T2* measurements in human brain at 1.5, 3 and 7 T

Measurements have been carried out in six subjects at magnetic fields of 1.5, 3 and 7 T, with the aim of characterizing the variation of T2* with field strength in human brain. Accurate measurement of T2* in the presence of macroscopic magnetic field inhomogeneity is problematic due to signal decay resulting from through-slice dephasing. The approach employed here allowed the signal decay due to through-slice dephasing to be characterized and removed from data, thus facilitating an accurate measurement of T2* even at ultrahigh field. Using double inversion recovery turbo spin-echo images for tissue classification, an analysis of T2* relaxation times in cortical grey matter and white matter was carried out, along with an evaluation of the variation of T2* with field strength in the caudate nucleus and putamen. The results show an approximately linear increase in relaxation rate R2* with field strength for all tissues, leading to a greater range of relaxation times across tissue types at 7 T that can be exploited in high-resolution T2*-weighted imaging.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

Nuclear magnetic resonance for cultural heritage

Nuclear magnetic resonance (NMR) portable devices are now being used for nondestructive in situ analysis of water content, pore space structure and protective treatment performance in porous media in the field of cultural heritage. It is a standard procedure to invert T(1) and T(2) relaxation data of fully water-saturated samples to get "pore size" distributions, but the use of T(2) requires great caution. It is well known that dephasing effects due to water molecule diffusion in a magnetic field gradient can affect transverse relaxation data, even if the smallest experimentally available half echo time tau is used in Carr-Purcell-Meiboom-Gill experiments. When a portable single-sided NMR apparatus is used, large field gradients due to the instrument, at the scale of the sample, are thought to be the dominant dephasing cause. In this paper, T(1) and T(2) (at different tau values) distributions were measured in natural (Lecce stone) and artificial (brick samples coming from the Greek-Roman Theatre of Taormina) porous media of interest for cultural heritage by a standard laboratory instrument and a portable device. While T(1) distributions do not show any appreciable effect from inhomogeneous fields, T(2) distributions can show strong effects, and a procedure is presented based on the dependence of 1/T(2) on tau to separate pore-scale gradient effects from sample-scale gradient effects. Unexpectedly, the gradient at the pore scale can be, in some cases, strong enough to make negligible the effects of gradients at the sample scale of the single-sided device.     

Multi-dimensional inverse Laplace spectroscopy in the NMR of porous media

Multi-dimensional NMR methods based on Inverse Laplace Transformations (ILT) may be used to examine the behavior of liquid state molecules in a porous matrix. The ILT is particularly useful when the signal is characterized by multi-exponential decay, for example in spin relaxation or in the dephasing of the NMR spin echo signal associated with molecular diffusion under the influence of pulsed magnetic or internal field gradients. Both correlation and exchange experiments are possible, the latter providing insight regarding the migration of molecules between regions characterized by different local dynamics.     

Transverse NMR relaxation as a probe of mesoscopic structure

Transverse NMR relaxation in a macroscopic sample is shown to be extremely sensitive to the structure of mesoscopic magnetic susceptibility variations. Such a sensitivity is proposed as a novel kind of contrast in the NMR measurements. For suspensions of arbitrary-shaped paramagnetic objects, the transverse relaxation is found in the case of a small dephasing effect of an individual object. Strong relaxation rate dependence on the objects' shape agrees with experiments on whole blood. Demonstrated structure sensitivity is a generic effect that arises in NMR relaxation in porous media, biological systems, as well as in kinetics of diffusion limited reactions.     

