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Chinese Journal of Lasers

Theoretical and Experimental Studies on Classic Physical Picture of Two-Level Magnetic Resonance

杨宝 Yang Bao, 缪培贤 Miao Peixian, 史彦超 Shi Yanchao, 冯浩 Feng Hao, 张金海 Zhang Jinhai, 崔敬忠 Cui Jingzhong, 刘志栋 Liu Zhidong

Published Jan 1, 2020• 3 citations
Publisher
DOI
10.3788/cjl202047.1012001

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The purpose of this tutorial is to derive the precessional characteristics of the magnetic moments of hydrogen nuclei in the presence of a constant external magnetic field using the Dirac bra-ket formulation of quantum mechanics (QM). This behaviour has many applications, most notably in nuclear magnetic resonance (NMR) and magnetic resonance (MR) imaging. Many NMR and MR imaging textbooks claim that the QM expectation value of the magnetic moment of a proton in a magnetic field reduces to the classical picture of a precessing magnetic dipole. This paper validates this conclusion by reducing the cumbersome QM integrals using Dirac notation and matrix algebra, and then comparing this result with the classical picture. It illustrates the connections between the quantum and classical pictures and demonstrates quantitatively how they differ and how they are similar. This tutorial targets students and researchers interested in the fundamental physics behind the MR phenomenon and assumes that the reader has a basic understanding of QM. This may be helpful for undergraduate QM students learning about spin angular momentum and Dirac notation.
It is shown by theory and experiment how coherent superpositions of quantum states in three-level systems can be manipulated by irradiating two connected transitions with two resonant fields with suitably shaped time-dependent amplitudes and phases. Three variants are discussed in detail; (i) adiabatic coherence transfer (ACT) between two transitions, which may be either allowed or forbidden; (ii) nonadiabatic transfer of coherence to a nonirradiated transition by controlled violation of adiabaticity (CVA); (iii) coherence transfer to a nonirradiated transition by antiparallel double resonant irradiation (APDRI). A geometrical representation of these experiments gives a clear physical picture of the phenomena and provides a tool for the development of new methods. The principles are illustrated experimentally by applications to magnetic resonance of deuterium (I=1) in anisotropic phase at high magnetic field, but could also be applied to three level-systems in nuclear quadrupole resonance, optics, and other areas of spectroscopy.