Collective states, excitation

As is well known, in crystalline solids there may be formed collective electron-excitation states called excitons.8182 Such states are excited only in media with periodic structure and are delocalized over a large volume of atoms (or molecules), their excitation energy being 0.1-0.5 eV lower than the energy of the electron states of isolated molecules that produced them. The nature and spectroscopy of exciton states have been thoroughly studied both experimentally and theoretically. In this section we will... 

The energy losses are maximum at maxima of e2(q, to), which corresponds to discrete transitions in isolated molecules, as well as at zeros of the denominator, that is, for solutions of Eq. (3.12), which corresponds to excitation of collective states. In order to find the frequencies of the latter we must know the explicit form of e(q, to). 

In condensed media, the transition with the largest value of F0n usually does not correspond to the transitions of an individual molecule into an excited state. For a number of substances the largest F0n corresponds to excitation of collective states of the plasmon type, such as the h[Pg.315]

Figure 7. Collection of emission-wavelength-dependent steady-state excitation scans for 100 pM pyrene in sub- and supercritical C02. For the monomer and excimer scans, the emission wavelength (16 nm bandpass) is adjusted to 380 and 460 nm, respectively.

The two-exciton manifold consists of two types of doubly excited vibrational states. The first are overtones (local), where a single bond is doubly excited. The other are collective (nonlocal), where two bonds are simultaneously excited (43,50). We denote the former OTE (overtone two-excitation) and the latter CTE (collective two-excitation). A pentapeptide has 5 OTE and 10 CTE. The two-exciton energies are determined by the parameters gn in the Hamiltonian [Equation (17)], which in turn depend on the peptide group energies G , the anharmonicity An, and dipole moment ratio Kn, n = l,...,5. We set them equal for all CO units... 

In the case of the coherent vibronic state excitations, we shall take into account a change of the frequency of the collective vibrations in the polyene chain caused by the exciton excitation ... 

The couplings within the sub-systems consisting of the atomic states and the two radiation modes corresponding to at most a single excitation are shown in Fig. 7. The set of collective states can be separated into groups with specific excitation numbers n+, ii- in the two polarization modes. 

Adiabatically rotating the mixing angles 6 from 0 to 7t/2 leads to a complete and reversible transfer of all photonic states to a collective atomic excitation if the maximum number of photons n + m is less than the number of atoms N. Let the initial quantum state of the light field be described by the density matrix... 

The paper is organized as follows. Section 2 shortly introduces the exciton model and its approximations. Section 3 reviews calculations of ground state properties (mainly the polarization and polarizability) paying special attention to the mean-field approximation. Push-pull chromophores, the special family of polar and polarizable molecules studied in this contribution, are presented in Section 4, with a brief discussion of their properties in solution and of relevant models. In Section 5 we present a model for interacting push-pull chromophores that will be the basis for the discussion of collective and cooperative effects in relevant materials. Static susceptibilities of clusters of push-pull chromophores are discussed in Section 6, focusing attention on cooperative effects in tlie ground state. Excited state properties are addressed in Section 7, with special emphasis to systems where intermolecular interactions lead to extreme consequences. Section 8 finally summarizes main results. 

In that case, the Coulomb interaction is assumed to play a secondary role. Then, the scheme of energy levels appearing in Fig. 5 becomes that one given in Fig. 6. Clearly, the ground state is one of the singlets g, + g,-) or u, + u, ) owing to the relative stabihty of the orbital states g,a) and IM, CT> (G-type collective state). The first excited state is the triplet with S = 0, 1. 

After presenting the sample preparation in Sect. 5.2, we give an introduction to the theoretical background in Sect. 5.3. In Sect. 5.4, we briefly review the electronic influence on structure and phase stability of crystalline Hume-Rothery phases. In Sect. 5.5, we discuss the properties of non-magnetic amorphous alloys of the type just mentioned. The electronic influence on structure (5.5.1) and consequences for the phase stability (5.5.2) are also discussed. Structural influences on the electronic density of states are shown in 5.5.3. Electronic transport properties versus composition indicate additionally the electron-structure interrelation (5.5.4), and those versus temperature, the influence of low-lying collective density excitations (5.5.5). An extension of the model of the electronic influence on structure and stability was proposed by Hdussler and Kay [5.21,22] whenever local moments are involved as, for example, in Fe-containing alloys. In Sect. 5.6, experimental indications for such an influence are presented, and additional consequences on phase stability and magnetic properties are briefly discussed. 

Fig. 5.5. Schematic dispersion relation of collective density excitations in the crystalline case (al) as well as in the disordered case (bl). Phonon-roton states are shown in bl) at Kpt. Corresponding dynamic density of states are included (a2, b2)...

We now consider excitation and population transfer processes that can lead to a preparation of the two-atom system in one of the collective states. In particular, we will focus on processes that can prepare the two-atom system in the... 

There are two other collective states of the two-atom system the double atomic ground state g) = gi) g2) and the double atomic excited state e) = ei) e2), which are also product states of the individual atomic states. These states are not affected by the dipole-dipole interaction Q.n, the detuning A and the spontaneous emission rates. 

The two-photon entangled states cannot be generated by a simple coherent excitation. A coherent field applied to the two-atom system couples to one-photon transitions. The problem is that coherent excitation populates the upper state e) but also populated the intermediate states. v) and u). The two-photon entangled states (92) are superpositions of the collective ground and excited states with no contribution from the intermediate collective states j) and a). 

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