Anomalous dephasing of bosonic excitons interacting with phonons in the vicinity of the Bose-Einstein condensation

The dephasing and relaxation kinetics of bosonic excitons interacting with a thermal bath of acoustic phonons is studied after coherent pulse excitation. The kinetics of the induced excitonic polarization is calculated within Markovian equations both for subcritical and supercritical excitation with respect to a Bose-Einstein condensation (BEC). For excited densities n below the critical density , an exponential polarization decay is obtained, which is characterized by a dephasing rate . This dephasing rate due to phonon scattering shows a pronounced exciton-density dependence in the vicinity of the phase transition. It is well described by the power law that can be understood by linearization of the equations around the equilibrium solution. Above the critical density we get a non-exponential relaxation to the final condensate value p⁰ with that holds for all densities. Furthermore we include the full self-consistent Hartree-Fock-Bogoliubov (HFB) terms due to the exciton-exciton interaction and the kinetics of the anomalous functions . The collision terms are analyzed and an approximation is used which is consistent with the existence of BEC. The inclusion of the coherent exciton-exciton interaction does not change the dephasing laws. The anomalous function F_k exhibits a clear threshold behaviour at the critical density. Received 13 December 1999     

Paramagnetic relaxation in sandstones: distinguishing T1 and T2 dependence on surface relaxation, internal gradients and dependence on echo spacing

This work provides a generalized theory of proton relaxation in inhomogeneous magnetic fields. Three asymptotic regimes of relaxation are identified depending on the shortest characteristic time scale. Numerical simulations illustrate that the relaxation characteristics in the regimes such as the T(1)/T(2) ratio and echo spacing dependence are determined by the time scales. The theoretical interpretation is validated for fluid relaxation in porous media in which field inhomogeneity is induced due to susceptibility contrast of fluids and paramagnetic sites on pore surfaces. From a set of measurements on model porous media, we conclude that when the sites are small enough, no dependence on echo spacing is observed with conventional low-field NMR spectrometers. Echo spacing dependence is observed when the paramagnetic materials become large enough or form a 'shell' around each grain such that the length scale of the region of induced magnetic gradients is large compared to the diffusion length during the time of the echo spacing. The theory can aid in interpretation of diffusion measurements in porous media as well as imaging experiments in presence of contrast agents used in MRI.     

Symmetry and spin dephasing in (110)-grown quantum wells

Symmetry and spin dephasing in (110)-grown GaAs quantum wells (QWs) are investigated applying magnetic field induced photogalvanic effect and time-resolved Kerr rotation. We show that magnetic field induced photogalvanic effect provides a tool to probe the symmetry of (110)-grown quantum wells. The photocurrent is only observed for asymmetric structures but vanishes for symmetric QWs. Applying Kerr rotation we prove that in the latter case the spin relaxation time is maximal; therefore, these structures set the upper limit of spin dephasing in GaAs QWs. We also demonstrate that structure inversion asymmetry can be controllably tuned to zero by variation of delta-doping layer positions.     

Empirical models of transverse relaxation for spherical magnetic perturbers

Ferromagnetic or superparamagnetic particles as MRI contrast agent present many advantages for bringing about soft tissue contrast as compared to single-ion complexes. The classic microscopic outersphere theory that works successfully for small molecules in understanding the transverse relaxation rate 1/T(2) is not valid for these larger and stronger magnetic spheres. We categorize the relaxation behavior of the tissue-sphere system for ferromagnetic spherical perturbers in five diffusion regimes. Over the entire range of perturber size a general understanding of the relaxation mechanisms is described in terms of basic physical features of the system, and, through empiric models, the imaging sequences of spin echo and gradient echo. The models are verified with results of our spectroscopic measurements as well as simulations and experiments in the literature. Normalized models, obtained through proper scaling of the sphere radius and the relaxation rate, can be used to quantitatively estimate 1/T(2) for various combinations of the variables. Effects of diffusion upon image contrast and effects of sphere size change upon relaxation with their possible applications in microvascular dilatation and other areas are then discussed.     

