Stokes-pump sequence

This can be analyzed with the help of Fig. 8, where we have taken AP = 0. The intuitive pump-Stokes sequence induces first a lifting of degeneracy with equal sharing between the dressed states /+) (the upper one, associated to the eigenenergy X+) and v / ) (the lower one, associated to the eigenenergy X ) initially connected to 1) and 2). If we assume that the peak pump field amplitude is beyond the conical intersection, then the branches / ) and v(/+), respectively, connect —12) and 3) at the end. When As < 0 (as in Fig. 8), this leads at the end of the process to the coherent superposition with a dynamical phase (up to an irrelevant global phase)... 

Figure 3.24 Schematic diagram of the pulse sequence in the composite STIRAP protocol. Note the Stokes and pump pulses are reversed between successive pulse pairs when the Stokes and pump pulses are resonant with the level spacing, whereas they are not reversed between successive pulse pairs when the Stokes and pump pulses are off resonance with the level spacing. (From Ref. 77).

An example of a STIRAP simulation and experiment is illustrated in Figs. 24 and 25 for SO2. Figure 24 shows the energies of the laser pulses used to transfer population from the vibrationless level to the (9, 1, 0) level of the ground electronic state. Figure 25 shows the experimentally measured and numerically simulated fraction of the population transferred to the excited state as a function of the time delay between the pump and Stokes pulses. The greater efficiency of a counterintuitive pulse sequence is evident. 

The adiabatic passage induced by two delayed laser pulses, the well-known process of STIRAP [69], produces a population transfer in A systems (see Fig. 7a). The pump field couples the transition 1-2, and the Stokes field couples the transition 2-3. It is known that, with the initial population in state 11), a complete population transfer is achieved with delayed pulses, either (i) with a so-called counterintuitive temporal sequence (Stokes pulse before pump) for various detunings as identified in Refs. 73 and 74 or (ii) with two-photon resonant (or quasi-resonant) pulses but far from the one-photon resonance with the intermediate state 2), for any pulse sequence (demonstrated in the approximation of adiabatic elimination of the intermediate state [75]). Here we analyze the STIRAP process through the topology of the associated surfaces of eigenenergies as functions of the two field amplitudes. Our results are also valid for ladder and V systems. 

In the following, we describe in detail the case of Fig. 8. For the process in A or ladder systems, where the initial population resides in state 1), two different adiabatic paths lead to the complete population transfer, depending on the pulse sequence. The path denoted (a) corresponds to an intuitive sequence for the rise of the pulses. The pump pulse is switched on first, making the levels connected to the states 1) and 2) repel each other (dynamical Stark shift) until the level connected to 11) crosses the level connected to 3). The Stokes pulse is switched on after the crossing. Next the two pulses can decrease in any order. Path (b) is associated to a counterintuitive sequence for the decrease of the pulses. The two... 

Figure 10 shows that, for the process in A (or ladder) systems, two different adiabatic paths lead to different complete population transfers, depending on the pulse sequence. Path (a) corresponds to an intuitive pulse sequence (for the decrease of the pulses) and allows pulses to populate at the end the state 2). The Stokes and pump pulses can be switched on in any sequence and the pump pulse is switched off before the Stokes one. The path (b) corresponds to a counterintuitive pulse sequence (for the rise of the pulses) and allows pulses to populate at the end the state 3). The Stokes pulse is switched on before the pump, and the stokes pulse has to be switched off before the pump. We can thus selectively populate the states 2) or 3), provided that the peak amplitudes are sufficiently strong to induce the adiabatic path to cross the intersection involved. 

The counterintuitive Stokes-pump sequence leads to the transfer to the unique state 3). 

The topological analysis thus shows that with two quasi-resonant delayed lasers it is not possible to end in a superposition of states between the lowest states 1) and 13) in a robust way. We can remark that in Ref. 76, it has been shown that one can create such a superposition—however, in a nonrobust way but still by adiabatic passage, by modifying the end of the STIRAP process (with the counterintuitive sequence), maintaining a fixed ratio of Stokes and pump pulse amplitudes. 

Contrary to stimulated emission pumping with the time sequence pump pulse-Stokes pulse, where a maximum of 50 % of the population can be transferred to 3) (because a maximum population difference 2 - A i = 0 N2 = Ni(0)/2 and N3 - N2 = 0 N3 = N2 = Ni (0)/2 can be reached), a transfer efficiency of 100 % can be achieved with the SIRAP technique [889]. The population N3 can be monitored through the laser-induced fluorescence induced by a weak third laser (probe laser in Fig. 7.15e). 

The corresponding reorientational relaxation times for these linear anions were also studied by the infrared pump/probe technique by Li et al. [162]. However, NMR spin-lattice relaxation times have been employed for other polyatomic ions, using the nuclei NforNOj" [162], forClO " [163], N for NH/ [164], and C for several tetraalkylammonium cations [165] according to Masuda and coworkers. The results are shown in Table 5.10. It was concluded that these times do not follow the expected (Stokes-Einstein-Debye) hydrodynamic solvent sequences according to the solvent... 

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