Feynman double-sided diagram

Figure 14. Liouville space coupling schemes and their respective double-sided Feynman diagrams for three of the six pathways in Liouville space which contribute to p 2. The complex conjugates are not shown. All pathways proceed only via coherences, created by the interactions with the two fields shown as incoming arrows. Solid curves pertain to e( 11 and dashed curves to r/2T (Reproduced with permission from Ref. 47, Copyright 2005 American Institute of Physics.)...

In the response function formalism developed by Mukamel [1], all four wave-mixing spectroscopies are described by four response functions, R, ..., i 4, and their complex conjugates. Double-sided Feynman diagrams are shown in Fig. 12 representing these response functions. The response functions in turn are described by a single line shape function g t) given by... 

Figure 2 The double-sided Feynman diagrams, which have to be considered in (a) a linear absorption experiment and (b) a nonlinear third-order experiment such as photon echo, pump-probe, transient grating. The diagrams are arranged according to the possible time orderings, as discussed in the text and illustrated in Fig. 4.

Figure 5 Double-sided Feynman diagrams representing the two Liouville space pathways contributing to photon echo representing (1) correlations between one-exciton states, and (2) correlations between one- and two-exciton states.

In this appendix we present the sum-over-one- and two-exciton state expressions for the third-order response function. Double-sided Feynman diagrams representing the Liouville space pathways contributing to the four wave mixing in the RWA are given in Fig. IB. The response function is... 

Figure Al.6.17. Double-sided Feynman diagrams, showing the interaction time with the ket (left) and the bra (right). Time moves forward from down to up (adapted from [36]).

The main cost of this enhanced time resolution compared to fluorescence upconversion, however, is the aforementioned problem of time ordering of the photons that arrive from the pump and probe pulses. When the probe pulse either precedes or trails the arrival of the pump pulse by a time interval that is significantly longer than the pulse duration, the action of the probe and pump pulses on the populations resident in the various resonant states is unambiguous. When the pump and probe pulses temporally overlap in the sample, however, all possible time orderings of field-molecule interactions contribute to the response and complicate the interpretation. Double-sided Feynman diagrams, which provide a pictorial view of the density matrix s time evolution under the action of the laser pulses, can be used to determine the various contributions to the sample response [125]. 

Fig. 11.5 Double-sided Feynman diagrams for third-order polarization in a two-state system. The symbols have the same meanings as in Fig. 11.2. The times between the interactions with the radiation field are indicated by tj, and T3. Diagrams Ri-R4 correspond to the Liouville-space paths in Fig. 11.4B and to third-order nonlinear response functions/fj to/f4 (Eq. 11.37). However, only stimulated emission that repopulates the ground state is shown fin the fourth interaction with the field. This interaction also could convert the last coherence or its ctnnplex conjugate to...

Fig. 11.6 Double-sided Feynman diagrams for the third-order polarization in a three-state system. Pathways that generate or pass through a coherence involving the third state are shown. Each of these has a complex conjugate that is not shown. Only formation of the third state is shown for the fourth interaction in pathways / j to R, and only regeneration of the groimd state in R4...

Fig. 11.9 Double-sided Feynman diagrams for the third-order polarization pathways that generate photon echoes within the rotating-wave approximation (paths R2, R3, and their complex conjugates), and the pathways that survive the rotating-wave approximation but do not goierate photon echoes (paths Ri, R4, and their complex conjugates). If the first three infi actitnis with the field occur during three separate pulses as in Fig. 11.8, delaying pulse 1 so that it follows pulse 2 converts R2 into Ri and R3 into R4...

Su, J.-J., Yu, I.A. The study of coherence-induced phenomena using double-sided Feynman diagrams. Chin. J. Phys. 41, 627-642 (2003)... 

Fig. 12.3 Liouville-space diagrams for spontaneous fluorescence and Raman scattering. (A) Liouville-space pathways connecting an initial state (a), intermediate state (k) and a flnal state (h). (See Sect. 11.1, Figs. 11.1 and 11.4 for an explanation of these diagrams.) (B-D) Three of the six possible paths from atoh with four steps (four interactions with a radiation held). The other three paths are the complex conjugates of the ones shown. All six paths contribute to spontaneous fluorescence Raman scattering involves only path (D) (and its complex conjugate), in which the intermediate state is never populated. (E) A double-sided Feynman diagram for path (D)...

Fig. 12.9 Liouville-space and double-sided Feynman diagrams for two-photon absOTptirai (A, B) and a representative pathway resulting in ordinary excited-state absorption (C, D). The ground state and the final excited state are labeled a and b. Excited-state absorption requires populating an intermediate state (i), whereas two-photon absorption proceeds entirely through coherences. Both processes also occur by the complex conjugates of the pathways shown. Excited-state absorption also can occur by the pathway shown in Fig. 12.3B and its complex conjugate...

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