Publications

Internal gradient distributions: A susceptibility-derived tensor delivering morphologies by magnetic resonance | Scientific Reports

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Gonzalo A. Álvarez, Noam Shemesh & Lucio Frydman

Scientific Reports 7, 3311 (2017)

doi:10.1038/s41598-017-03277-9

Nuclear magnetic resonance is a powerful tool for probing the structures of chemical and biological systems. Combined with field gradients it leads to NMR imaging (MRI), a widespread tool in non-invasive examinations. Sensitivity usually limits MRI’s spatial resolution to tens of micrometers, but other sources of information like those delivered by constrained diffusion processes, enable one extract morphological information down to micron and sub-micron scales. We report here on a new method that also exploits diffusion – isotropic or anisotropic– to sense morphological parameters in the nm-mm range, based on distributions of susceptibility-induced magnetic field gradients. A theoretical framework is developed to define this source of information, leading to the proposition of internal gradient-distribution tensors. Gradient-based spin-echo sequences are designed to measure these new observables. These methods can be used to map orientations even when dealing with unconstrained diffusion, as is here demonstrated with studies of structured systems, including tissues.

Source: Internal gradient distributions: A susceptibility-derived tensor delivering morphologies by magnetic resonance | Scientific Reports

 

Mapping Internal Gradient Distribution Tensors (IGDT) in biological tissues
Mapping IGDT in biological tissues. (a) IGDT eigenvalues observed for a spinal cord specimen, examined in a 10 mm NMR tube filled with Fluorinert® (cartoon in center exemplifies this model phantom). (b) Color-coded orientation maps generated from the directions of the first eigenvector (the one with lowest eigenvalue) with respect to the main magnetic field [red: z-axis (up-down), blue: x-axis (in-out), green: y-axis (left-right)]. The vector magnitude was weighted with a fractional anisotropy to highlight its orientation. Parameters for the NOGSE MRI measurements were: TR/TE = 4000/50 ms, resolution = 156 × 156 × 1000 μm3, six pairs of opposing-gradient NOGSE encodings according to the orientations given in Fig. 3, NA = 4, G = 35 G/cm, total number of NOGSE oscillations of ten, total NOGSE gradient modulation time =20 ms. A T 2~50–60 ms was measured in these white matter experiments, and the shortest delay x was 140 μs. (c) Microscopic DTI tensor determined from the sNOGSE amplitude modulation Δβ S is shown for comparison to demonstrate the consistency of the orientations. EPI sequences were used for collecting all images, the typical SNR was >35 at its lowest. A full set of measurements took 13 minutes to complete.

Rev. Mod. Phys.:Protecting quantum information against environmental noise

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Colloquium: Protecting quantum information against environmental noise

Dieter Suter and Gonzalo A. Álvarez
Rev. Mod. Phys. 88, 041001 (2016)
Published 10 October 2016

RevModPhys.88.041001Quantum-mechanical systems retain their properties so long as the phase of quantum superpositions evolve stably over time. Contact with an environment can disrupt this phase evolution. But for environments that do not exchange energy with the quantum system, strategies exist where the controlled driving of the system can recover or maintain the quantum phase. This Colloquium surveys the host of techniques that are available to “refocus” the phase when disturbed by various forms of classical or quantum environment. While the first such techniques were developed long ago, ideas from quantum information theory have introduced new strategies for accomplishing this goal.

Source: Reviews of Modern Physics – Volume 88 Issue 4

Phys. Rev. Applied: Maximizing Information on the Environment by Dynamically Controlled Qubit Probes

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Maximizing Information on the Environment by Dynamically Controlled Qubit Probes

Analia Zwick, Gonzalo A. Álvarez, and Gershon Kurizki
Phys. Rev. Applied 5, 014007 (2016)
Published 25 January 2016

PhysRevApplied.5.014007-2From computers to medicine, miniaturization approaches the atomic scale, where device operation can be dominated by quantum effects that are strongly coupled to the local environment. These influences may be seen not as a nuisance, but rather a nearly untapped source of information about physical or biochemical processes playing out nearby. How can one extract maximum information from such fluctuations with an atomic probe, under typical experimental constraints? The authors use quantum estimation theory to outline a general strategy for dynamical measurement of a broad class of environmental processes.

