Excitons incoherent

The mechanism of control with multipulse excitation is likely due to dynamics of the carotenoid donor. The presumably incoherent EET process [1] would not support the observed dependence on the carrier phase via the parameter c. Furthermore, the control effect does not suffer from annihilation at higher excitation intensities [2], as would be characteristic for the delocalised excitons in the B850 ring [1], However, it is well known that femtosecond pulses populate higher ground state vibrational levels by impulsive Raman scattering (IRS) [4], and that the periodic phase modulation (Eq. 1) makes IRS selective for specific vibrations... 

Section IV is devoted to excitons in a disordered lattice. In the first subsection, restricted to the 2D radiant exciton, we study how the coherent emission is hampered by such disorder as thermal fluctuation, static disorder, or surface annihilation by surface-molecule photodimerization. A sharp transition is shown to take place between coherent emission at low temperature (or weak extended disorder) and incoherent emission of small excitonic coherence domains at high temperature (strong extended disorder). Whereas a mean-field theory correctly deals with the long-range forces involved in emission, these approximations are reviewed and tested on a simple model case the nondipolar triplet naphthalene exciton. The very strong disorder then makes the inclusion of aggregates in the theory compulsory. From all this study, our conclusion is that an effective-medium theory needs an effective interaction as well as an effective potential, as shown by the comparison of our theoretical results with exact numerical calculations, with very satisfactory agreement at all concentrations. Lastly, the 3D case of a dipolar exciton with disorder is discussed qualitatively. 

The model of an isolated layer was refined by introducing substrate effects by coupling the surface 2D excitons to the bulk polaritons with coherent effects modulating the surface emission and incoherent k-dependent effects damping the surface reflectivity and emission, both effects being treated by a KK analysis of the bulk reflectivity. The excitation spectra of the surface emission allowed a detailed analysis of the intrasurface relaxation dominated by resonant Raman scattering, by vibron fission, and by nonlocal transfer of... 

Figure 4.2. Variation of the radiative width y, or coherent emission rate, of a 2D disordered exciton as a function of the disorder strength A. For A > g,r, the emission becomes incoherent. For all distributions, including the gaussian distribution, there is threshold behavior with a sudden takeoff of the coherent emission.

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

The ground state population Green function is Ggg = 1, and the one-exciton population Green function Ge,e can be partitioned into the coherent and the incoherent parts, respectively ... 

The description of excitation motion outlined in the previous sections assumes completely incoherent nearest neighbor hopping. This was treated in detail because it is the case of widest applicability especially with the materials of interest discussed in the final section. However, it should be noted that in some cases excitons can move coherently over several lattice spacings before being scattered i). For this case the diffusion coefficient is expressed in terms of the group velocity of the exciton v and the time between scattering events r. 

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. 

The spectrum of the excitations is shown in Fig. 10.5 for 2 A = 80 meV. The dashed lines show the uncoupled molecular excitons and photons, and the solid lines show the coherent part of the spectrum with well-defined wavevector. The crosses show the end-points of the spectrum of excitations for which q is a good quantum number. The spectrum of incoherent (weakly coupled to light) states is shown by a broadened line centered at the energy Eq. It follows from the expression for the dielectric tensor that this spectrum is the same as the spectrum of out-of-cavity organics. The spectrum of absorption as well as the dielectric tensor depend on temperature. This means that in the calculation of the temperature dependence of the polariton spectrum we have to use the temperature dependence of the resonance frequency Eo as well as the temperature dependence of 7 determining the width of the absorption maximum. However, the spectrum of emission of local states which pump polariton states can be different from the spectrum of absorption. The Stokes shift in many cases... 

Various methods have been developed that interpolate between the coherent and incoherent regimes (for reviews see, e.g. (3)-(5)). Well-known approaches use the stochastic Liouville equation, of which the Haken-Strobl-Reineker (3) model is an example, and the generalized master equation (4). A powerful technique, which in principle deals with all aspects of the problem, uses the reduced density matrix of the exciton subsystem, which is obtained by projecting out all degrees of freedom (the bath) from the total statistical operator (6). This reduced density operator obeys a closed non-Markovian (integrodifferential) equation with a memory kernel that includes the effects of (multiple) interactions between the excitons and the bath. In practice, one is often forced to truncate this kernel at the level of two interactions. In the Markov approximation, the resulting description is known as Redfield theory (7). 

As can be seen from eqn (14.8), the calculation of the tensor reduces to the calculation of two-particle correlation functions. The lack of sufficiently detailed data on the exciton band structure and the exciton-phonon coupling constants considerably complicates the accurate calculation of the two-particle correlation functions and the exciton diffusion coefficients. However, the temperature dependence of this coefficient differs significantly for coherent and incoherent excitons (see below). Therefore, studying the temperature dependence of diffusion has always been an important tool to analyze the character of the energy transfer in molecular crystals. In the remainder of this chapter, we will focus on the main characteristics of the diffusion constant and its temperature dependence... 

Strong exciton phonon coupling incoherent excitons... 

STRONG EXCITON-PHONON COUPLING INCOHERENT EXCITONS 419... 

In some molecular crystals a crossover from coherent excitons (exciton mean free path l A) to incoherent ones ( k, A, Ioffe-Regel criterion) takes place with increasing temperature. We then expect that upon increasing the temperature from very low values, at some threshold temperature the decreasing behavior of the diffusion constant for coherent excitons goes over into an increasing behavior. 

FlG. 14.1. The decay rate of the transient grating signal versus 92 (9 is the angle between the pump pulses) for anthracene crystals at 10 and 20 K (23). The magnitude of the slope is proportional to the diffusion constant of the excitations in the crystal. With increasing temperature, the diffusion constant decreases. The average diffusion constant obtained from these data is about 10 times larger than the value expected for incoherent exciton motion (25). 

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