Spectrum of the effective fermionic system (rectangular bars) which interacts with the bath-modes k (red-even k and blue-odd k vertical lines) with strengths J ̃_k* α(t). Dashed contour: noise spectrum described by the Wigner-semicircle (maximal-disorder) lineshape with a central gap around ω_z. In the central gap, the optimal spectral-filters F_T(ω) generated by dynamical boundary-control with α_p(t) (p = 0 (black dotted), p = 2 (orange thin)) are shown. Bottom inset: a zoom of the tails of the filter spectrum that protect the state transfer against a general noisy bath with a central gap. (b) Infidelity as a function of transfer time T under optimal control (filter) with p = 0 (black dotted) and p = 2 (orange thin).

Acting Locally, Reporting Globally: From quantum physics to biology, a new approach to magnetic resonance turns protons into “spies”.

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Acting Locally, Reporting Globally: From quantum physics to biology, a new approach to magnetic resonance turns protons into “spies”. 

Mapping of size distributions of a mouse’s gray matter by quantum-controlled proton MRI. (l) Brain proton MRI; (c) mean cellular size; (r) distribution peak
Mapping of size distributions of a mouse’s gray matter by quantum-controlled proton MRI. (l) Brain proton MRI; (c) mean cellular size; (r) distribution peak

Please see the article published in the Interface Magazine of the Weizmann Institute about our work on “Coherent Dynamical Recoupling of Diffusion-Driven Decoherence in Magnetic Resonance“: 

 

elink: Interface Magazine, Winter 2014: Acting Locally, Reporting Globally.

 

 

 

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

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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

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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.