Source: Physical Review Applied – Volume 5 Issue 1

 

Simulation of an experimental real-time adaptive-estimation protocol for realistic conditions with a NVC spin probe. (a),(b) Convergence of the real-time adaptive-estimation protocol to the theoretically predicted values for estimating τc. Free evolution of the probe (blue circles) is contrasted with that of a dynamically controlled probe under a CPMG (green square) sequence with N=8 pulses in the presence of an Ornstein-Uhlenbeck process with Lorentzian spectrum with τc=10μs, a coupling with the environment g=1 MHz consistently with the spectral density of a HPHT diamond sample. The simulated curves derived from exact analytical results are averaged over 600 realizations. In (a), the optimal measurement time tm as a function of the number of measurements Nm converges to the optimal value to perform the measurements t^{opt} for the CPMG case. Similar curves converging to the corresponding t^{opt} are observed for other controls and free evolution. In (b), the minimal relative error ϵ(τc,t^{opt}) converges to the (Cramer-Rao) bound. Under free evolution, the regime where ϵ∝(1/√Nm) is attained for Nm≫100. The ultimate bound (ϵ0/√Nm dashed line, α=β−1) is attained only by optimal control. (c) Convergence to the minimal relative error ϵ(g,t^{opt}) to the (Cramer-Rao) bound for estimating g by N=500 consecutive projective measurements in the Zeno regime (green triangle) compared to the estimation under free evolution (blue circle). In this case, G_{β=2}(g=0.03 MHz,ω), with τc=10 μs, consistently with the spectral density of a 12C diamond sample. Here too the ultimate bound (ϵ0/2√Nm dashed line, α=2) is attained only by optimal control. (d) Proposed scheme for using a NVC as a qubit probe for its environment. The ms=0 (|0⟩) state is fully populated by laser irradiation (dashed curly arrow). Microwave (MW) pulses are selectively applied between the states with ms=0 and −1 (|0⟩ and |−1⟩) of the electronic ground states to initialize the spin probe in a |+⟩=(1/√2)(|0⟩+|−1⟩) state and effect the π pulse CPMG sequence for estimating τc. For estimating g, projective measurements are emulated by combining MW π/2 pulses on the 0↔−1 transition and laser-induced relaxation between the ground and exited electronic states that conserve the spin components (solid curly arrows). The readout is done at the end of the N-pulse sequence by detecting the laser-induced fluorescence signal.
Simulation of an experimental real-time adaptive-estimation protocol for realistic conditions with a NVC spin probe. (a),(b) Convergence of the real-time adaptive-estimation protocol to the theoretically predicted values for estimating τc. Free evolution of the probe (blue circles) is contrasted with that of a dynamically controlled probe under a CPMG (green square) sequence with N=8 pulses in the presence of an Ornstein-Uhlenbeck process with Lorentzian spectrum with τc=10μs, a coupling with the environment g=1 MHz consistently with the spectral density of a HPHT diamond sample. The simulated curves derived from exact analytical results are averaged over 600 realizations. In (a), the optimal measurement time tm as a function of the number of measurements Nm converges to the optimal value to perform the measurements t^{opt} for the CPMG case. Similar curves converging to the corresponding t^{opt} are observed for other controls and free evolution. In (b), the minimal relative error ϵ(τc,t^{opt}) converges to the (Cramer-Rao) bound. Under free evolution, the regime where ϵ∝(1/√Nm) is attained for Nm≫100. The ultimate bound (ϵ0/√Nm dashed line, α=β−1) is attained only by optimal control. (c) Convergence to the minimal relative error ϵ(g,t^{opt}) to the (Cramer-Rao) bound for estimating g by N=500 consecutive projective measurements in the Zeno regime (green triangle) compared to the estimation under free evolution (blue circle). In this case, G_{β=2}(g=0.03 MHz,ω), with τc=10 μs, consistently with the spectral density of a 12C diamond sample. Here too the ultimate bound (ϵ0/2√Nm dashed line, α=2) is attained only by optimal control. (d) Proposed scheme for using a NVC as a qubit probe for its environment. The ms=0 (|0⟩) state is fully populated by laser irradiation (dashed curly arrow). Microwave (MW) pulses are selectively applied between the states with ms=0 and −1 (|0⟩ and |−1⟩) of the electronic ground states to initialize the spin probe in a |+⟩=(1/√2)(|0⟩+|−1⟩) state and effect the π pulse CPMG sequence for estimating τc. For estimating g, projective measurements are emulated by combining MW π/2 pulses on the 0↔−1 transition and laser-induced relaxation between the ground and exited electronic states that conserve the spin components (solid curly arrows). The readout is done at the end of the N-pulse sequence by detecting the laser-induced fluorescence signal.

