Pump-probe signal wavepackets

Figure 8. Frequency-filtered Na2+ pump-probe signal in comparison to the averaged signal of Fig, 4. The filtered signal measures by how much the Na2+ signal is modulated with the laser frequency. Such modulations occur when there is interference between excitation by the probe pulse and the wavepackets formed by the pump laser pulse. This interference effect causes both the A EJ and the 2 1 Ilg state wavepacket motion to be observable in the signal.

Appendix C Four-Point Correlation Function Expression for Fluorescence Spectra Appendix D Phase-Space Doorway-Window Wavepackets for Fluorescence Appendix E Doorway-Window Phase-Space Wavepackets for Pump-Probe Signals References... 

The first term in Eq. (4.3) is reminiscent of Eq. (3.2) for the spontaneous emission spectrum. It represents a doorway wavepacket created by the pump in the excited state, which is then detected by its overlap with a window. The only difference is that the role of the gate in determining the window in SLE is now played by the probe Wigner function W2. In addition, the pump-probe signal contains a second term that does not show up in fluorescence. This term represents a wavepacket created in the ground state (a hole ) that evolves in time as well and is finally determined by a different window Wg [24]. In the snapshot limit, defined in the preceding section, we have... 

APPENDIX E DOORWAY-WINDOW PHASE-SPACE WAVEPACKETS FOR PUMP-PROBE SIGNALS... 

We shall calculate here the pump-probe signal (4.1) using the doorway window wavepackets representation. The polarization 3 2(/> to third order in the external field is given in Ref. 17 and is shown to be expressed in terms of the four-point correlation function (2.8) ... 

It is seen that the bifurcations are nearly removed and that now the motion is much more in favor of a counterclockwise rotation. In fact, one finds that 83% of the rotational wavepackets move in this direction. The classical trajectories exhibit a dynamics similar to that of the quantum densities. This is true for the ones moving freely but also for the trapped trajectories which do not have enough energy to escape the potential wells for a discussion of similar features and their relation to femtosecond pump-probe signals, see Ref. 214. 

When the pump-probe delay is varied slowly and continuously (i.e., both parameters are varied simultaneously), the high-frequency oscillations due to the optical phase of the wavepacket can be resolved in the transient signal, as shown by Blanchet et al. [27], who monitored the wavepacket motion and... 

We have employed this phase-sensitive pump-probe technique to further investigate the multiphoton ionization of Na2 with 618-nm femtosecond pulses as discussed in the previous paragraph and have observed the interference of the A E and 2 Tlg wavepackets created by the first pulse and those created by the second pulse in the Na2+ signal. The amplitude of the high-frequency oscillations in the Na2+ signal was obtained as a function of pump-probe delay by filtering the transient with the laser frequency. It is shown in Fig. 8 (top). Below the averaged Na2+ transient of Fig. 4 is... 

On the other hand, additional spectroscopic information can be obtained by making use of this technique The Fourier transform of the frequency-filtered transient (inset in Fig. 8) shows that the time-dependent modulations occur with the vibrational frequencies of the A E and the 2 IIg state. In the averaged Na2+ transient there was only a vanishingly small contribution from the 2 IIg state, because in the absence of interference at the inner turning point ionization out of the 2 IIg state is independent of intemuclear distance, and this wavepacket motion was more difficult to detect. In addition, by filtering the Na2+ signal obtained for a slowly varying pump-probe delay with different multiples of the laser frequency, excitation processes of different order may be resolved. This application is, however, outside the scope of this contribution and will be published elsewhere. 

Figure 18. Transient Na3+ signal for strongly attenuated 80-fs pump-probe laser pulses of 620 nm. The frequencies observed in the Fourier transform are due to vibrational wavepacket motion on the B state potential.

The wavepacket calculation for the femtosecond pump-probe experiment presented in Fig. 16 (bottom) is the result of the first consistent ab initio treatment for three coupled potential-energy surfaces in the complete three-dimensional vibrational space of the Naa molecule. In order to simulate the experimental femtosecond ion signal, the experimental pulse parameters were used duration A/fWhm = 120 fs, intensity I - 520 MW/cm2, and central... 

H. Rabitz The information in the recurrence time alone is minimal. However, the temporal structure of the recurrence signal contains detailed information on the surface explored by the wandering scout wavepacket during its excursion. Further experiments may be necessary to follow (i.e., track) the wavepacket through its excursion over the potential surface. Such pump-probe experiments go beyond conventional spectroscopy. 

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