Magnetic resonance classical theory

However interesting may be, QC and QIP would be restricted to a bunch of mathematical results if there was no way to implement them in the physical world, as much as a Turing Machine (see below) would be a mere theoretical curiosity without the existence of computers This book deals with a particular way to implement QC and QIP it is called Nuclear Magnetic Resonance, or simply NMR. There are excellent books in the subjects of quantum computation and quantum information [6,7], in NMR [8] and in (classical) computation [9]. This book exploits elements of these three different fields, and put them together in order we can understand NMR-QIP. In this chapter we will introduce the basic elements of computation, and will discuss the physics of computational processes. Chapters 2 and 3 introduce the necessary background of NMR and quantum computation theories, in order we can exploit the realizations of NMR-QIP in the subsequent chapters. 

Magnetic resonance methods have been used extensively to probe the structure and dynamics of thermotropic nematic liquid crystals both in the bulk and in confined geometry. Soon after de Gennes [27] stressed the importance of long range collective director fluctuations in the nematic phase, a variable frequency proton spin-lattice relaxation Tx) study [32] showed that the usual BPP theory [33] developed for classical liquids does not work in the case of nematic liquid crystals. In contrast to liquids, the spectral density of the autocorrelation function is non-Lorentzian in nematics. As first predicted independently by Pincus [34] and Blinc et al. [35], collective, nematic type director fluctuations should lead to a characteristic square root type dependence of the spin-lattice relaxation rate rf(DF) on the Larmor frequency % ... 

This chapter opens with an account of resonance fluorescence and its depolarization by external magnetic fields, a phenomenon now knovm as the Hanle effect. Experiments of this type in mercury vapour are described and we develop a classical theory to explain the shape of the observed signals. This is followed by a discussion of the applications of this technique to the accurate measurement of atomic lifetimes. For the sake of simplicity the effects of interatomic collisions and of trapping or reabsorption of resonance radiation in these experiments are not considered... 

Soon afterwards Wood and Ellet (1924) showed that the polarization of the fluorescent light was destroyed by applying small magnetic fields to the resonance cell. Further experimental studies of this effect were made by Hanle (1924), who also worked out a classical theory describing the influence of the magnetic field on the polarization of the... 

Introduction and experimental technique. The classical theory of resonance fluorescence, in which the atoms are treated as dipole oscillators processing at the Larmor frequency, leads one to predict that interesting effects will also occur if the atoms are excited by light whose intensity is periodically modulated. As the external magnetic field is varied in these experiments a point is reached at which the Larmor frequency, equals the angu-... 

As already pointed out, terms such as wave function, electron orbit, resonance, etc., with which we describe the formulations and results of wave mechanics, are borrowed from classical mechanics of matter in which concepts occur which, in certain respects at least, show a correspondence to the wave mechanical concepts in question. The same is the case with the electron spin. In Bohr s quantum theory, Uhlenbeck and Goudsmit s hypothesis meant the introduction of a fourth quantum number j, which can only take on the values +1/2 and —1/2- In wave mechanics it means that the total wave function, besides the orbital function, contains another factor, the spin function. This spin function can be represented by a or (3, whereby, for example, a describes the state j = +1/2 and P that with s = —1/2. The correspondence with the mechanical analogy, the top, from which the name spin has been borrowed, is appropriate in so far that the laevo and dextro rotatory character, or the pointing of the top in the + or — direction, can be connected with it. A magnetic moment and a... 

Introduction and experimental techniques. In previous sections we drew attention to the fact that, in both the classical and quantum theories, expressions derived for the intensity of resonance fluorescence from atoms subjected to an external magnetic field, equations (15,3) and (15.23) respectively, contain terms which may lead to a modulation of the intensity at the Larmor frequency or its second harmonic. This radio-frequency modulation has been observed in several different kinds of experiment, the simplest of which makes use of pulsed excitation and time-resolved detection of the fluorescent light. 

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