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By Abello T.P.

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For evolution-operator control, the goal is to generate U(T ) such that it is as close as possible to the target unitary transformation W. The Mayer-type cost functional in this case can be generally expressed as F1 (U(T )) = 1 − W − U(T ) (17) where · is an appropriate normalized matrix norm; that is, F1 (U(T )) is maximized when the distance between U(T ) and W is minimized. This type of objective is common in quantum computing applications [158], where F1 (U(T )) is the fidelity of a quantum gate [205, 206].

B. 1. , maxima of the objective functional) for realistic situations that involve practical constraints on the applied laser fields. It is important to distinguish between the existence of an optimal control field and controllability; in the former case, a field is designed, subject to particular constraints, that guides the evolution of the system toward a specified target until a maximum of the objective functional is reached, while in the latter case, the exact coincidence between the attained evolution operator (or state) and the target evolution operator (or state) is sought.

By using optimally shaped pulses, it was possible to enhance or suppress the quantity of molecules in the 13-cis state by about 20%, relative to the yield observed using a transform-limited pulse with the same energy. They further explored the mechanism of coherent control of retinal photoisomerization in bacteriorhodopsin using time- and frequency-resolved pump-probe measurements [538]. Experimental data together with a theoretical analysis suggest that the isomerization yield depends on the coherent evolution of the vibrational wave packet on the excited-state PES in the presence of a conical intersection.

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Absorption of Ultra-Sonic Waves by Hydrogen and Carbon Dioxide by Abello T.P.

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