Optical pumping nuclear magnetic resonance system rotating in a plane parallel to the quantization axis

A model of an optical pumping nuclear magnetic resonance system rotating in a plane parallel to the quantization axis is presented. Different coordinate frames for nuclear spin polarization vector are introduced, and theoretical calculation is conducted to analyze this model. We demonstrate that when the optical pumping nuclear magnetic resonance system rotates in a plane parallel to the quantization axis, it will maintain a steady state with respect to the quantization axis which is independent of rotational speed and direction.     

The transition to a rotating coordinate system in the magnetic resonance theory

A new approach is proposed for the transition to a rotating coordinate system under magic angle conditions. In contrast to the Redfield result, the obtained Hamiltonian contains additional secular terms differing from zero even for a magic angle. Their origin is associated with the presence of non-secular terms in the dipole-dipole spin interaction Hamiltonian corresponding to the laboratory reference frame. These additional terms should apparently be taken into account while interpreting experiments on the investigation of the behavior of the spin system under magic angle conditions.V. I. Lenin Education Institute, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 60–64, June, 1992.     

On the resonance effect in a rotating magnetic fluid

Data for the low-frequency magnetic susceptibility of a rotating magnetic fluid measured in a permanent bias field are presented. It is found that the susceptibility of the medium resonantly grows when the rotation frequency coincides with the measuring field frequency. Reasons for and mechanisms behind this phenomenon are discussed.     

Fluorine nuclear magnetic resonance: calibration and system optimization

Fluorine-19 magnetic resonance imaging (MRI) offers advantages for imaging organs and tissues. 19F is readily synthesized into a variety of compounds and offers the potential for in-vivo imaging as a complement to hydrogen MRI. The purpose of this work was to determine the minimum detection sensitivity for a fluorinated compound (CF3-CO2H) as a function of pulse sequence, interpulse times (TE, TI, and TR), gradient values and the number of data averages. CF3-CO2H was chosen because it has a single spectral line and exhibits a minimal frequency shift under the experimental conditions used for this experiment. A resistance MR scanner operating at a resonance frequency of 6.255 MHz was used for imaging both fluorine (.156 T) and hydrogen (.147 T). Critical factors determining the minimum detection sensitivity included system signal-to-noise ratio (S/N), acquisition time, relaxation times (T1, T2), and sample volume. Samples were measured over the range of 0.05 M to 20.0 M and showed a linear relationship between signal strength and concentration. The minimum detection sensitivity was 0.1 M. Use of higher static fields and optimized coils as well as improved system signal-to-noise ratios will improve detection sensitivity. We conclude that imaging of fluorine on low-field system is feasible, although it is necessary to optimize many parameters to maximize detection sensitivity.     

Experimental quantum simulation of Avian Compass in a nuclear magnetic resonance system

Avian magnetoreception is the capacity for avians to sense the direction of the Earth’s magnetic field. Discovered more than forty years ago, it has attracted intensive studies over the years. One promising model for describing this capacity in avians is the widely used reference-and-probe model where radical pairs within the eyes of bird combines to form singlet and triplet quantum states. The yield depends on the angle between the Earth’s magnetic field and the molecules’ axis, hence the relative value of yield of the singlet state or triplet state enables avians to sense the direction. Here we report the experimental demonstration of avian magnetoreception in a nuclear magnetic resonance quantum information processor. It is shown clearly from the experiment that the yield of the singlet state attains maximum when it is normal to the Earth’s magnetic field, and the experimental results agree with theory very well.     

Magnetic fields associated with a nuclear magnetic resonance medical imaging system

Measurements were made of magnetic and electric field levels in and around a nuclear magnetic resonance imaging system undergoing a clinical trial. Magnetic field levels ranged from 0.04 tesla (T) in the imaging volume down to about 0.0006 T at the end of the patient table. The peak radio-frequency magnetic field level was 15 amperes per meter (A/m) in the imaging volume, while the rms value was 4.6 A/m. The specific absorption rate resulting from the radio-frequency magnetic field was calculated to be no more than 0.017 watts per kilogram (W/kg). The radio-frequency electric field was detectable only within a few centimeters of the coil assembly, and does not significantly contribute to the specific absorption rate. These exposure levels were much lower than existing guidelines for clinical NMR procedures.     

Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system

Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid-crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.     

