decoherence

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.
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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).

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.

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

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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.

Robustness of Spin-Chain State-Transfer Schemes – Springer

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Robustness of Spin-Chain State-Transfer Schemes

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

in Quantum State Transfer and Network Engineering, edited by G. M. Nikolopoulos and I. Jex (Springer Berlin Heidelberg, 2014), pp. 149–182.

Abstract

Spin chains are linear arrangements of qubits (spin-1/2 objects) with interactions between nearest or more distant neighbors. They have been considered for quantum information transfer between subunits of a quantum information processing device at short or intermediate distances. The most frequently studied task is the transfer of a single-qubit state. Several protocols have been developed to achieve this goal, broadly divisible into two classes, fully-engineered and boundary-controlled spin chains. We discuss state transfer induced by the natural dynamics of these two classes of systems, and the influence of deviations from the ideal system configuration, that is, manufacturing errors in the nearest-neighbor spin couplings. The fidelity of state transfer depends on the chain length and the disorder strength. We observe a power-law scaling of the fidelity deficit, i.e. the deviation from perfect transfer. Boundary-controlled chains can provide excellent fidelity under suitable circumstances and are potentially less difficult to manufacture and control than fully-engineered chains. We also review other existing theoretical work on the robustness of quantum state transfer as well as proposals for experimental implementation.

via Robustness of Spin-Chain State-Transfer Schemes – Springer.