The control pulse

Another important extension is known as concatenated DD [50] that treats increasingly higher order corrections of the noise, where each concatenation level of the control pulses reduces the previous level s induced errors. This powerful protocol cannot be easily incorporated into our formalism since it goes beyond the second-order approximation used in our derivation of the universal formula. 

Now we consider the situation in which the control pulse illuminates a vibronic system at a delay t after the initial pump pulse. Assuming the pulse characteristics are identical between the pump and control pulses, the total WP after the irradiation of the control pulse is given as... 

An intuitive method for controlling the motion of a wave packet is to use a pair of pump-probe laser pulses, as shown in Fig. 13. This method is called the pump-dump control scenario, in which the probe is a controlling pulse that is used to create a desired product of a chemical reaction. The controlling pulse is applied to the system just at the time when the wave packet on the excited state potential energy surface has propagated to the position of the desired reaction product on the ground state surface. In this scenario the control parameter is the delay time r. This type of control scheme is sometimes referred to as the Tannor-Rice model. 

Control and optimization of combustion processes will require controllers capable of reacting to fast processes, such as combustion instabilities, as well as controllers capable of optimizing the combustion parameters on a slower scale to achieve desired performance objectives, such as flame compactness or minimal emissions. The focus of research has been on refining two suites of control tools one based on LMS techniques and suited to control of instabilities, and another based on direct descent techniques and suited for either instability control or combustion process optimization. In addition, investigation of the performance consequences of using pulsed (on-off) as opposed to proportional actuators has been completed, and this chapter presents experimental results of the effect of varying the subharmonic order of the control pulses on instability suppression. 

Fig. 7 shows the experimental data of the light storage and release processes. Fig. 7(a) gives the time sequences of the three pulses before Pr YSO crystal. We set the back edge of the control pulse being the same as that of the signal pulse to store the latter one. Due to fraction STIRAP,... 

Fig. 8. The relative amplitude of the restored pulse against time delay between the control pulse and signal pulse. Zero time delay corresponds to F-STIRAP.

It is often desirable to process information stored in memory elements and then restore the information in the memory element. If the memory element is a latch, such as shown in Fig. 1.69, the feedback would cause a problem. Signals can propagate around such a feedbackloop an unknown number oftimes causing unknown results at the time the control pulse is turned oft", breaking the feedback loop. 

First, the following components will have to be included into the operational behavior analysis the mechanical design of the valve, the hydraulic control element, the control pulse, the position transmitter of valve (2), the manual control of valve (2), the operation of the manual control element by the operator from the control panel, the acoustical alarm sounded for faulty positioning, and the information on the operational mode of the valve (visual display). Furthermore, a second position indicator (2z) is introduced as an additional component. The function of the acoustical alarm and the level indicator are dependent on the proper functioning of the position transmitter. An analysis based on the decision table (see Figure 5.23) provides the following information. 

Beyond the above computation, and with the help of a Monte Carlo simulation (see, also, Section 3), the degree to which the individual component contributes to a system failure was determined. The above method also permits taking into account specific maintenance strategies. The life histories of the individual components are created over a period of time from 5 x 10 h and thereby it is also determined whether the system failure can be traced to corresponding component failures at any specific point in time. Here the failure-prone components are recorded in connection with each individual failure. Results demonstrate that position transmission (2) is involved in 100% of all system failures, which is natural because of the system s logical structure (Figure 5.23). The mechanical system of the valve is involved in 12%, the hydraulic control element in 29%, and the control pulse in 59% of all cases of system failure. 

The field shape consists of two symmetric half-cycles with zero field amplitude at the pulse center. The upper panel of Fig. 5.13 shows the effective potential curves Vf R,t) obtained under the control field (to = 51 fs). The plotted curves at t = 44 fs represent the maximum shifts of the PECs in the first half-cycle of the control pulse, and those at t = 58 fs represent the maximum shifts in the later half-cycle of the control pulse. In the first half-cycle of the pulse, the control field, through the positive transition amplitude function /xn(7 ), acts to shift the Vn R) potential curve upwards, and thus the dynamical crossing position Rx t) is first shifted to the left. It reaches the leftmost position R ett at the height of the control field, and then is shifted right and restored to 7 cross by t = to- The lower panel of Fig. 5.13 shows the resulting time-dependence of Rx(t). The fact that the... 

Figure 5.14(a) shows the time dependence of the diabatic state 1 population Pi t) for various delay times to of the control pulse between 30 and 120 fs. In each panel, the black curve shows P t) computed without application of the control pulse. The curve shows a drop in population between —20 to 20 fs this is the pump pulse excitation. The diabatic representation and the significant V 2 (R) around the initial wavefunction position results in the oscillatory features on top of the population drop seen in this time range (these oscillations are not seen in the adiabatic representation). Then the pump-excited state decrease by 13% (from P2 t) = 0.31 to 0.27) around t = 110 fs this is due to the static crossing at i cross- Without the control pulse, this is the only population transfer seen. 

The curves in the upper panels of Fig. 5.14(a) show P t) under control pulses with various to. The pump pulse excitation (t < 20 fs) is common to all the cases, and the control pulse affects the dynamics after the pump. We see the final population (Pi t) at t = 250 fs) increase from to = 30 to 60 fs, reach the maximum around 70 fs, then decrease as to is made larger, and become even less than the final population found for the case without control by to > 100 fs. For to > 120 fs, the effect of the control pulse becomes smaller, and is completely without effect for to > 140 fs (not shown in Figure). The initial rise in Pi (t) increases as to is increased from 30 to 65 fs, and then decreases as to is increased from 65 to 120 fs. For to < 80 fs, we see an immediate drop in Pi(t) following the initial rise. Then after some time (t > 100 fs), we see the population increase at Pcross that is also present without the control pulse. For 80 < to < 100 fs, we instead see a slow but lasting decrease some time after the initial rise. 

To see the geometrical relation between the dynamical crossing point and the wavepacket propagation, we show in Fig. 5.14(b) the time-dependence of Rx t) during the first half-cycle of the control pulse, for to = 30, 51, 65,... 

When Rx t) first being shifted towards the left by the control pulse meets the rightmost tail of t), the transfer of the wavepacket from... 

For to > 120 fs, 2 R,t) will have already reached the original crossing before the control pulse is switched on so that the effect of the control pulse is small, and completely without effect for to > 140 fs. 

Wavepacket dynamics under effect of the control pulse... 

We now see the effect of the control pulse on the wavepacket dynamics. The center of the pulse are taken to be to = 8 fs, about the time the center of excited state wavepacket is at the conical intersection. Field shape is shown as thick curve of Fig. 5.27(b), as the value of off diagonal of VE(i x,0 in... 

Fig. 5.28 Time evolution of diabatic state 2 population following the pump pulse, (a) without and (b) with the control pulse. (Reprinted with permission from Y. Arasaki et ai, Phys. Chem. Chem. Phys. 13, 8681 (2011)).

Without the control pulse [Fig. 5.29(a)], there is no transfer between diabatic states at the center of the wavepacket (ri = T2) and the center of the wavepacket goes through the conical intersection, where the interaction potential between diabatic states is zero (V12 = 0 at the conical intersection). Thus, population transfer from the initially excited state 2 to state 1 occurs away from the position of the conical intersection and symmetrically for ri < T2 and ri > r2- There are thus two regions of state 1 population at 8 fs. After passage through the region of conical intersection, the state 2... 

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