Two methods to deal with an inhomogenous Rabi frequency in microwave transition

We analyse the influence of an inhomogenous microwave field on the coherence of atom ensembles. Two methods are proposed to suppress the dephasing generated by the inhomogenous Rabi frequency. One of them is realized by using a spin echo, and the other one is based on the identical spin rotation effect. The calculation results show that the contrast of a signal acquired in experiment can be improved by using the two methods. Their advantages and drawbacks are discussed. We hope they can be used to improve the contrast of experimental signals in situations where microwave fields are very inhomogenous. Finally, we discuss the case of a continuous working microwave field and show that the dipole force raised with the inhomogeneity can be eased by spin flip.     

Coherence times and Rabi oscillations in CaWO₄:Cr(5+) crystal

The coherence times of dopant pentavalent chromium ions in CaWO? single crystal (0.0006at.% Cr(5+)) were investigated both theoretically and experimentally. Temperature dependences of spin-lattice relaxation time T? and phase memory time T(M) were measured in the temperature range 6-30 K at high (94 GHz, W band) and low (3.5 GHz, S band) frequencies of electron spin resonance. It follows from T(M) calculations that phase relaxation of Cr(5+) ion arises mainly from magnetic dipole interactions between the chromium ions. Anomalously fast damping of Rabi oscillations is detected in both S- and W-band experiments. It is shown that this phenomenon is caused by microwave field inhomogeneity inside the resonator. Relations between the damping time of Rabi oscillations, Rabi frequency and the crystal sample size are obtained. Lumped-element resonators and smaller sample dimensions are suggested to lower spin dephasing during transient nutations.     

Dephasing effect on transport of a graphene p-n junction in a quantum Hall regime

The influence of the dephasing effect on the conductance distribution of disordered graphene p-n junctions is studied. Without the dephasing, the conductance distribution has a very wide range and the conductance fluctuation is large. In this case, the conductance plateaus cannot be obtained in a single sample with the fixed disorder configuration. However, by introducing the dephasing, we find that the distribution becomes narrow dramatically and the fluctuation is suppressed strongly, so that the conductance plateaus are obtained clearly for one single sample, which is consistent with experimental measurements. Furthermore, we also investigate the scaling feature of the conductance distribution and find that it has good scaling behavior in the strong dephasing case.     

Relationship between susceptibility induced field inhomogeneities, restricted diffusion, and relaxation in sedimentary rocks

Low field relaxation and diffusion measurements have become essential tools to study the pore space of sedimentary rocks with important practical applications in the field of well logging and hydrocarbon extractions. Even at Larmor frequencies below 2 MHz, diffusion measurements are often affected noticeably by internal field inhomogeneities. These field inhomogeneities are induced by susceptibility contrast between the rock and the fluid and are evident in most sandstones. Using sets of two-dimensional diffusion-relaxation measurements in applied and internal gradients, we study in detail the correlation between the field inhomogeneities, restricted diffusion, and relaxation time in three rocks of different susceptibility. We find that in the sandstone cores, the field inhomogeneities in large pores can be described by a local gradient that scales inversely with relaxation time above 250 ms. At shorter relaxation times, the extracted internal gradients deviate from this scaling relationship and we observe a dependence on diffusion time. This demonstrates that in this case, the internal field has structure on a length scale of a few microns.     

Spin-flip limited exciton dephasing in CdSe/ZnS colloidal quantum dots

The dephasing time of the lowest bright exciton in CdSe/ZnS wurtzite quantum dots is measured from 5 to 170 K and compared with density dynamics within the exciton fine structure using a sensitive three-beam four-wave-mixing technique unaffected by spectral diffusion. Pure dephasing via acoustic phonons dominates the initial dynamics, followed by an exponential zero-phonon line dephasing of 109 ps at 5 K, much faster than the ~10 ns exciton radiative lifetime. The zero-phonon line dephasing is explained by phonon-assisted spin flip from the lowest bright state to dark-exciton states. This is confirmed by the temperature dependence of the exciton lifetime and by direct measurements of the bright-dark-exciton relaxation. Our results give an unambiguous evidence of the physical origin of the exciton dephasing in these nanocrystals.     

