Creation Of Coherences Research Articles

Effective Hamiltonian and spin dynamics in fast MAS TRAPDOR-HMQC experiments involving spin-3/2 quadrupolar nuclei

We present a theoretical and numerical description of the spin dynamics associated with TRAPDOR-HMQC (T-HMQC) experiment for a 1H (I) – 35Cl (S) spin system under fast magic angle spinning (MAS). Towards this an exact effective Hamiltonian describing the system is numerically evaluated with matrix logarithm approach. The different magnitudes of the heteronuclear and pure S terms in the effective Hamiltonian allow us to suggest a truncation approximation, which is shown to be in excellent agreement with the exact time evolution. Limitations of this approximation, especially at the rotary resonance condition, are discussed. The truncated effective Hamiltonian is further employed to monitor the buildup of various coherences during TRAPDOR irradiation. We observe and explain a functional resemblance between the magnitude of different terms in the truncated effective Hamiltonian and the amplitudes of various coherences during TRAPDOR irradiation, as function of crystallite orientation. Subsequently, the dependence of the sign (phase) of the T-HMQC signal on the coherence type generated is investigated numerically and analytically. We examine the continuous creation and evolution of various coherences at arbitrary times, i.e., at and between avoided level crossings. Behavior between consecutive crossings is described analytically and reveals ‘quadrature’ evolution of pairs of coherences and coherence interconversions. The adiabatic, sudden, and intermediate regimes for T-HMQC experiments are discussed within the approach established by A. J. Vega. Equations as well as numerical simulations suggest the existence of a driving coherence which builds up between consecutive crossings and then gets distributed at crossings among other coherences. In the intermediate regime, redistribution of the driving coherence to other coherences is almost uniform such that coherences involving S-spin double-quantum terms may be efficiently produced.

On the use of radio-frequency offsets for improving double-quantum homonuclear dipolar recoupling of half-integer-spin quadrupolar nuclei.

Detecting proximities between nuclei is crucial for atomic-scale structure determination with nuclear magnetic resonance (NMR) spectroscopy. Different from spin-1/2 nuclei, the methodology for quadrupolar nuclei is limited for solids due to the complex spin dynamics under simultaneous magic-angle spinning (MAS) and radio-frequency irradiation. Herein, the performances of several homonuclear rotary recoupling (HORROR)-based homonuclear dipolar recoupling sequences are evaluated for 27 Al (spin-5/2). It is shown numerically and experimentally on mesoporous alumina that outperforms the supercycled S3 sequence and its pure double-quantum (DQ) (bracketed) version, [S3 ], both in terms of DQ transfer efficiency and bandwidth. This result is surprising since the S3 sequence is among the best low-power recoupling schemes for spin-1/2. The superiority of is thoroughly explained, and the crucial role of radio-frequency offsets during its spin dynamics is highlighted. The analytical approximation of , derived in an offset-toggling frame, clarifies the interplay between offset and DQ efficiency, namely, the benefits of off-resonance irradiation and the trough in DQ efficiency for when the irradiation is central between two resonances, both for spin-1/2 and half-integer-spin quadrupolar nuclei. Additionally, density matrix propagations show that the sequence, applied to quadrupolar nuclei subject to quadrupolar interaction much larger than radio-frequency frequency field, can create single- and multiple-quantum coherences for near on-resonance irradiation. This significantly perturbs the creation of DQ coherences between central transitions of neighboring quadrupolar nuclei. This effect explains the DQ efficiency trough for near on-resonance irradiation, in the case of both cross-correlation and autocorrelation peaks. Overall, this work aids experimental acquisition of homonuclear dipolar correlation spectra of half-integer-spin quadrupolar nuclei and provides theoretical insights towards improving recoupling schemes at high magnetic field and fast MAS.

Quantum Kerr oscillators' evolution in phase space: Wigner current, symmetries, shear suppression, and special states

The creation of quantum coherences requires a system to be anharmonic. The simplest such continuous 1D quantum system is the Kerr oscillator. It has a number of interesting symmetries we derive. Its quantum dynamics is best studied in phase space, using Wigner's distribution W and the associated Wigner phase space current J. Expressions for the continuity equation governing its time evolution are derived in terms of J and it is shown that J for Kerr oscillators follows circles in phase space. Using J we also show that the evolution's classical shear in phase space is quantum suppressed by an effective `viscosity'. Quantifying this shear suppression provides measures to contrast classical with quantum evolution and allows us to identify special quantum states.

