Interference between wave-packets

Upper trace no phase difference between the two laser pulses. The wave-packet promoted by the first pulse and the newly promoted wave-packet can interfere constructively whenever the time delay between the pulses is a multiple of 300 fs so that the first wave-packet is back in the Franck-Condon window. Lower trace a jc phase difference between the two laser pulses. At intervals of 300 fs the returning wave-packet interferes destructively with the new wave-packet (adapted from N. F. Scherer eta/., J. Chem. Phys. 95, 1487 (1991). For other experiments showing interference between wave-packets excited by two pulses see Baumert eta . (1997). Even an electron can be so controlled during electron transfer (Barthel eta/., 2001 Martini eta ., 2001 Bardeen, 2001)]. 

The choice of the ground state of the ion as the final state charged particles is extremely sensitive. Second, the detection of the ions provides mass information, and third, the ionization is always an allowed process. Any molecular state can be ionized, whereas the electronic spectroscopy relies on the existence of optically allowed transitions. Besides this, no Rabi oscillation between bound states, which can interfere with wave packet measurements, can occur in ionization. Further information can be obtained by analyzing the photoelectron (e.g. as to its kinetic energy), analogous to dispersed fluorescence methods. 

Figure 7.10 Wave packet interference observed with die ns probe pulse. The delay between the pump and control pulses was scanned around (a) 1.0 and (b) 1.5 The abscissa is converted into the relative phase of averaged oscillation period of y = 30—33 levels, (c) ns excitation spectra taken at fixed timings giving die phases tuned around a and shown in (a). Ref. is a reference data...

Figure 1. The creation, evolution, and detection of wave packets. The pump laser pulse pump (black) creates a coherent superposition of molecular eigenstates at t — 0 from the ground state I k,). The set of excited-state eigenstates N) in the superposition (wave packet) have different energy-phase factors, leading to nonstationary behavior (wave packet evolution). At time t = At the wave packet is projected by a probe pulse i probe (gray) onto a set of final states I kf) that act as a template for the dynamics. The time-dependent probability of being in a given final state f) is modulated by the interferences between all degenerate coherent two-photon transition amplitudes leading to that final state.

There are now direct experimental confirmations [41-43], to be discussed in Section 13.3, of the effect of the pulse shaping. In addition, the role of the phase j-1 between two pulses, predicted in both OCT [104,119] and in CC studies [94,96,1R>J. has been confirmed experimentally by Fleming et al. [137,138], Girard et al. [JO- j 142], Kinrot et al, [143], and Warmuth et al. [144] in the so-called wave paiket interferometry experiments [145], For example, Fleming et al, [137,138] [and Warmuth et al. [144] describe experiments where the fluorescence from I2 in the F t state is influenced by constructive or destructive interference between two wave pad.-, j ets induced by two-phase related excitation pulses. This study relates to a large voliuiiejy of work on wave packet interferometry in atoms [146-148], as well as to various." femtochemistry experiments, where similar effects were seen in absorption [106] . jj... 

While we have developed the theory of wave-packet scattering and resonances in the context of potential scattering of electrons it is easy to generalise. In particular there is no reason why the scattered particle should not be a photon. In this case the wave packet does not spread and the formalism is valid for general values of 3. Wave packets are known whose widths correspond to a lifetime of order lO s, which is easily resolved with nanosecond electronics. Such wave packets arise in the photon decay of many atomic states. The time spectrum of detected photons is given by (r,t)p for X < 0. We see from (4.166) that this involves an interference between a term whose lifetime is h/3 and one whose lifetime is Xr. The resulting time oscillations have been observed experimentally. They are called quantum beats. 

The picture of a single wave packet is in any case inappropriate for the description of a continuous source because it implies a well-defined internal phase structure. This is not provided in our experiment, and the beam can only be regarded as a statistical, and therefore incoherent, mixture of the various momenta. Nevertheless, the beam can operationally be characterized by a coherence length, which is the length that measures the fall-off of the interference visibility when the difference between two interfering paths increases. The longitudinal coherence length is determined by the Fourier transformation of the velocity distribution and it is of the order Lc A2/A A = Xv/ Av. 

The quantity in square brackets in (3.5) resembles the overlap kernel in the time-dependent theory of the continuous-wave absorption spectrum [34], but here involves the nonstationary ground state wave packet vibrational wave function. The interference signal in the impulsive limit directly measures the overlap between pseudo-rotating wave packets propagated in the ground and excited states for a time... 

Equations (4.1) and (4.4) predict vanishing interference for delay times halfway between complete pseudorotations, despite the fact that the ground and excited state packets are still spatially overlapping. This absence of interference is a consequence of the perpendicular and parallel selection rules mentioned below Eq. (3.8) as a result of them, the initial and reference wave packets go to different excited adiabatic surfaces for... 

Figure 6. A superposition of positive and negative energies before and after a Lorentz boost. Apart from the Lorentz contraction, the relative motion between observer and wave packet produces interference effects. The interference is caused by the separation of the negative and positive-energy parts in momentum space.

Interference Between Nuclear Wave Packets Through Nonadiabatic Coupling... 

Since nuiny processses demonstrate substantial quantum effects of tunneling, wave packet break-up and interference, and, obviously, discrete energy spectra, symmetry induced selection rules, etc., it is clearly desirable to develop meAods by which more complex dynamical problems can be solved quantum mechanically both accurately and efficiently. There is a reciprocity between the number of particles which can be treated quantum mechanically and die number of states of impcxtance. Thus the ground states of many electron systems can be determined as can the bound state (and continuum) dynamics of diatomic molecules. Our focus in this manuscript will be on nuclear dynamics of few particle systems which are not restricted to small amplitude motion. This can encompass vibrational states and isomerizations of triatomic molecules, photodissociation and exchange reactions of triatomic systems, some atom-surface collisions, etc. 

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