Absorption spectrum, quantum interference

The quantum theory of spectral collapse presented in Chapter 4 aims at even lower gas densities where the Stark or Zeeman multiplets of atomic spectra as well as the rotational structure of all the branches of absorption or Raman spectra are well resolved. The evolution of basic ideas of line broadening and interference (spectral exchange) is reviewed. Adiabatic and non-adiabatic spectral broadening are described in the frame of binary non-Markovian theory and compared with the impact approximation. The conditions for spectral collapse and subsequent narrowing of the spectra are analysed for the simplest examples, which model typical situations in atomic and molecular spectroscopy. Special attention is paid to collapse of the isotropic Raman spectrum. Quantum theory, based on first principles, attempts to predict the. /-dependence of the widths of the rotational component as well as the envelope of the unresolved and then collapsed spectrum (Fig. 0.4). 

As can be seen, the interference in each pair of lines does not disappear even in the lower order of perturbation theory when off-diagonal elements of the S-matrix are linear in V. In the doublet, which represents the absorption spectrum, pi is the quantum equivalent of Gordon s classical... 

The narrow resonances produced by quantum interference may also be observed in the absorption spectrum of a three-level atom probed by a weak field of the frequency o> ). Zhou and Swain [10] have calculated the absorption spectrum of a probe field monitoring E-type three-level atoms with degenerate (A = 0) as well as nondegenerate (A / 0) transitions and have demonstrated that quantum... 

Zhou and Swain [10] have shown that in the presence of initial correlations between the upper states, the hole in the center of the spectrum can reach negative values, indicating that the probe can be amplified as a result of quantum interference. Paspalakis and Knight [39] have calculated the absorption... 

If the excited state potential surface is repulsive, so that the dissociative trajectories are direct , the dipole matrix element will be a smooth function of 2, i.e. the absorption spectrum is continuous . If, on the other hand, V2 t) is attractive so that the complex ABC lives a long time before dissociating into A and BC, the quantum number function nfN Q ) will be highly structured (cf, Fig, 8) and thus a large number of terms will contribute to(125). Analogous to the semiclassical discussion of resonances in Section III.C, these many terms will interfere destructively at all but certain specific values of E2 at which the interference is constructive and the matrix element extremely large. In such cases, therefore, there will be a line spectrum , with the width of the absorption lines related to the time the excited state lives before dissociating,... 

To conclude, the results presented in this section demonstrate that the semiclassical implementation of the mapping approach is able to describe the ultrafast dynamics in the pyrazine system. In particular, it is capable of describing the correct relaxation dynamics as well as the structures of the absorption spectrum. The former is related to a correct treatment of the zero-point energy, the latter reflects the correct inclusion of quantum interference effects. The ability to describe these quantum effects is in contrast to the quasiclassical implementation of the mapping approach discussed in Sec. 6. The semiclassical version of the mapping approach should, therefore, also be well suited to describe time-resolved nonlinear spectra. 

In fact, the broadening of particle size distribution can interfere sufficiently in the absorbance spectrum near the onset to deviate gap measurements significantly by the onset of extrapolation. Pesika and collaborators [77,78] proposed the inverse observation, i.e., particle size distribution by absorbance spectra measurements. The absorbance A at any wavelength A in the quantum regime is related to the total volume of particles with radius greater than or equal to the size corresponding to the onset of absorption, in a diluted concenttation limit (absorbance will occur continuously since the critical size is reached). For spherical particles, assuming that the absorption coefQcient is independent of particle size, we have... 

The continuous spectrum is also present, both in physical processes and in the quantum mechanical formalism, when an atomic (molecular) state is made to interact with an external electromagnetic field of appropriate frequency and strength. In conjunction with energy shifts, the normal processes involve ionization, or electron detachment, or molecular dissociation by absorption of one or more photons, or electron tunneling. Treated as stationary systems with time-independent atom - - field Hamiltonians, these problems are equivalent to the CESE scheme of a decaying state with a complex eigenvalue. For the treatment of the related MEPs, the implementation of the CESE approach has led to the state-specific, nonperturbative many-electron, many-photon (MEMP) theory [179-190] which was presented in Section 11. Its various applications include the ab initio calculation of properties from the interaction with electric and magnetic fields, of multiphoton above threshold ionization and detachment, of analysis of path interference in the ionization by di- and tri-chromatic ac-fields, of cross-sections for double electron photoionization and photodetachment, etc. 

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