Intermediate target states

Figure 6.9 Generic five-state system for ultrafast efficient switching. The resonant two-state system of Figure 6.6 is extended by three target states for selective excitation. While the intermediate target state 4) is in exact two-photon resonance with the laser pulse, both outer target states 3) and 5) lie well outside the bandwidth of the two-photon spectrum. Therefore, these states are energetically inaccessible under weak-field excitation. Intense femtosecond laser pulses, however, utilize the resonant AC Stark effect to modify the energy landscape. As a result, new excitation pathways open up, enabling efficient population transfer to the outer target states as well.

To overcome this difficulty, we divide the whole process into a sequence of steps with the optimization procedure used to control each step. The control is performed by setting appropriate intermediate target states, and the wavepacket obtained as a result of the previous step is set to be an initial state for the next. 

The two intermediate target states are set to be symmetric Gaussians with the same width parameters as those of the initial and target states and zero central momenta. The central coordinates of the wavepackets are set to be Ritsi = (2.51,1.81)t and RitS2 = (1.81,2.51)T (see Fig. 6.7). The initial guess held used to control the overall process is constructed by joining the optimal helds found for three intermediate steps the control from the initial state to the hrst intermediate target state, the control from the hrst intermediate... 

Fig. 6.7. Ground state of two-dimensional H2O model system. The white circles contain the initial and target wavepackets and two intermediate target states...

Fig. 2.4. Schematic representation of the different relationships between the important regions in phase space for the reference (0) and the target (1) systems, and their possible interpretation in terms of probability distributions - it should be clarified that because AU can be distributed in a number of different ways, there is no obvious one-to-one relation between P0(AU), or Pi (AU), and the actual level of overlap of the ensembles [14]. (a) The two important regions do not overlap, (b) The important region of the target system is a subset of the important region of the reference system, (c) The important region of the reference system overlaps with only a part of the important region of the target state. Then enhanced sampling techniques of stratification or importance sampling that require the introduction of an intermediate ensemble should be employed (d)...

The initial and the target state wave functions are To(r, 0) and T oCr, T) at times t = 0 and t = T, respectively. We aim to derive the driving potential Fpp(r, t) that generates the target state from the initial state in time Tp < T. The wave function of the intermediate state in the acceleration is assumed to be representable in the form... 

The fast-forward protocol can be regarded as a prescription for finding a shortcut in state space, [50] from the initial state to the target state. There are, of course, many possible shortcuts in state space but very few proposals to find those shortcuts. In this section, we generalize the fast-forward protocol in a two-level system, developing different shortcuts in which, in contrast to fast-forward field (FFE)-driven dynamics, the amplitude and the phase of the wave function of the intermediate state are modulated [50]. 

Because the Stokes pulse precedes but overlaps the pump pulse, initially Up and all population initially in field-free state 11) coincides with flo(0)- At the final time, ilp Q5 so all of the population in flo(0) projects onto the target state 6). Note that flo(0) has no projeetion on the intermediate field-free state 5 ). The Rabi frequencies of the Stokes and pump pulses that are required for efficient STIRAP-generated population transfer satisfy the condition [66]... 

Figure 3.8 Time dependence of the population of the initial, intermediate and target states for (a) STIRAP (A = 0) and (b) STIRAP + CDF control with i = 1. (From Ref. 67).

FWHM/(2Vln 2) these generate the population transfers shown in Figure 3.28. Note the very rapid oscillations in population and the very poor yields of the target state these phenomena are the consequence of the large transition moments between the background state and the intermediate state. 

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