Interference between electronic states

This approach was used by Elliott and co-workers to control the ionization of alkali atoms by one- and two-photon excitation. Wang and Elliott [72] measured the interference between outgoing electrons in different angular momentum states. They showed, for example, that the angular flux of the p2P and the d2D continua of Rb is determined by the phase difference... 

The physical meaning of the linear combination is that individual electrons are not necessarily in either state <3>a or and that interference between ipi and t/j2 has an important influence on the physical properties of the system. 

A more sophisticated version of the Tannor-Rice scheme exploits both amplitude and phase control by pump-dump pulse separation. In this case the second pulse of the sequence, whose phase is locked to that of the first one, creates amplitude in the excited electronic state that is in superposition with the initial, propagated amplitude. The intramolecular superposition of amplitudes is subject to interference whether the interference is constructive or destructive, giving rise to larger or smaller excited-state population for a given delay between pulses, depends on the optical phase difference between the two pulses and on the detailed nature of the evolution of the initial amplitude. Just as for the Brumer-Shapiro scheme, the situation described is analogous to a two-slit experiment. This more sophisticated Tannor-Rice method has been used by Scherer et al. [18] to control the population of a level of I2. The success of this experiment confirms that it is possible to control population flow with interference that is local in time. 

An example of the use of Eq. (2) is provided by the wavepacket interferometry experiments of Scherer, Fleming et al. [11]. These workers have demonstrated that the phase of the light can be used to control constructive versus destructive interference of wavepackets in the excited electronic state. An alternative way of interpreting their experiment is that the phase of the second pulse relative to the first determines the direction of population transfer between the two electronic states. In the spirit of the present discussion, absorption versus stimulated emission is being controlled by the choice of phase of the light relative to the instantaneous pge peg Since the direction of population transfer is not determined in this case by population inversion... 

Fig. 9. The absorption spectrum of quinoxaline in durene at 4.2°K. The transition to the lower electronic state ( w ) is very sharp, that to the higher state (V77 ) is diffuse. The structure on the diffuse origin of the mr transition is real and very complex In this region there is interference between the two states.

Figure 5.13 Helium photoelectron angular distribution in the He+(2p) channel (logarithmic scale). x-Axis cosine of the electron ejection angle relative the laser polarization, y-axis total energy (1 a.u. 27 eV). (a) After the XUV-pulse after the IR-pulse for three different time delays, separated from each other by half the IR-pulse period, 15.53 fs (b), 16.87 fs(c), and 18.21 (d). The fringes in (b)-(d) arise due to the interference between the (XUV-pulse) direct ionization from the ground state and the (IR-pulse) ionization from the doubly excited populated by the XUV-pulse.

Fig. 15.8. Schematic one-dimensional illustration of electronic predissociation. The photon is assumed to excite simultaneously both excited states, leading to a structureless absorption spectrum for state 1 and a discrete spectrum for state 2, provided there is no coupling between these states. The resultant is a broad spectrum with sharp superimposed spikes. However, if state 2 is coupled to the dissociative state, the discrete absorption lines turn into resonances with lineshapes that depend on the strength of the coupling between the two excited electronic states. Two examples are schematically drawn on the right-hand side (weak and strong coupling). Due to interference between the non-resonant and the resonant contributions to the spectrum the resonance lineshapes can have a more complicated appearance than shown here (Lefebvre-Brion and Field 1986 ch.6). In the first case, the autocorrelation function S(t) shows a long sequence of recurrences, while in the second case only a single recurrence with small amplitude is developed. The diffuseness of the resonances or vibrational structures is a direct measure of the electronic coupling strength.

Extended X-ray absorption fine structure (EXAFS) on the other hand, is due to the interference of electron waves between atoms, and provides local structure information that is limited to a few interatomic distances. Here, we talk about the distance and the number of nearest and next-nearest neighbors of atoms in the catalyst. The more uniform the environment is through the catalyst, the more meaningful is the EXAFS information. Related to this method is X-ray absorption near edge spectroscopy (XANES), which deals with the detailed shape of the absorption edge, and yields important information on the chemical state of the absorbing atom. Commonly, one uses nowadays the acronym XAFS to include both EXAFS and XANES. 

---