Nat. Commun.: Local and bulk 13C hyperpolarization in nitrogen-vacancy-centred diamonds at variable fields and orientations

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Gonzalo A. Álvarez, Christian O. Bretschneider, Ran Fischer, Paz London, Hisao Kanda, Shinobu Onoda, Junichi Isoya, David Gershoni & Lucio Frydman

Nature Communications 6, 8456 (2015). doi:10.1038/ncomms9456

 

 
Combined Optical and Nuclear Magnetic Resonance (NMR) setup for hyperpolarizing nuclear spins in diamonds at room- temperature. During the polarization transfer phase, the entire single-crystal diamond (red in the picture) is irradiated with green laser light and microwaves underneath the NMR magnet at a low magnetic field. The hyperpolarized diamond is then shuttled into a high field superconducting magnet, for a directly detected NMR experiment on the 13C spins.Polarizing nuclear spins is of fundamental importance in biology, chemistry and physics. Methods for hyperpolarizing 13C nuclei from free electrons in bulk usually demand operation at cryogenic temperatures. Room temperature approaches targeting diamonds with nitrogen-vacancy centres could alleviate this need; however, hitherto proposed strategies lack generality as they demand stringent conditions on the strength and/or alignment of the magnetic field. We report here an approach for achieving efficient electron-13C spin-alignment transfers, compatible with a broad range of magnetic field strengths and field orientations with respect to the diamond crystal. This versatility results from combining coherent microwave- and incoherent laser-induced transitions between selected energy states of the coupled electron–nuclear spin manifold. 13C-detected nuclear magnetic resonance experiments demonstrate that this hyperpolarization can be transferred via first-shell or via distant 13Cs throughout the nuclear bulk ensemble. This method opens new perspectives for applications of diamond nitrogen-vacancy centres in nuclear magnetic resonance, and in quantum information processing.

 

Source: Local and bulk 13C hyperpolarization in nitrogen-vacancy-centred diamonds at variable fields and orientations : Nature Communications : Nature Publishing Group

 

Acquiring ensemble 13C polarization spectra for varying NV orientations with respect to B0. (a) Opto-NMR set-up and (b) detection sequence used in these experiments. During the polarization transfer phase, the entire single-crystal diamond is irradiated with laser light and MW underneath the NMR magnet at a low B0. The hyperpolarized diamond is then shuttled (in <1 s) into a 4.7-T superconducting magnet to directly detect its macroscopic 13C magnetization via a spin-echo sequence. The low B0 magnetic field is aligned to one of the nitrogen-vacancy-centre orientations (in red), while the other three orientations (in blue) subtend an angle of ≈109° with respect to the field. (c) Typical 13C polarization enhancement patterns observed by NMR as a function of the MW frequency ω with signals normalized with respect to the thermal 13C response at 4.7 T (inset). The left part of the plot corresponds the nuclear polarization generated by MW transitions for the aligned orientation (red circles), while the right part corresponds to nuclear polarization enhanced via the three non-aligned, equivalent orientations (blue circles). The ≈1:3 intensity ratio reflects the relative abundances of aligned and non-aligned sites in the diamond’s tetrahedral structure. In each of the patterns, the central peaks represent bulk nuclear hyperpolarization pumped via 13C spins coupled with hyperfine interactions lower than 20 MHz, while the outer peaks originate from first-shell 13Cs whose hyperfine splitting is ≈130 MHz (refs 26, 29). The antiphase structure of each of these peaks corresponds to the MW transitions and at one side of the central peaks, and to the state at the other side. The inset shows NMR spectra obtained for a thermally polarized sample, and at the maxima of the central peaks for the aligned and non-aligned orientations. p.p.m. refers to parts-per-million of the high-field NMR 13C resonance frequency, which in our case is 50.5 MHz.
Acquiring ensemble 13C polarization spectra for varying NV orientations with respect to B0. (a) Opto-NMR set-up and (b) detection sequence used in these experiments. During the polarization transfer phase, the entire single-crystal diamond is irradiated with laser light and MW underneath the NMR magnet at a low B0. The hyperpolarized diamond is then shuttled (in <1 s) into a 4.7-T superconducting magnet to directly detect its macroscopic 13C magnetization via a spin-echo sequence. The low B0 magnetic field is aligned to one of the nitrogen-vacancy-centre orientations (in red), while the other three orientations (in blue) subtend an angle of ≈109° with respect to the field. (c) Typical 13C polarization enhancement patterns observed by NMR as a function of the MW frequency ω with signals normalized with respect to the thermal 13C response at 4.7 T (inset). The left part of the plot corresponds the nuclear polarization generated by MW transitions for the aligned orientation (red circles), while the right part corresponds to nuclear polarization enhanced via the three non-aligned, equivalent orientations (blue circles). The ≈1:3 intensity ratio reflects the relative abundances of aligned and non-aligned sites in the diamond’s tetrahedral structure. In each of the patterns, the central peaks represent bulk nuclear hyperpolarization pumped via 13C spins coupled with hyperfine interactions lower than 20 MHz, while the outer peaks originate from first-shell 13Cs whose hyperfine splitting is ≈130 MHz. The inset shows NMR spectra obtained for a thermally polarized sample, and at the maxima of the central peaks for the aligned and non-aligned orientations. p.p.m. refers to parts-per-million of the high-field NMR 13C resonance frequency, which in our case is 50.5 MHz.

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.