Control target state

Joachim C (1987) Control of the quantum path-target state distance bistable-like characteristic in a small tight-binding system. J Phys A 20 L1149... 

Demirplak and Rice developed the counter-diabatic control protocol while studying control methods that efficiently transfer population between a selected initial state and a selected target state of an isolated molecule [11-13]. The protocol has been studied for manipulation of atomic and molecular states [11, 12, 19] and spin chain systems [20, 21]. Experiments with the counter-diabatic protocol have been demonstrated for the control of BECs [22] and the electron spin of a single nitrogen-vacancy center in diamond [23]. The counter-diabatic field (CDF) protocol is identical with the transitionless driving protocol, independently proposed by Berry a few years later [24]. A discussion of the relationship between these approaches and several of the other proposed shortcuts to adiabaticity can be found in the review by Torrontegui and coworkers [10]. 

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).

We have examined two assisted adiabatic transfer schemes designed to control the dynamical evolution of a quantum many-body system. That control is achieved by active manipulation with external fields that work cooperatively with coherence and interference effects embedded in the system quantum dynamics. The schemes we have discussed are a small subset of the many that have been proposed to induce complete transfer of population from an arbitrary initial state to a selected target state of a system, yet they illuminate the generic character of the... 

Figure 6.2 Steering of photochemical reactions by coherent control of ultrafast electron dynamics in molecules by shaped femtosecond laser pulses. Ultrafast excitation of electronic target states in molecules launches distinct nuclear dynamics, which eventually lead to specific outcomes of the photochemical reaction. The ability to switch efficiently between different electronic target channels, optimally achieved by turning only a single control knob on the control field, provides an enhanced flexibility in the triggering of photochemical events, such as fragmentation, excited state vibration, and isomerization.

Figure 6.10 Ultrafast efficient switching in the five-state system via SPODS based on multipulse sequences from sinusoidal phase modulation (PL). The shaped laser pulse shown in (a) results from complete forward design of the control field. Frame (b) shows die induced bare state population dynamics. After preparation of the resonant subsystem in a state of maximum electronic coherence by the pre-pulse, the optical phase jump of = —7r/2 shifts die main pulse in-phase with the induced charge oscillation. Therefore, the interaction energy is minimized, resulting in the selective population of the lower dressed state /), as seen in the dressed state population dynamics in (d) around t = —50 fs. Due to the efficient energy splitting of the dressed states, induced in the resonant subsystem by the main pulse, the lower dressed state is shifted into resonance widi die lower target state 3) (see frame (c) around t = 0). As a result, 100% of the population is transferred nonadiabatically to this particular target state, which is selectively populated by the end of the pulse.

Within the quantum formulation of OCT, the basic variational procedure leads to a set of equations for the optimal laser held, which include two Schrodinger equations to describe the dynamics starting from the initial and the target state wavepackets. The optimal laser held is given by the imaginary part of the correlation function for these two wavepackets. This system of equations of optimal control must generally be solved iteratively, making it an extremely computationally expensive approach for multidimensional systems. 

Calculate the corrected optimized field as E +1 t) = E t) + a 6E t), with the parameter a adjusted to maximize the absolute value of the overlap between the controlled wavepacket and the target state. To do so, (6.3) should be integrated forward in time from t = 0 to t = T, starting from the initial wavefunction < >(0)) = 14>,), several times for different values of a. 

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. 

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