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.

Quanten-Computer löst Quanten-Problem :: pro-physik.de

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Quanten-Computer löst Quanten-Problem

Einfluss von Störungen auf das Ausbreiten eines Quantensystems untersucht.

Source: :: Quanten-Computer löst Quanten-Problem :: pro-physik.de