Polymer translocation in the presence of excluded volume and explicit hydrodynamic interactions

Molecular Dynamics simulations of polymer translocation are hereby reported. No external force was applied to the polymer during translocation, and the dynamics was dominated by polymer–pore interactions. It was found that hydrodynamic interactions play an important role in the relaxation of the polymer on each side of the membrane but have a negligible impact on the translocation process itself. Also, the scaling laws obtained for the relaxation and translocation times indicate that long translocating polymers may be considered to be following a quasi-equilibrium anomalous diffusion process in the absence of external forces.     

Two methods to deal with inhomogenous Rabi frequency in microwave transition

We analysed the influence of inhomogenous microwave field on the coherence of atom ensembles. Two methods were proposed to suppress the dephasing generated by the inhomogenous Rabi frequency. One of them was realized by spin echo, and the other one was based on the identical spin rotation effect. The results of calculation showed that the contrast of signal acquired in experiment can be improved by the two methods. Their advantages and drawbacks were discussed. We hope they could be used to improve the contrast of experimental signal in the situation that the microwave fields are very inhomogenous. Finally, we discussed the case of continuous working microwave field and showed that the dipole force raised with the inhomogeneity can be eased by spin flip.     

Oscillating two-stream instability of a lower hybrid wave in aninhomogenous plasma

The effect of the density inhomogeneity on the oscillating two-stream instability of a lower hybrid pump wave with a finite wavelength is investigated. The density inhomogeneity introduces dephasing that restricts the interaction region where the matching conditions hold. The loss of energy due to convection from this region introduces a certain convection threshold for the onset of this instability. The coupled differential equations are solved in Fourier space by converting them into an uncoupled eigenvalue equation and then applying a quantization condition. Expressions are obtained for the growth rate and the convective threshold, and the results are applied to the Princeton Large Torus parameters     

The shape of the relaxation curve in diffusion measurements with the aid of photoinduced gratings

It is shown by experimental examples how the postexposure relaxation of a photochemically induced grating used to study the diffusion of a molecular probe by the holographic relaxation method depends on the molecular mechanism of the grating formation, medium inhomogeneity, and relative shift of grating parts, as well as the grating strength. The adequate consideration of the factors influencing the observed behavior of the grating provides for the possibility not only to correctly retrieve information about the diffusion, but also to extend the range of studied phenomena.     

Reduced apparent longitudinal relaxation times in slice-selective experiments in strong magnetic field gradients

In contrast to transverse nuclear magnetizations, longitudinal spin magnetizations are usually considered as insensitive to magnetic field gradients. While this assumption is valid for homogeneously excited samples, the apparent longitudinal spin relaxation behavior of thin magnetization slices in high magnetic fields is strongly modified by diffusion. In this contribution, we present the results of theoretical and experimental studies on this effect. Furthermore, possible applications and the impact on different types of NMR techniques using strong magnetic field gradients are discussed.     

Selective detection of echoEPR signals due to naturally substituted13C radicals in a single crystal of ammonium tartrate

Echo-detected electron paramagnetic resonance (echoEPR) profiles for irradiated deuterated ammonium tartrate single crystals depend strongly on the delays between pulses of the echo sequence. This is mainly due to instantaneous and spectral diffusion that plays a crucial role in determining the decay of the echo at every field position: the dephasing rate 1/7_M depends on the number of spins excited by the pulses and on the total number of interacting spins. A rigorous simulation of the echoEPR profiles at different delays requires the evaluation of the modulation pattern (ESEEM) and of the dephasing processes at every field position. From the simulations, information on the microscopic radical concentration, and on the electron-electron flip-flop rates of the single radical species can be obtained. Natural isotope¹³C substitution generates low-concentration radicals with relaxation properties different from the equivalent¹²C-substitued radicals. The different behavior is discussed.