The Use of Language Elements in the Creation of Coherences in Discourse

Good discourse has a coherence that binds statements involved in it based on logical thinking. In a coherent discourse, the reader finds the order thoughts which is clearly the tip of the base as a form of the regular mode of thinking of the author. Coherence is the final character of writing that reflects the perfection of the author in controlling his or her way of thinking in order to realize a discourse. Coherence in discourse can be seen primarily as the sentences involved in it are intertwined each other and the ideas flow smoothly. One sentence relation to another sentence or the smooth movement of ideas in discourse is formed by the use of certain language elements as a grammatical form that embodies the cohesiveness of a discourse. The language elements, in this case, are transitional words/phrases, pronouns, and repetitions of keywords. The use of these elements is quite important in constructing sentences that mesh and flow logically in a discourse. It also happens between a paragraph one and another paragraph in a discourse, the elements of language is a bridge that is vital for the transition of thoughts or ideas in a writer's writings.

Toward Label-Free Super-Resolution Microscopy

We propose and implement a far-field spectroscopic system for imaging below the diffraction limit without the need for fluorescence labeling. Our technique combines concepts from Stimulated Emission Depletion (STED) microscopy and Femtosecond Stimulated Raman Spectroscopy (FSRS). The FSRS process generates signal through the creation of vibrational coherences, and here we use a toroidal-shaped decoherence pulse to eliminate vibrational signal from the edges of the focal spot. The nonlinear dependence on decoherence pulse power enables subdiffraction imaging. As in STED, the resolution is in theory infinitely small given infinite decoherence pulse power. Here, we first experimentally demonstrate that the photophysical principles behind our super-resolution Raman imaging method are sound. We then prove that addition of the decoherence pulse significantly improves the spatial resolution of our microscope, achieving values beyond the diffraction limit. We discuss future directions for this technique, includin...

Magneto-optical effects and rf magnetic field detection in cold rubidium atoms

We present the results of our latest experiments on atomic coherences in cold atoms. Interaction of atoms with a near-resonant, linearly polarized light leads to an effective creation of long-lived ground-state Zeeman coherences which is observed through the nonlinear Faraday effect or free induction decay signals of the Larmor precession. Both optically and radio-frequency induced Zeeman coherences are observed, with relaxation rates around a 100 Hz.

1H and 19F ultra-fast MAS double-quantum single-quantum NMR correlation experiments using three-spin terms of the dipolar homonuclear Hamiltonian

Measuring internuclear distances through dipolar interaction is a major challenge for solid-state nuclear magnetic resonance (NMR) spectroscopy. Obtaining reliable interatomic distances provides an access to the local structure in ordered or disordered solids. We show that at magic angle spinning (MAS) frequencies larger than ca. 50 kHz, some of the three-spin terms of the homogeneous homonuclear dipolar Hamiltonian can be used to promote the creation of double-quantum coherences between neighbouring (1)H or (19)F spins without using dipolar recoupling pulse sequences in the Dipolar Homonuclear Homogeneous Hamiltonian (DH(3)) double-quantum/single-quantum correlation experiment. This makes it possible to probe inter-nuclear spatial proximity with limited risk of probe or sample damage from radio-frequency (RF) irradiation, and is fully appropriate for fast repetition rate offering sensitivity gains in favourable cases. Experimental demonstrations are supported by multi-spin numerical simulations, which points to new possibilities for the characterization of spin-system geometries.

Brain γ‐aminobutyric acid measurement by proton double‐quantum filtering with selective J rewinding

An optimized single-shot proton double-quantum (DQ) filter for the quantification of gamma-aminobutyric acid (GABA) levels in human brain is reported. It is demonstrated that creation of DQ coherences following dual-resonance-selective refocusing gives a theoretical editing efficiency of 50% for the detection of the GABA resonance at 3.01 ppm. The sequence times are optimized with both numerical and experimental analyses of the editing performance, giving an experimental editing efficiency of 42%. It is acknowledged that homocarnosine is partially coedited, leading to a 20% contribution to the edited signal; however, macromolecule contamination is negligible in vivo under these experimental conditions. The GABA concentration in human prefrontal cortex is estimated to be 0.8 +/- 0.1 micromol/g (mean +/- SD, n = 6), with reference to the internal standard creatine at 9 micromol/g.

