Initial state preparation laser excitation

However, some of the recent experiments cast doubt on the applicability of this assumption. First, experiments done in the gas phase are few-body problems where taking the thermodynamic limit is not always appropriate. In other words, we have to take into account the fact that the size of the environment is finite. Second, initial states prepared by laser are so highly excited that the timescale for the energy redistribution would be comparable to that of the reaction. Third, the timescale for observing reactions can be much shorter than that for relaxation. Therefore, dynamical behavior of reactions should be studied without assuming local equilibrium. 

From a theoretical perspective, the object that is initially created in the excited state is a coherent superposition of all the wavefunctions encompassed by the broad frequency spread of the laser. Because the laser pulse is so short in comparison with the characteristic nuclear dynamical time scales of the motion, each excited wavefunction is prepared with a definite phase relation with respect to all the others in the superposition. It is this initial coherence and its rate of dissipation which determine all spectroscopic and collisional properties of the molecule as it evolves over a femtosecond time scale. For IBr, the nascent superposition state, or wavepacket, spreads and executes either periodic vibrational motion as it oscillates between the inner and outer turning points of the bound potential, or dissociates to form separated atoms, as indicated by the trajectories shown in Figure 1.3. 

In order to achieve coherent control in a laboratory experiment, three major requirements are to be met. Well-defined final states cannot be reached without the preparation of a well-defined initial state. Ultrashort, spectrally wide and intense laser pulses at different wavelengths must be produced for excitation and a good characterization of the final product states must be achieved. 

Once the cluster is prepared in its initial state, described usually by the ground state wavefuiiction the exciting laser pulse is switched on. Let s assume... 

Collision-induced electronic transitions between ion-pair states of the iodine molecule have been investigated in several laboratories (Ubachs, et al, 1993, Akopyan, et al., 2001, Fecko, et al, 2002). Initial levels in the E(0+) state were prepared by two-step laser excitation through the B3IIoe state, and final levels were monitored by dispersed fluorescence. Both near resonant and broad vibrational level distributions were observed for transfer to the D(0+) state, depending upon the initial vibrational level and collision partner. 

Once the cluster is prepared in its initial state, described usually by the ground state wavefunction 4 o(t), the exciting laser pulse is switelied on. Let s assume for the moment that the laser pulse is infinitely short (we modify this assumption later). This simply means that the whole wavefunction is promoted into the excited state, i.c., the Hamiltonian has instantaneously changed from Hj into the excited state Hamiltonian H. The wavefunction is then no more an eigenfunction of the Hamiltonian H and the system starts to evolve according to the time-dependent Sclirodingcr eejuation... 

Figure 4.4 Illustration of different state preparations by laser excitation (a) transition from a single initial state to one final state, (b) transition from a single initial state to a superposition of final states, (c) exciting a Boltzmann distribution of initial states.

Resonantly enhanced n photon PES is often best described as the preparation of an excited neutral state by (n-l)-photons, followed by one-photon ionization. Thus, the PES will contain the same information as conventional one-photon PES except that the "initial state in the ionization event will be an electronic excited state rather than the ground state. Thus, the structure of the n-photon PES will reflect the difference between the excited neutral state and the states of the ion. The use of pulsed laser ionization creates the electrons at a well defined point in time and space. This makes it possible to design relatively simple spectrometers which measure the time-of-flight TOF for the electron to travel from the point of ionization to the detector. 

Excited n molecules are not discussed here. However, energy transfer in-electronically excited states has been recently studied. In this case a complete preparation of different initial quantum states is possible by laser excitation. The subsequent collisional redistribution can be studied by dispersing the fluorescence or probing the neighboring levels with a second laser. In this way state-to-state data can be obtained. Systems investigated include ZnH, CdH and CaF(A n 2 3/2 gases. 

Section 4 contains an analysis of the proper description of the state of the system which is initially prepared in a collision experiment involving a laser-excited atom. Here an adiabatic analysis will be used to point out several inadequacies in simple semiclassical treatment of these spin-changing transitions. Finally, section 5 is devoted to a presentation of the orbital-locking models of Hertel and co-woikers [10-12]. The insights gained in our more exact quantum treatment will be used to examine critically the validity of these models. A brief conclusion follows. 

The primary difficulty arises from the fact that although it is most convenient to carry out the scattering calculation in a coupled basis [section 2] in which the total angular momentum is a good quantum number, the wavefunction of two atoms at infinite separation can best be expressed in an uncoupled basis. To illustrate this point, consider the initial state of the diatomic (atom+laser-excited atom) prior to collision. Prior to the collision the relative oibital angular momentum d is always oriented peipendicular to the collision plane, in other words d is always perpendicular to the collision-frame z-axis, which, as discussed in section 3, is coincident with Vj i, the initial relative velocity vector. If the electric field vector of the pump laser, which defines the laboratoiy-fixed Z axis, is chosen to lie parallel to Vi i(Fig. 3), and if we consider a P<- S excitation process, then, as discussed in section 3, only the P =o(ij=l ttij=0>) atomic state is prepared [13-15,31]. Since Z and Vj i are coincident pnor to the collision, the collision-frame and laboratory-frame z-axes are identical This we shall refer to as parallel... 

The ability of fs laser excitation to prepare localized initial states has been discussed in Chapter 8. Here we describe a remarkable early experiment that shows the localization of the region where non-adiabatic transitions are important. The system is again Nal where, cf Figure 9.11, the upper adiabatic electronic state, that near equilibrium is essentially covalent in character and has its shallow minimum much to the right compared with the ground state. A 50 fs UV pulse prepares a localized state with a fair amount of vibrational energy, at the left turning point of the upper adiabatic electronic state. This non-stationary localized initial state... 

Figure 1. Intramolecular vibrational density redistribution IVR of Na3

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