David T. Pegg

Proton‐polarization transfer enhancement of a heteronuclear spin multiplet with preservation of phase coherency and relative component intensities

The DEPT pulse sequence (π/2)(H,y)−(2J)−1−π(H), (π/2)(C,x)−(2J)−1 −ϑ(H,x)π(C)−(2J)−1−(acquire 13C) is analyzed theoretically for a variable ϑ pulse for three spin systems: CH, CH2, and CH3. It is shown that the pulse train produces an enhanced distortion‐free 13C signal which has the following characteristics: (a) there is phase coherency within and between the components of the 13C multiplets; (b) the enhancements vary with ϑ as (γH/γC)sin ϑ for CH, (γH/γC)sin 2ϑ for CH2, and (3γH/4γC) (sin ϑ+sin 3ϑ) for CH3. Experimental evidence is provided for these predictions. An important application of the DEPT pulse train is for the generation of both individual proton‐coupled and proton‐decoupled 13C methine (CH), methylene (CH2), and methyl (CH3) subspectra. This can be readily achieved by forming suitable combinations of DEPT spectra determined at ϑ = (π/4), (π/2), and (3π/4). Such spectral editing is less sensitive to variations in J values than the INEPT pulse sequence. Signal enhancement for 195Pt and 29Si ...

Unitary Phase Operator in Quantum Mechanics

The difficulties in formulating a natural and simple operator description of the phase of a quantum oscillator or single-mode electromagnetic field have been known for some time. We present a unitary phase operator whose eigenstates are well-defined phase states and whose properties coincide with those normally associated with a phase. The corresponding phase eigenvalues form only a dense subset of the real numbers. A natural extension to the definition of a time-measurement operator yields a corresponding countable infinity of eigenvalues.

On the Hermitian Optical Phase Operator

Abstract It has long been believed that no Hermitian optical phase operator exists. However, such an operator can be constructed from the phase states. We demonstrate that its properties are precisely in accord with the results of semiclassical and phenomenological approaches when such approximate methods are valid. We find that the number-phase commutator differs from that originally postulated by Dirac. This difference allows the consistent use of the commutator for inherently quantum states. It also leads to the correct periodic phase behaviour of the Poisson bracket in the classical regime.

Complete accurate editing of decoupled 13C spectra using DEPT and a quaternary-only sequence

Abstract Recently, it has been shown that the DEPT sequence may be used to provide separate methyl, methylene, and methine subspectra and preliminary results have indicated it is quite an accurate sequence for this purpose. Here, the errors involved in using DEPT over the normal range of aliphatic and aromatic 1J13C-1H, values are assessed by analyzing DEPT with variable time delay periods using the Heisenberg quantum picture approach. The limitations of the sequence when used across the whole range of organic compounds is discussed. An experimental approach to setting up and using the sequence is described. The possibility of improving the sequence with additional phase-alternation schemes or composite pulses, for example, is explored. The editing of a 13C spectrum is completed by generation of a spectrum containing unprotonated (quaternary) carbons only. The theoretical basis of the pulse sequence used for this purpose is described and errors are assessed.

Phase in quantum optics

Diracs prescription for quantisation does not lead to a unique phase operator for the electromagnetic field. The authors consider the commonly employed phase operators due to Susskind and Glogower (1964) and their extension to unitary exponential phase operators. However, they find that phase measuring experiments respond to a different operator. They discuss the form of the measured phase operator and its properties.

Proton polarization transfer enhancement for a nucleus with arbitrary spin quantum number from n scalar coupled protons for arbitrary preparation times

Abstract Polarization transfer enhancement of the NMR resonance from a nucleus with spin quantum number l (l = 1 2 , 1, 3 2 , …) from n scalar coupled protons using the pulse sequence (90 x H)-τ-(180 x H)(180 x I)-τ-(90 y H)(90 x I)-Δ-(acquire with or without H decoupling) is studied theoretically. It is shown that the enhancement of the components of the I multiplet varies with τ as Σ m I m I sin (4 πJm I τ ) where J is the scalar coupling constant and m I takes the values l, l - l, …, -l . Values of τ opt which result in the maximum enhancement are calculated, as well as the size of these maximum enhancements. Values of Δ opt which yield the maximum decoupled signal are also computed, along with the maximum decoupled enhancements. The theory is confirmed experimentally for l = 3 2 and l = 3 by studying proton polarization transfer spectra of the 10 B and 11 B resonances in NaBH 4 .

Heisenberg vector model for precession via heteronuclear scalar coupling

Abstract Simple vector models have been considered as useful heuristic descriptions of the behavior of magnetization vectors of nuclei under the influence of heteronuclear scalar coupling during some straightforward multipulse sequences. However, it is generally held in the literature that the rigorous quantum-mechanical evolution should be treated by a density matrix approach, particularly where neither of the nuclei involved is in a pure z -spin eigenstate. In this paper, based on several selected pulsed NMR experiments, we develop and extend the simple vector model to deal with more complicated multipulse situations. We show that the vector model not only provides a good simple physical insight into these selected problems but is also a rigorous description of the quantum-mechanical evolution. As such, it will prove a viable and useful simple alternative to the density matrix approach for the understanding and design of new specific pulse sequences.

Polarization transfer pulse sequences for two-dimensional NMR by heisenberg vector analysis

Abstract There are 24 possible polarization transfer pulse sequences having two or three precessional periods in which the effects of heteronuclear coupling and chemical shift are separated by refocusing pulses. Six of the most useful of these pulse sequences are described in detail using the Heisenberg vector approach. The vector description enables a clear analysis of the outcome of each sequence and of the modifications which are necessary to optimize each sequence. Each sequence is analyzed for the production of artifacts and a simple general method for the phase correction of the two-dimensional spectra is described.

Phase properties of squeezed states of light

Abstract Recently introduced unitary and hermitian phase operators are used to examine the phase properties of squeezed states of light with particular reference to the squeezed vacuum. The results differ markedly from previous calculations involving the Susskind and Glogower operators. The new formalism allows the construction of a phase probability density which, on a polar diagram, is a circle for the vacuum state, becomes elliptical with gentle squeezing and collapses to a line through the origin for full squeezing. This probability density together with the calculation of expectation values of various trigonometrical functions of phase show how squeezing impresses phase information onto the vacuum.

Two-dimensional 13C1H polarization transfer J spectroscopy

Abstract Modification of the INEPT sequence enables application of the sequence to two-dimensional NMR and provides a simplified form of two-dimensional 13 C J spectroscopy. The problem of phase correcting the final spectrum has been solved and the source of artifact signals has been identified and the problem alleviated. The uses and advantages of this form of two-dimensional spectroscopy are briefly described.