A way of visualizing NMR experiments on quadrupolar nuclei

A graphical representation of the spin states of quadrupolar nuclei in NMR experiments is described. The spherical harmonics represent the irreducible spherical tensor operator basis set, and therefore any density matrix can be illustrated with computer graphics by converting it to a sum of spherical harmonics. Using a multiple quantum-filtered experiment as an example, we demonstrate how the phase and flip angle of RF pulses can be used to create multiple quantum coherences, to suppress the creation of particular coherences, and to select coherences by exploiting their symmetry. This visual approach complements the algebraic description of pulse sequences, providing an intuitive way of designing and analyzing pulse sequences. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part A 25A: 40–52, 2005.

Spin-locking of half-integer quadrupolar nuclei in nuclear magnetic resonance of solids: creation and evolution of coherences.

Spin-locking of half-integer quadrupolar nuclei, such as 23Na (I=3/2) and 27Al (I=5/2), is of renewed interest owing to the development of variants of the multiple-quantum and satellite-transition magic angle spinning (MAS) nuclear magnetic resonance experiments that either utilize spin-locking directly or offer the possibility that spin-locked states may arise. However, the large magnitude and, under MAS, the time dependence of the quadrupolar interaction often result in complex spin-locking phenomena that are not widely understood. Here we show that, following the application of a spin-locking pulse, a variety of coherence transfer processes occur on a time scale of approximately 1/omegaQ before the spin system settles down into a spin-locked state which may itself be time dependent if MAS is performed. We show theoretically for both spin I=3/2 and 5/2 nuclei that the spin-locked state created by this initial rapid dephasing typically consists of a variety of single- and multiple-quantum coherences and nonequilibrium population states and we discuss the subsequent evolution of these under MAS. In contrast to previous work, we consider spin-locking using a wide range of radio frequency field strengths, i.e., a range that covers both the "strong-field" (omega1 >> omegaQPAS and "weak-field" (omega1 << omegaQPAS limits. Single- and multiple-quantum filtered spin-locking experiments on NaNO2, NaNO3, and Al(acac)3, under both static and MAS conditions, are used to illustrate and confirm the results of the theoretical discussion.

ChemInform Abstract: Quantum Beat Spectroscopy in Chemistry

Quantum beat spectroscopy is a Doppler-free time domain method based on the creation of molecular coherences with a laser pulse and the measurement of their subsequent time evolution. Fourier transformation of the time evolution allows a spectrum in the frequency domain with lifetime- limited resolution to be recovered. This article gives an account of the technique applied in high resolution mode which allows the study of isolated molecules, radicals and complexes in extensive detail and with great accuracy.

Quantum beat spectroscopy in chemistry

Quantum beat spectroscopy is a Doppler-free time domain method based on the creation of molecular coherences with a laser pulse and the measurement of their subsequent time evolution. Fourier transformation of the time evolution allows a spectrum in the frequency domain with lifetime- limited resolution to be recovered. This article gives an account of the technique applied in high resolution mode which allows the study of isolated molecules, radicals and complexes in extensive detail and with great accuracy.

Creation and manipulation of coherences in molecules with a pulsed magnetic field

We demonstrate the application of a pulsed magnetic field for the creation and manipulation of coherences in molecular systems, using quantum beat spectroscopy for the detection of the dynamics of the molecular superposition states. In all cases, the experiments are performed on energy levels in electronically excited states of the (jet-cooled) CS2 molecule populated by a short laser pulse. In the basic experiment, following excitation of initially degenerate Zeeman sublevels under zero field conditions with suitable laser polarization, quantum beats are generated at the moment the magnetic field is switched on, even when the field is delayed by several excited state lifetimes. By quenching of the field, it is shown that the molecule may be “frozen” in any superposition state of the participating sublevels. Using a combination of static and pulsed fields with different orientations, the molecule can be prepared in a more general state, described by coherences among all Zeeman substrates. This is achieved by choosing an appropriate time delay for the switched field, without any change to the geometrical parameters of the experiment such as laser polarization or detection direction. Numerical simulations of these dynamical coherence phenomena have been performed to support assignment and interpretation of the experimental results.

