Excitation incoherent

Figure B2.5.13. Schematic representation of the four different mechanisms of multiphoton excitation (i) direct, (ii) Goeppert-Mayer (iii) quasi-resonant stepwise and (iv) incoherent stepwise. Full lines (right) represent the coupling path between the energy levels and broken arrows the photon energies with angular frequency to (Aco is the frequency width of the excitation light in the case of incoherent excitation), see also [111].

Due to Eq. (A.3) the above theories only permit the excitation of one quantum of vibration at a time (b and b+ connect vibrational states where their populations differ by only one quantum). This is a consequence of the linear approximation because the nuclear coordinates deviate slightly from the equilibrium situation the molecule can only change its vibrational state by the smallest of the allowed quantities one quantum. In order to account for the excitation of several quanta at a step (coherent excitation) one needs to use other kind of theories (see for example [24]). Nevertheless, the presented approaches permit the sequential excitation of quanta in a ladder climbing fashion (incoherent excitation). 

Both qualitative and quantitative applications of Eq. (8.8) are possible. Qualita- tively, for example, a traditional scheme where the ground electronic state of L and D are incoherently excited to bound levels of an excited state, gives 5 = 0. This is because all processes connecting the initial and final Lt) and D,) states, that is, 5 J contributions to the matrix elements in Eq. (8.8), are even in the amplitude of the. Xj electric field. Hence, propagation under E and —E are identical. By contrast, -) consider the four-level model scheme in Figure 8.1, and discussed in detail in Section 8.2. When 0( ) 0 there exist processes connecting the initial and final L) and D) states that are of the form L) - 1) - 2) D), and hence there are... 

The off-diagonal elements of p give a measure of the interference that exists between the various magnetic substates following excitation, since they contain information on the relative phases of the excitation amplitudes. The normal convention is to say that coherent excitation has occurred if the corresponding off-diagonal elements of p are not zero. Incoherent excitation is said to have taken place if the density matrix is diagonal in m. 

A similar enhancement of the dephasing rate has been observed for K/Pt(lll). Figure 19.7 shows Fourier spectra of the oscillatory components when varying the pump fluence. It is evident that K—Pt stretching mode at 4.8 THz shows a marked red shift and broadening. This feature can be ascribed to the incoherent excitation of the lateral modes, as in the case of Cs/Pt(lll), but also notable in this system is that... 

A method for calculating observables resulting from incoherent excitation transport among chromophores randomly tagged in low concentration on isolated, flexible polymer chains is described. The theory relates the ensemble average root-mean-square radius of gyration ) of a polymer coil to the rate... 

Above we had in mind that the wavevector k is a good quantum number and thus that all exciton states are coherent. In the opposite case, which can occur, for example, as a result of exciton-phonon scattering or scattering by lattice defects, the exciton energy bands are not characterized by the k value. In this case incoherent localized states can appear, for which the translation symmetry of the crystal is not important and which are similar, for example, to excitations in amorphous materials. In some solids the coexistence of coherent and incoherent excitations can also be possible. 

From this macroscopic consideration it is seen that the states for which the wavevector is not a good quantum number do not form in a certain vicinity of q = 0 for both branches, and for q > q lx for the lower branch. In other words, the states with the well-defined wavevector exist in the intermediate region of the wavevectors only q n < q < qitlx for the lower branch, and q > q Pn for the upper branch. However, in contrast to the case of vanishing q, one can say that for q A> 1 the coherent polaritonic states do not form at all. The excited states from this part of the spectrum are not resonant with the cavity photon, and as a result no hybridization happens. Instead, these excited states are similar to the localized excited states in a non-cavity material, i.e. they are to be treated just as incoherent excited states. 

Thus, the populations are cycled or optically pumped by the coherent radiation field at a frequency Q, an effect which is not observed for incoherent excitation. 

Fig. 1 Schematic representation of the pressure effect on the singlet (S(r)=log<(s ip(r)) ) and triplet (/-(r)=log ) content of the excited molecular state. Crosses, collision-free conditions, points and solid line, increasing inert-gas pressure, (a) statistical-limit (b) strongcoupling case (incoherent excitation) (c) strong coupling case (coherent excitation) (d) weak-coupling case (small polyatomics) (e) weak-coupling case (CO,N2).

Light amplification by stimulated emission of radiation was first demonstrated by Maiman in 1960, the result of a population inversion produced between energy levels of chromium ions in a ruby crystal when irradiated with a xenon flashlamp. Since then population inversions and coherent emission have been generated in literally thousands of substances (neutral and ionized gases, liquids, and solids) using a variety of incoherent excitation techniques (optical pumping, electrical discharges, gas-dynamic flow, electron-beams, chemical reactions, nuclear decay). 

The maximum transfer efficiency by STIRAP in systems involving con-tinua is far less than 100%, due to dynamic Stark shifts and incoherent losses from the target state induced by the pump laser, as theory predicts [202, 215, 219, 220]. However, since techniques based on incoherent excitation via resonant continuum couplings do not usually permit any transfer at all, the STIRAP technique offers an advantage in such environments, even though the efficiency of STIRAP in such cases is far less than in purely bound systems. 

Either two or more molecular levels of a molecule are excited coherently by a spectrally broad, short laser pulse (level-crossing and quantum-beat spectroscopy) or a whole ensemble of many atoms or molecules is coherently excited simultaneously into identical levels (photon-echo spectroscopy). This coherent excitation alters the spatial distribution or the time dependence of the total, emitted, or absorbed radiation amplitude, when compared with incoherent excitation. Whereas methods of incoherent spectroscopy measure only the total intensity, which is proportional to the population density and therefore to the square ir of the wave function iff, the coherent techniques, on the other hand, yield additional information on the amplitudes and phases of ir. 

Broad-band incoherent excitation, with A > 5e but A g < Se, which implies that A c > Se. Here, only initial populations are prepared, as represented by diagonal matrix elements of the form... 

By inserting into Eq. (213) the appropriate form of pit) from Eq. (211), we obtain the expressions for S(r) and L(r) corresponding to the coherent and incoherent excitation conditions. We may deduce, in this way, the general form of the decay in typical cases, summarized in Table 1. These are represented schematically in Figs. 8-10. The weak-coupling case is approximated... 

Under an incoherent excitation, the overall decay is described as a sum of exponentials in the weak-coupling, as well as in the strong-coupling case. S and L decrease monotonically with time, but not necessarily with the same rate. The decay time of levels with high s content is more rapid. The main difference between both cases is the initial value of the S(to)/L to) ratio. In the weak-coupling case, we have on the average 1 and... 

For aromatic carbonyls (benzophenone, benzoquinone), where S-T coupling is particularly efficient, F 1cm , i.e., F > AE. We may thus expect an incoherent excitation of v states (or a very rapid dephasing escaping observation) resulting in the absence of initial prompt fluorescence. 

Note that an elegant theoretical way of describing observable quantities of a coherently or incoherently excited system of atoms and molecules is based on the density-matrix formalism. This formalism will not be described in detail here however, a basic summary is given in Box 2.6. 

If the phases 0 of the atomic wave function (2.124) are randomly distributed for the different atoms of the ensemble, the nondiagonal elements of the density matrix (2.125) average to zero and the incoherently excited system is therefore described by the diagonal matrix... 

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