Antisymmetric states intensity

Guo and Yang [53] have analyzed spontaneous decay from two atoms initially prepared in an entangled state. They have shown that the time evolution of the population inversion, which is proportional to the intensity (87), depends on the degree of entanglement of the initial state of the system. Ficek et al. [10] have shown that in the case of two nonidentical atoms, the time evolution of the intensity 7(R, t) can exhibit quantum beats that result from the presence of correlations between the symmetric and antisymmetric states. In fact, quantum beats are present only if initially the system is in a nonmaximally entangled state, and no quantum beats are predicted for maximally entangled as well as unentangled states. 

Similar to the fluorescence intensity distribution, the visibility can provide us an information about the internal state of the system. When the system is prepared in the antisymmetric state or in a superposition of the antisymmetric and the ground states, p55 = pee = 0, and then the visibility has the optimum negative value V = — 1. On the other hand, when the system is prepared in the symmetric state or in a linear superposition of the symmetric and ground states, the visibility has the maximum positive value "V - 1. 

Figure 13. Photodissociation spectrum of V (OCO), with assignments. Insets and their assignments show the photodissociation spectrum of molecules excited with one quanmm of OCO antisymmetric stretch, v" at 2390.9 cm . These intensities have been multiplied by a factor of 2. The shifts show that Vj (excited state) lies 24 cm below v ( (ground state), and that there is a small amount of vibrational cross-anharmonicity. The box shows a hot band at 15,591 cm that is shifted by 210 cm from the origin peak and is assigned to the V" -OCO stretch in the ground state.

Clearly the symmetric It = 2 and 0 functions satisfy (6.258) and are therefore associated with rotational levels having odd N. Conversely, the antisymmetric / / = I functions satisfy (6.257) and must be associated with even N levels. These nuclear spin statistical results are very important, because they determine the nature of the nuclear hyperfine structure if the different nuclear spin states remain degenerate, the spin statistics then help to determine rotational level populations and hence spectroscopic intensities. 

As in the ABC case, the basis functions divide into four sets according to fz with 1,3, 3, and 1 functions in each set. However, of the three functions in the set with fz = % or — V2 two are symmetric and one antisymmetric. Hence each of the two 3X3 blocks of the secular equation factors into a 2 X 2 block and 1X1 block. Algebraic solutions are thus possible. Furthermore, the presence of symmetry reduces the number of allowed transitions from 15 to 9, because no transitions are allowed between states of different symmetry. (One of the nine is of extremely low intensity and is not observed.) Thus the A2B system provides a good example of the importance of symmetry in determining the structure of NMR spectra. 

Table Infrared and Raman stretching frequency ranges (cm ) for phosphate anions in the solid state. The intensities of the bands (s = strong, m = medium, w = weak) and their assignments (s = symmetric, as = antisymmetric vibrations) are shown...

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