Selective creation of quasiparticles in trapped Bose condensates

We investigate theoretically the use of time-varying magnetic fields to selectively create and manipulate quasiparticles in magnetically trapped Bose condensates. To maximize the transition matrix element connecting two desired quasiparticle states, the spatial symmetry of the applied magnetic field must be tailored to exploit the different spatial distributions of magnetization in the two quasiparticle states. This ``spatial magnetic resonance'' effect is analogous to the Franck-Condon factor in electric dipole transitions in diatomic molecules. Experimentally, the spatial magnetic resonance technique may allow the creation of coherences between quasiparticle states, the inversion of quasiparticle state populations, the measurement of quasiparticle lifetimes (${T}_{1}$) and decoherence times (${T}_{2}$), the creation of quasiparticle echoes, etc., in analogy with conventional spin magnetic resonance.

Livestock and landscape

Abstract This short discussion considers the role that livestock play in the creation and dilution of landscape coherences. Using the example of the cattle breeds found in the British Isles, it argues that variations in breed types are an important but neglected part of the landscape. Selected examples are discussed and it is contended that cattle represent significant cultural aspects of the landscape. It is also acknowledged that variations in regional cattle types reflect the impact of past and present agricultural practice on the landscape. Consequently, the paper suggests that types of breeds should also be taken into account when considering policy measures to conserve the appearance of local landscapes. The paper concludes by calling for a more systematic study of local livestock.

A theoretical model of laser-control photodissociation of molecules

We present a theoretical description of a laser-control photodissociation of molecules. While the Liouvillian formalism is required to describe the creation of coherences by the pump pulse, the effective Hamiltonian method suffices to evaluate the reaction yield of the subsequent photodissociation induced by the probe pulse. In this work, a simple model is examined to see how the vibrational coherences created in the intermediate electronic configuration can affect the photodissociation reaction yield. For this purpose, the dissociation potential has been modeled by a decreasing exponential which enables the evaluation of the corresponding dipole matrix elements and vibrational overlaps. Finally, the vibrational and electronic dephasing processes, as well as the temperature effects, are also included in the theory.

Comparison of quantum-state diffusion and quantum-jump simulations of two-photon processes in a dissipative environment.

Recent work on the dynamics of open systems has shown how the density operator may be unraveled into component state-vector trajectories using quantum-state diffusion or the quantum-jump model. In traditional dissipative environments the coherent evolution is stochastically perturbed by the action of the reservoir or environment, so that superposition states are dephased. We examine a system in which both coherent driving and dissipative damping involve the simultaneous creation and annihilation of pairs of photons. This has unusual consequences for the creation and decay of coherences. We analyze this problem using the two recently proposed simulation methods and compare the results of the simulation methods with each other and with density-matrix calculations. We also demonstrate the formation of Schr\"odinger ``cat'' states of the field through the action of dissipation and depict them using the Wigner and Husimi quasiprobability functions.

Multiple-quantum NMR dynamics in the quasi-one-dimensional distribution of protons in hydroxyapatite

Multiple-quantum NMR dynamics are reported for the quasi-one-dimensional distribution of uniformly spaced proton spins in hydroxyapatite, Ca 5(OH)(PO 4) 3, using a phase-incremented even-order selective time-reversal pulse sequence. The initial increase of the effective size N with the preparation time for creation of multiple-quantum coherences is linear, in qualitative (but not quantitative) agreement with calculations based upon an “incremental shell” model recently developed by Levy and Gleason. An upward curvature observed at longer preparation times is qualitatively ascribed to the incomplete isolation of the linear chains. Slight deficiencies of hydroxyl groups in the linear chain lead to a measurable decrease in the slope of the linear portion of the curve.

The effect of a single non-selective radiofrequency pulse on the creation of multiple quantum coherences and on coherence transfer

The creation of multiple-quantum coherences is not forbidden in experiments that employ a single non-selective radiofrequency pulse of arbitrary flip angle. In addition, such a pulse does not forbid coherence transfer between any two coherences. The role of population distribution in creating multiple-quantum coherences for equilibrium is discussed.

Creation of multiquantum coherences from equilibrium spin systems

Recently it has been suggested that zero quantum coherence in scalar coupled spin systems at thermal equilibrium can be created by a single non-selective pulse. In this note, it is shown that the proposed effect will be masked as a consequence of the failure of the conventional high-temperature approximation normally applied to the equilibrium spin density operator. For exacting experiments, its appears that the approximation ϱ(eq) ≈ 1- Hħ/kT may not suffice.