Wavepacket interferometry

Figure Al.6.8. Wavepacket interferometry. The interference contribution to the exeited-state fluoreseenee of I2 as a fiinotion of the time delay between a pair of ultrashort pulses. The interferenee eontribution is isolated by heterodyne deteetion. Note that the stnieture in the interferogram oeeurs only at multiples of 300 fs, the exeited-state vibrational period of f. it is only at these times that the wavepaeket promoted by the first pulse is baek in the Franek-Condon region. For a phase shift of 0 between the pulses the returning wavepaeket and the newly promoted wavepaeket are in phase, leading to eonstnietive interferenee (upper traee), while for a phase shift of n the two wavepaekets are out of phase, and interfere destnietively (lower traee). Reprinted from Seherer N F et 0/1991 J. Chem. Phys. 95 1487.

D. J. Tannor I would like to point out that the Scherer-Fleming wavepacket interferometry experiment is very different from the Tannor-Rice pump-dump scheme, in that it exploits optical phase coherence of the laser light (optical phase coherence translates into electronic phase coherence between the wavepackets on different potential surfaces). However, there was a paragraph in the first paper of Tannor and Rice [7. Chem. Phys. 83, 5013 (1985), paragraph above Eq. (11)] that did in fact discuss the role of optical phase and suggested the possibility of experiments of the type performed by Scherer and Fleming. 

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... 

One of the most important yet simple ideas that ignited excitement about fem-tochemistry is wavepacket interferometry (Salour and Cohen-Tannoudji, 1977 Scherer, et al., 1990, 1991, 1992 Jonas and Fleming, 1995 Weinacht, et al., 1999), an optical form of Ramsey-fringe spectroscopy (Ramsey, 1990). A molecular system is subjected to two identical optical pulses created by splitting one pulse at a beam splitter. The two pulses are called the pump and the probe . The time delay between pump and probe pulses is scanned systematically using an optical delay line. The optical arrangement is very similar to that of a Fourier Transform Spectrometer (Heller, 1990). The difference in the paths traveled by the pump and probe pulses, Ad, before the two pulses are recombined at a second beam splitter corresponds to a time delay, At = Ad/c, where c is the speed of light. 

Things are not quite as simple as they seem. In order for the constructive interference, which is at the core of wavepacket interferometry, to occur, not only must (t + At) = (t), but also the phases of apump and aprobe> which depend on the optical phase of the femtosecond laser rather than the molecular phase, must match. A rigorous treatment of the phase coherent pump/probe scheme using optically phase-locked pulse pairs is presented by Scherer, et al., [1990, 1991, 1992] and refined by Albrecht, et al., (1999), who discuss the distinction between and consequences of pulse envelope delays vs. carrier wave phase shifts (see Fig. 9.6). A simplified treatment, valid only for weak optical pulses is presented here. 

For 900 nm radiation, the path difference between pump and probe is stepped in 0.9 /j,m increments (or integer multiples), which corresponds to At, = 3 fs. This crucial modification is called phase coherent wavepacket interferometry (Scherer, et al, 1990, 1991, 1992) and it results in a profound simplification of... 

In this section, by applying the heterodyne interferometry to a mixed gas of H2 and D2 molecules, we probe attosecond dynamics of nuclear wavepackets in the molecules. We find that not only the single molecule responses but also the propagation effects of harmonics differ between the two isotopes and that to discuss dynamics of molecules in the single molecule responses, the propagation effects need to be excluded from the raw harmonic signals. The measured relative phase as well as intensity ratio are found to be monotonic functions of the harmonic order and are successfully reproduced by applying... 

Currently, a major theme in atomic, molecular, and optical physics is coherent control of quantum states. This theme is manifested in a number of topics such as atom interferometry, Bose-Einstein condensation and the atom laser, cavity QED, quantum confutation, quantum-state engineering, wavepacket dynamics, and coherent control of chemical reactions. 

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