Local atomic oscillator

All atomic clocks are based on the same servo-loop scheme (Figure 11.1). An internal atomic oscillator at cOai is used to lock an external or local atomic oscillator at frequency (Dq- The local oscillator is used to probe the atomic transition at (0, and... 

Minimized structures gained from MD simulations are also often basis of normal mode analysis (NMA) [41-43]. NMA assumes that all atoms harmonically oscillate around their equilibrium points. The oscillations deflned by frequency and amplitude (normal mode) are extracted and reflect directions of internal protein motions. Given all its normal modes, the entire protein motion can be expressed as a superposition of modes. The modes vith lo vest frequency correspond to rather delocalized motions in proteins in vhich a large number of atoms oscillate in coordinated motion vith considerable amplitude. Modes vith higher frequency represent more localized motions. Linear combinations of the most relevant normal modes can be employed to depict essential protein motions. Stepwise displacement of atoms of the original structure along the modes can be applied to build up an ensemble of relevant protein conformations [44, 45]. 

Thus, with allowance for both the first-order and second-order processes, the secondary electron spectrum fine structure is formed by oscillations of two types, which are determined by the same local atomic structure but different wave numbers this is the main difference of SEFS spectra from EXAFS and EELFS spectra. It is just this qualitative difference that must determine the characteristic features of SEFS spectra, and it must be taken into account in obtaining parameters of the local atomic structure from experimental data. However, it should be pointed out that a signal from two final states can be observed also in EXAFS and EELFS spectra in the case of the excitation of two closely spaced levels. And though the mechanism of appearance of these signals differs from that in the case of SEFS, nevertheless conceivably the analogous problem must be solved also for these traditional methods. 

The first approach is based on a calculation of the oscillating signal of the a priori prescribed local atomic configuration and a comparison between calculated and experimental results. By varying the local atomic configuration, the calculated result is then fitted to the experimental spectrum, and thereby the local atomic... 

At the present time, of all EXAFS-like methods of analysis of local atomic structure, the SEES method is the least used. The reason is that the theory of the SEES process is not sufficiently developed. However the standard EXAES procedure of the Fourier transformation has been applied also to SEES spectra. The Fourier transforms of MW SEES spectra of a number of pure 3d metals have been compared with the corresponding Fourier transforms of EELFS and EX-AFS spectra. Besides the EXAFS-like nature of SEES oscillations shown by this comparison, parameters of the local atomic structure of studied surfaces (the interatomic distances and the mean squared atomic deviations from the equilibrium positions [12, 13, 15-17, 21, 23, 24]) have been obtained from an analysis of Fourier transforms of SEES spectra. The results obtained have, at best, a semi-quantitative character, since the Fourier transforms of SEES spectra differ qualitatively from both the bulk crystallographic atomic pair correlation functions and the relevant Fourier transforms of EXAFS and EELFS spectra. 

Compared to the diffraction methods, the main advantages of the spectral methods of structural analysis, in particular SEFS spectroscopy, are due to their physical nature, namely, their sensitivity to the local atomic structure only. That is, no matter what the structural state of the matter (crystalline or amorphous), the oscillating signal in the spectrum is determined by the nearest atomic environment of the ionized atom of the particular chemical element. Owing to this, the spectral methods of structural analysis make it possible to use the results obtained from a sample with known atomic structure as standards in the study of the structure of unknown objects by determining all parameters of the extended fine structure... 

As mentioned in the Introduction, there are two approaches to obtaining information on the local atomic structure from SEFS spectra in both EXAFS and EXAFS-like methods. The first approach is based on the calculation of the oscillating structure of the spectrum for a local atomic configuration and subsequent comparison between the obtained result and the experimental data. The second approach consist in solving the inverse problem to obtain the atomic pair correlation function (PCF) from the experimental oscillating part of a spectrum. 

But, in spite of the simplicity and availability of the Fourier transformation and qualitative agreement between the results obtained by this method and the known experimental data, the use of the Fourier procedure for the determination of the local atomic structure parameters from SEFS spectra turns out to be unsatisfactory even on the semiquantitative level. Taking into account oscillations of two types in the kernel of the integral equation of the SEFS method [Eqs. (92), (93)] calls for direct solution of the inverse problem. 

FIGURE 11.21 An example of a clock atomic transition. The excitation probability of the clock transition (the atomic oscillator) is measured through the quantum jump number vs. the laser tuning of the local oscillator. Each probe pulse is of 90 ms duration, and twenty probe cycles were performed for each value of the detuning. (Reproduced with the permission of the Physikalisch-Technisehe Bundesanstalt.)... 

Another experimental proof of the localization of cold atoms at the minima of a periodic optical potential was obtained by recording the resonance fluorescence spectra of cesium atoms trapped in three-dimensional optical molasses (Westbrook et al. 1990) and rubidium atoms in a one-dimensional optical potential (Jessen et al. 1992) The resonance fluorescence spectrum of a motionless two-level atom consists of the well-known Mollow triplet, which includes a central peak at the laser frequency u> and two side components displaced to the red and blue sides by an amount equal to the Rabi frequency (Mollow 1969). For a two-level atom oscillating in a potential well at a frequency lower than the Rabi frequency, each component of the Mollow triplet is split into side components corresponding to changes in the vibrational state of the atom. If the ratio between the oscillation amplitude of the atom in the potential well and the radiation wavelength (the Lamb-Dicke factor) is small, each component of the... 

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