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The Journal of Chemical Physics

Comment on: Is multiple quantum nuclear magnetic resonance spectroscopy of liquid water real?

Daniel Abergel, Marc‐André Delsuc, Jean‐Yves Lallemand

Published Jan 15, 1992• 32 citations
Publisher

Abstract

Recently, two-dimensional NMR experiments have been performed, which were likely to show that a coupling between otherwise uncoupled or equivalent spins was observable, yielding signals originating from multiple-spin multiple-quantum operators in the density matrix. According to the authors, such surprising results could be interpreted as a consequence of the radiation damping phenomenon. For this purpose, a fully quantum-mechanical frame was used, thus treating the radiation field in a quantized manner. Our analysis, based on the same theoretical grounds, as well as on new experimental arguments, lead us to diverging conclusions.

DOI
10.1063/1.462155

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Reply to the Comment on: Is multiple quantum nuclear magnetic resonance of water real?

W. S. Warren, Qiuhong He, Mark A. McCoy +1 more

The Journal of Chemical Physics•Jan 15, 1992•38 citations
Recently, two-dimensional NMR experiments have been performed, which were likely to show that a coupling between otherwise uncoupled or equivalent spins was observable, yielding signals originating from multiple-spin multiple-quantum operators in the density matrix. According to the authors, such surprising results could be interpreted as a consequence of the radiation damping phenomenon. For this purpose, a fully quantum-mechanical frame was used, thus treating the radiation field in a quantized manner. Our analysis, based on the same theoretical grounds, as well as on new experimental arguments, lead us to diverging conclusions.
Multiple quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated analytically in infinite one-dimensional (1D) chains of spins 1/2. The representation of spin 1/2 operators with fermion field operators allows to calculate exactly the spin density operator, and hence NMR observables, under a variety of different conditions for 1D spin systems. The exact expressions are valid for all times and for a macroscopic number of coupled spins. The calculations for a 1D spin system initially at thermal equilibrium, and evolving under a 2-quantum/2-spin average dipolar Hamiltonian, in the presence of nearest-neighbor dipolar interactions yield MQ NMR spectra with 0- and 2-quantum coherences only. For a nonequilibrium initial condition with transverse magnetization, the analogous spin dynamics calculations produce MQ NMR spectra with all possible coherences of odd orders. Calculations at the level of perturbation theory, which include next-nearest-neighbor dipolar interactions, generate MQ spectra with higher even order coherences for equilibrium initial condition and evolution under a 2-quantum/2-spin propagator. Consideration of multiple spin correlations, 0-quantum coherences, and rf pulse imperfections are also presented. The relevance and implications of these theoretical results for comparison with the recent MQ NMR experiments of Yesinowski et al. on materials with quasi-one-dimensional distributions of spins, and for MQ NMR of solids in general are discussed.
Nuclear magnetic resonance (NMR) is a direct macroscopic manifestation of the quantum mechanics of the intrinsic angular momentum of atomic nuclei. It is best known for its extraordinary range of applications, which include molecular structure determination, medical imaging, and measurements of flow and diffusion rates. Most recently, liquid-state NMR spectroscopy has been found to provide a powerful experimental tool for the development and evaluation of the coherent control techniques needed for quantum information processing. This burgeoning new interdisciplinary field has the potential to achieve cryptographic, communications, and computational feats far beyond what is possible with known classical physics. Indeed, NMR has made the demonstration of many of these feats sufficiently simple to be carried out by high school summer interns working in our laboratory (see the last two authors). In this paper the basic principles of quantum information processing by NMR spectroscopy are described, along with several illustrative experiments suitable for incorporation into the undergraduate physics curriculum. These experiments are spin–spin interferometry, an implementation of the quantum Fourier transform, and the quantum simulation of a harmonic oscillator.
We apply the methods of cavity quantum electrodynamics (CQED), to obtain a microscopic and fully quantum-mechanical picture of radiation damping in magnetic resonance, and the nascent formation of the free induction signal. Numerical solution of the Tavis-Cummings model - i.e., multiple spins 1∕2 coupled to a lossless single-mode cavity - shows in fine detail the transfer of Zeeman energy, via spin coherence, to excite the cavity - represented here by a quantized LC resonator. The case of a single spin is also solved analytically. Although the motion of the Bloch vector is non-classical, we nonetheless show that the quantum mechanical Rabi nutation frequency (as enhanced by cavity coupling and stimulated emission) gives realistic estimates of macroscopic signal strength and the radiation damping constant in nuclear magnetic resonance. We also show how to introduce dissipation: cavity losses by means of a master equation, and relaxation by the phenomenological method of Bloch. The failure to obtain the full Bloch equations (unless semi-classical conditions are imposed on the cavity) is discussed in light of similar issues arising in CQED (and in earlier work in magnetic resonance as well), as are certain problems relative to quantization of the electromagnetic near-field.
We show that there is excellent quantitative agreement between the usual semiclassical predictions for nuclear magnetic resonance experiments (quantized spins interacting with a classical radio frequency magnetic field, including radiation damping), and the predictions of a fully quantized description of the same experiment. We also propose a pictorial description of the relevant dynamical quantum states, which helps to lead the intuition towards the same conclusion. Our model ignores spin relaxation, and simulates the equivalent damping resistor of the sample circuit by a very long piece of lossless coaxial cable. The classical rf field (pulses and free induction decay) is described quantum mechanically by means of Glauber’s “coherent” or “quasiclassical” states.
The 19F^{19}\text{F}19F spins in a crystal of fluorapatite have often been used to experimentally approximate a one-dimensional spin system. Under suitable multipulse control, the nuclear-spin dynamics may be modeled to first approximation by a double-quantum one-dimensional Hamiltonian, which is analytically solvable for nearest-neighbor couplings. Here, we use solid-state nuclear magnetic resonance techniques to investigate the multiple quantum coherence dynamics of fluorapatite, with an emphasis on understanding the region of validity for such a simplified picture. Using experimental, numerical, and analytical methods, we explore the effects of long-range intrachain couplings, cross-chain couplings, as well as couplings to a spin environment, all of which tend to damp the oscillations of the multiple quantum coherence signal at sufficiently long times. Our analysis characterizes the extent to which fluorapatite can faithfully simulate a one-dimensional quantum wire.