Ferromagnetic resonance in a uniaxial magnetic film subjected to magnetic biasing along its hard axis

The precession dynamics of the magnetization of a film with an in-plane uniaxial anisotropy is analyzed in the spectrum of ferromagnetic resonance corresponding to magnetic biasing along the hard axis of the film. An additional resonance peak is revealed near magnetic anisotropy field H _u . This peak is related to the appearance of angular bistability due to the presence of two symmetric angular equilibrium positions in field H < H _u .     

White noise nonlinear system analysis in nuclear magnetic resonance spectroscopy

Nonlinear noise excitation in nuclear magnetic resonance is a form of nonlinear spectroscopy which exploits the nonlinear susceptibilities in a very direct way. The nonlinear susceptibilities are defined by perturbation theory in the frequency domain. In nonlinear system analysis, on the other hand, the system response is described by a Volterra series in the time domain. The kernels of the Volterra functionals carry the information about the system and are to be determined by experiment.The series expansion of a molecular, atomic or nuclear system response is derived in quantum mechanics by time dependent perturbation theory, leading to a Volterra series with time ordered, triangular kernels. The kernels are multi-dimensional products of decaying exponentials, which describe coherence decays of particular density matrix elements. The Fourier transforms of the triangular Volterra kernels are the susceptibilies, which are formally identical in NMR spectroscopy and nonlinear optical spectroscopy. The nonlinear susceptibilities are multi-dimensional spectra, which in NMR spectroscopy reveal the spin communication pathways. These are established by various forms of single quantum coherence connectivities, such as indirect coupling, chemical exchange, cross-relaxation, dipolar and quadrupolar coupling.If the functionals of the Volterra series are orthogonalized with respect to Gaussian white noise excitation, the Wiener series results. The Wiener kernels can be derived by multi-dimensional cross-correlation of the system response with different powers of the Gaussian white noise excitation.Cross-correlation of the transverse magnetization response to noise excitation in NMR leads to multi-dimensional time functions, the Fourier transforms of which closely resemble the nonlinear susceptibilities. The cross-correlation spectra differ from the susceptibilities in the governing Liouvillean and the dynamic density matrix, which are affected by saturation for continuous excitation. Cross-correlation spectra and susceptibilities converge for vanishing excitation power. Therefore the cross-correlation spectra are referred to as stochastic susceptibilities.In stochastic NMR spectroscopy only odd order susceptibilities exist for transverse magnetization. The first nonlinear order is the third, and the nonlinear spectral information is derived from the third order susceptibility. Higher order susceptibilities are not feasible to derive from experimental data. An important share of the nonlinear information is found on the six subdiagonal 2D cross-sections through the third order susceptibility. These cross-sections arise in three pairs, which carry distinct information, separated according to longitudinal magnetization and population effects, zero quantum coherences, and double quantum coherences.In practice a nonlinear 3D spectrum is computed from experimental data by an algorithm in the frequency domain, which yields access to selected regions in the 3D spectrum. This spectrum is the symmetrized stochastic third order susceptibility. All its sub-diagonal 2D cross-sections are equivalent. They are the average of the six different sub-diagonal 2D cross-sections through the asymmetric third order susceptibility.The stochastic excitation technique in NMR is characterized by several unique attributes. (1) There is no minimum time for a data acquisition cycle, so that, at the expense of signal-to-noise ratio, strong samples can be investigated faster with stochastic NMR than with pulsed FT NMR. (2) Stochastic excitation tests the sample extensively, and measures a maximum amount of information in a single experiment. This feature is of particular interest for investigation of short-lived samples and of samples with little a priori information. (3) An experiment with stochastic excitation is simple to perform, but the data processing is more complex than in FT spectroscopy. (4) The nonlinear information about spin communication pathways is derived for individual frequency regions only, which are identified in the stochastic ID spectrum. This information is located primarily on the sub-diagonal 2D cross-sections through the third order susceptibility. (5) Stochastic NMR spectra derived from random noise excitation are contaminated by systematic noise. In the sub-diagonal 2D cross-sections the noise is reduced by filtering and symmetrization during data processing. (6) Sub-diagonal 2D cross-sections are sensitive to experimental phase distortions in one direction only. They are readily adjusted in phase with the same parameters as the ID spectrum. (7) Stochastic multi-dimensional spectra can be computed at variable resolution from one and the same set of raw data.So far stochastic NMR spectroscopy is not applied routinely in analytical spectroscopy. More practical experience is needed to evaluate its merits in comparison with Fourier transform NMR.Stochastic excitation is distinguished from continuous wave and sparsely pulsed excitation by low input power in connection with large bandwidth. This important property cannot be exploited in high resolution NMR in liquids, because excitation power is not a restricting factor in this case. The situation is different in NMR imaging, where large field gradients require large bandwidths and the excitation power becomes a point of concern. For this reason stochastic RF excitation is being investigated in NMR imaging.The multi-dimensional cross-correlation functions obtained from random noise excitation generally are contaminated by systematic noise. The occurrence of systematic noise can be avoided if pseudo-random excitation is used in combination with a transformation of the system response to obtain the kernels. This technique is used successfully in Hadamard spectroscopy, where the linear Volterra kernel is the Hadamard transform of the linear response functional. Nonlinear transformations^(220,221) for retrieval of nonlinear kernels have not yet been realized in NMR spectroscopy.The cross-correlation technique underlying the data evaluation in stochastic nonlinear system analysis is equivalent to interferometry in optical spectroscopy. The Michelson interferometer is the most prominent optical correlator. The time resolution of the kernels derived by cross-correlation is determined by the inverse bandwidth of the excitation. With the Michelson interferometer a time resolution of 10⁻¹⁴ s is achieved in IR spectroscopy. Since the IR correlogramm is Fourier transformed for spectral analysis, the time resolution cannot be exploited otherwise. For analysis of fast time dependent processes a two-dimensional interferometer should be constructed, which performs a 2D cross-correlation of the system response to two in general different noise inputs. One input pumps the time dependent process, the other is used to investigate the time dependence spectroscopically. This technique is introduced by the name of ‘two-dimensional interferometry’. It uses low excitation power, but provides high time resolution at large response energy. Related work is pursued in nonlinear optical spectroscopy with incoherent excitation. In this area the use of broad band lasers is investigated for generation of echoes and for correlation based measurements of relaxation times.     

