Overlapping resonances interference

The possibility that overlapping resonances interfere allows for the minimization of absorption of transient light through optical materials, which results in transparency for such systems under specific conditions. Two examples are discussed in this section the ORIT in the photoexcitation spectrum of pyrazine and the FIT with multicontinuum structures. The latter example is presented in detail since it elucidates the idea of overlapping resonances formation due to external laser fields, on which then the TOR can be applied. 

The important feature of resonances is that when the widths of states in Q are larger than their associated level spacing, such states, termed now overlapping resonances, can interfere with one another. The quantum dynamics of systems with overlapping resonances show a rich variety of interesting physical phenomena furthermore, in such systems there is potential for quantum control... 

An analytical theory for the study of CC of radiationless transitions, and in particular, IC leading to dissociation, in molecules possessing overlapping resonances is developed in Ref. [33]. The method is applied to a model diatomic system. In contrast to previous studies, the control of a molecule that is allowed to decay during and after the preparation process is studied. This theory is used to derive the shape of the laser pulse that creates the specific excited wave packet that best enhances or suppresses the radiationless transitions process. The results in Ref. [33] show the importance of resonance overlap in the molecule in order to achieve efficient CC over radiationless transitions via laser excitation. Specifically, resonance overlap is proven to be crucial in order to alter interference contributions to the controlled observable, and hence to achieve efficient CC by varying the phase of the laser field. 

ORIT in the Photoexcitation Spectrum in Pyrazine The ORIT phenomenon, where a photoabsorption transparency window occurs at certain frequencies due to interference between material waves within a molecule, is briefly considered here. Though ORIT is known for small systems [25,27], it has not been investigated for polyatomic molecules where overlapping resonances... 

The method is based on the fact that one can excite coherently a set of overlapping resonances such that their decay exhibits a steplike behavior the system starts in a quiescent period in which no spontaneous emission occurs, followed by a photon burst in which spontaneous emission is greatly accelerated, followed by another quiescent period, and so on. The quiescent period (and subsequent photon bursts) is due to destructive and constructive interferences between the overlapping resonances. The reason it is impossible to suppress the decay over all times in this... 

In this review, we have discussed the Feshbach-Lowdin PT as a tool for studying multidimensional quantum dynamics of (molecular) systems. The central element in this approach is the emergence of overlapping resonances through the application of the PT on the Hilbert space of the system under study, and the possibility that such resonances ultimately interfere. The TOR, which is the result of this approach, provides a fruitful method to understand and conceptually link diverse physical phenomena and processes. We have tried to demonstrate this by discussing various examples, as FIT and ORIT, the suppression of spontaneous decay in atoms and molecules, and the CC of IC in pyrazine and / -carotene, as well as of IVR in the OCS molecule. 

Pulsed laser-Raman spectroscopy is an attractive candidate for chemical diagnostics of reactions of explosives which take place on a sub-microsecond time scale. Inverse Raman (IRS) or stimulated Raman loss (.1, ) and Raman Induced Kerr Effect (2) Spectroscopies (RIKES) are particularly attractive for singlepulse work on such reactions in condensed phases for the following reasons (1) simplicity of operation, only beam overlap is required (2) no non-resonant interference with the spontaneous spectrum (3) for IRS and some variations of RIKES, the intensity is linear in concentration, pump power, and cross-secti on. 

The vanishing of the line shapes at certain points due to the interference between resonance, firs t discovered in the context of overlapping resonances of van der Waals complexes [14], is shown in Figure 9.6. 

FIG. 26. The high-field regions of spectra of l-dimethylamino-2-melhylpropene. (a) Proton-decoupled spectrum, (b)-(d) Multiplet sub-spectra corresponding to the three methyl resonances P, Q, and R respectively, (e) Full proton-coupled spectrum, showing overlapping and interference from acetone-df, and tetramethylsilane. From ref. 23. 

M. Shapiro (1972) has carried out a computational investigation of uni-molecular decomposition. He chose the Van der Waals complex Xe-D2 as an example and described interference effects due to overlapping resonances of the complex within the context of scattering theory. 

It was realized early on [109], following fhe analysis of Fano [3], that the interference between overlapping resonances can give rise to "dark states." Such dark states, which are characterized by the vanishing of photo-absorpfion, were found experimenfally a few years lafer [111, 112]. They feafure very highly in many applications in coherenf optics and in particular in "lasing without inversion" [13,113, 114] and adiabatic passage (AP) phenomena [20-23,115]. 

We start by briefly reviewing elements of "partitioning" theory [3, 5, 108-110, 118] used to treat the interference between overlapping resonances. The physical situation we address is illustrated in Figure 3.1 in which (as explained in Section 3.2) two overlapping resonances are created by optically splitting a single resonance. 

CC of photonic processes such as spontaneous emission has also been studied. Among the scenarios explored are interferences between overlapping resonances [158, 159] and direct interference between emission pathways [160-165]. The suppression of spontaneous emission in free space [160] or band-gap materials [162] results in the spectral narrowing, even the complete elimination, of the spectral lines [161,163]. 

This condition ensures that the concept of resonant states remains meaningful. If this condition does not hold, the resonances overlap and interfere and should be handled in a different way (Section 11,E). In the example of elastic scattering, where the final state detected is again k> = the detection amplitude (130) is of the form... 

The decrease of the transmission coefficient with increasing coupling strength P,a arises from interference between the overlapping resonances in this particular model. 

Spectral interferences in AAS arise mainly from overlap between the frequencies of a selected resonance line with lines emitted by some other element this arises because in practice a chosen line has in fact a finite bandwidth . Since in fact the line width of an absorption line is about 0.005 nm, only a few cases of spectral overlap between the emitted lines of a hollow cathode lamp and the absorption lines of metal atoms in flames have been reported. Table 21.3 includes some typical examples of spectral interferences which have been observed.47-50 However, most of these data relate to relatively minor resonance lines and the only interferences which occur with preferred resonance lines are with copper where europium at a concentration of about 150mgL 1 would interfere, and mercury where concentrations of cobalt higher than 200 mg L 1 would cause interference. 

Spectral overlap of emission and absorption wavelengths Is a potential cause of Interference In atomic absorption spectrometry (57) Thus, (a) the emission line of Fe at 352.424 nm Is close to the resonance line of N1 at 352.454, (b) the emission line of Sb at 217.023 nm Is close to the resonance line of Pb at 216.999 nm, and (c) the emission line of As at 228.812 nm Is close to the resonance line of Cd at 228.802 (57). To date, these practically coincident spectral lines have not been reported to be of practical Importance as sources of analytical Interference In atomic absorption analyses of biological materials. 

These are the only type of interference that do not require the presence of analyte. For AAS the problem of spectral interference is not very severe, and line overlap interferences are negligible. This is because the resolution is provided by the lock and key effect. To give spectral interference the lines must not merely be within the bandpass of the monochromator, but actually overlap each other s spectral profile (i.e. be within 0.01 nm). West [Analyst 99, 886, (1974)] has reviewed all the reported (and a number of other) spectral interferences in AAS. Most of them concern lines which would never be used for a real analysis, and his conclusion is that the only real problem is in the analysis of copper heavily contaminated with europium The most commonly used copper resonance line is 324.754 nm (characteristic concentration 0.1 pg cm- ) and this is overlapped by the europium 324.753 nm line (characteristic concentration 75 pg cm- ). 

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