Doorway wavepacket

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... 

We assume that the external field is peaked at the time -to and the temporal gate at the time t = 0. Changing in the doorway wavepacket the variable t" = t + to - t, we can rewrite equation (D2) as... 

III. Wigner Wavepackets in Phase Space The Doorway—Window Picture... 

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... 

Similar to the correlation measurements discussed in the previous sections, we can define the doorway and window wavepackets and write the signal as their overlap in phase space. The derivation is presented in Appendix E, and we have... 

The doorway-window picture applies here as well. We can use Eqs. (4.5)-(4.8) provided we replace the pump wavepacket by W2 and the probe wavepacket W 2 by 43. 

APPENDIX D PHASE-SPACE DOORWAY-WINDOW WAVEPACKETS FOR FLUORESCENCE... 

We now derive the expression for the fluorescence signal in terms of the doorway and window wavepackets instead of the four-point correlation function. We start with Eq. (3.1) and write the four-point correlation function F(4) explicitly as the trace with respect to the equilibrium density matrix. We then use the cyclic invariance of the trace and obtain... 

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) ... 

Similar to the fluoiesence discussed in Appendix D, we can define doorway and window wavepackets and write the signal as their phase-space overlap. Assuming that the delay time between the probe and the pump pulses is to, we obtain Eqs. (4.5)-(4.8). 

There are many useful tools to help focus attention on specifiable parts of the behavior of a many-body system, and many of these were listed in Section 9.1.4. The concepts of bright state, doorway state, and dark state, the experimental tools of state-selective excitation and detection, and the analysis tools of wavepackets and survival and transfer probabilities, can provide insights into the causes, preferred pathways, and possibilities for control of intramolecular dynamics. 

Whatever the detection technique, the window stage of the 4WM event must convert these evolved vibrational wavepackets into the third order polarization field that oscillates at an ensemble distribution of optical frequencies. One must be alert to the possibility that the window event after doorway channel B may involve resonances from electronic state manifold e to some higher manifold, say r. Thus channel B followed by an (ket) or a e (bra) event might be enhanced by an e-to-r resonance. However, it is normal to confine the... 

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