Optical antsotropy in the plane parallel to the surface of obliquely evaporated gold films

An experimental study by means of a return-path type ellipsometer is described. The results can be explained qualitatively by assuming that the directions of the principal axes (X, Y, Z) are as follows: (1) With thinner (e.g. 70 Å) films, the Y-axis lies parallel to the intersection of the plane of incidence of the vapor beam and the film plane, the X-axis lying in the film plane. (2) With thicker (e.g. 210 Å) films, the Y-axis lies in the plane of incidence of the vapor beam making a certain angle with the film plane, the X-axis lying in the film plane.     

Optical absorption and nuclear magnetic resonance in lithium titanium spinel doped by chromium

The optical absorption and nuclear magnetic resonance spectra of Li_{4 − x} Cr_3x Ti_{5 − 2x} O₁₂ (x = 0, 0.01, 0.02, 0.04) solid solutions have been investigated. It has been found that, in the Li₄Ti₅O₁₂ spinel, lithium ions migrate from tetrahedral to octahedral positions with increasing temperature. Doping of chromium to the spinel favors an increase in the fraction of tetrahedrally coordinated lithium and hinders diffusion.     

Eigenmodes in the long-time behavior of a coupled spin system measured with nuclear magnetic resonance

The many-body quantum dynamics of dipolar coupled nuclear spins I=1/2 on an otherwise isolated cubic lattice are studied with nuclear magnetic resonance. By increasing the signal-to-noise ratio by 2 orders of magnitude compared with previous reports for the free induction decay (FID) of (19)F in CaF(2) we obtain new insight into its long-time behavior. We confirm that the tail of the FID is an exponentially decaying cosine, but our measurements reveal a second decay mode with comparable frequency but twice the decay constant. This result is in agreement with a recent theoretical prediction for the FID in terms of eigenvalues for the time evolution of chaotic many-body quantum systems.     

Internal resonance in a plane system of rods

The transverse vibrations of a plane system of rods is considered. The analysis of internal resonance in the system is a primary purpose of the paper. The internal resonance analyzed has an autoparametric nature. The couplings of the elements of the system through internal longitudinal forces, which are transverse forces at the ends of neighbouring rods, are taken into account. The amplitudes of the vibrations in the stationary states of internal resonance are investigated. Non-linear terms appear in the equations of motion. These terms are non-linear damping and non-linear inertia, and have a geometrical nature. The approximate method of calculation gives formulae for the vibration amplitudes of the rods. Plots of the amplitudes against frequency are presented. The stabilizing effect of masses placed at the articulated joints of the system is shown. The influences of the inertia and damping values on the character of the curves is considered. The results obtained are of a qualitative character.     

Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system

In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given.