Interference between overlapping resonances

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]. 

Since the non-linear susceptibility is generally complex, each resonant term in the summation is associated with a relative phase, y , which describes the interference between overlapping vibrational modes. The resonant macroscopic susceptibility associated with a particular vibrational mode v, Xr, is related to the microscopic susceptibility also called the molecular hyperpolarizability, fiy, in the following way... 

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... 

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. 

In reality, one encounters overlapping multiple resonances interacting with multiple continua. The analytical expressions given here represent an idealized situation. Several examples involving interferences between different autoionization processes [for example, in H2, interference between rotational and vibrational autoionization (Fig. 8.12) in N2, interference between vibrational... 

Kim S-G, Ashe J, Hendrich K et al (1993) Functional magnetic resonance imaging of motor cortex hemispheric asymmetry and handedness. Science 261 615-617 Klingberg T, Roland PE (1997) Interference between two concurrent tasks is associated with activation of overlapping fields in the cortex. Brain Res Cogn Brain Res 6(1) 1-8 Link H27, Heath RA. A sequential theory of psychological discrimination. Psychometrika 40 77-105... 

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 interferences in AAS arise mainly from overlap between the frequencies of a selected resonance line with lines emitted by some other element, which arises because in practice a chosen line has in fact a finite band-width . With flame emission spectroscopy, there is... 

The resonance absorption lines of the various elements are very narrow, on the order of 0.002 nm, and at discrete wavelengths. Direct overlap between absorption lines of different elements is rare and can usually be ignored as a source of error. Absorption by the wings of the absorption lines of interfering elements present in high concentrations has been observed, but this is also a rare occurrence. A table of reported atomic spectral overlaps can be found in the handbook by Dean cited in the bibliography. The only cures for direct atomic spectral interference are (1) to choose an alternate analytical wavelength or... 

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