Optimal control quantum interference

As discussed by M. Shapiro and R Brumer in the book Quantum Control of Molecular Processes, there are two general control strategies that can be applied to harness and direct molecular dynamics optimal control and coherent control. The optimal control schemes aim to find a sef of external field parameters that conspire - through quantum interferences or by incoherent addition - to yield the best possible outcome for a specific, desired evolution of a quantum system. Coherent control relies on interferences, constructive or destructive, that prohibit or enhance certain reaction pathways. Both of these control strategies meet with challenges when applied to molecular collisions. 

The optimization procedure yields a set of coefficients a,-. Of considerable interiasff is the question of whether these coefficients merely define a new vector that is simply a vector in a rotated coordinate system. If so, this would indicate that the optimqifl solution corresponds to a simple classical reorientation of the di atomic-moleciilee angular momentum vector. Examination of the optimal results [238] indicate " this is not the case. That is, control is the result of quantum interference effects ... 

All of the quantum control scenarios involve a host of laser and system parameters. To obtain maximal control in any scenario necessitates a means of tuning the system and laser parameters to optimally achieve the desired objective. This topic, optimal control, is introduced and discussed in Chapters 4 and 13. The role of quantum interference effects in optimal control are discussed as well, providing a uniform picture of control via optimal pulse shaping and coherent control. 

Although the demonstration of this technique was a success, its efficiency is limited because CW lasers interact only with a small part of the thermal distribution of the molecules. The decay of the coherence of the molecules and radiation limits the amount of energy that can be used effectively for control pm poses, because such coherence is a must for stable quantmn wave interference. In this regard, the two-femtosecond-pulse approach (Section 12.2) seems to be more effective, especially when used in combination with optimally shaped electromagnetic fields. Optimal control of the shape of the laser pulses used can provide effective excitation of the desired final quantum mechanical state. 

The three dominant quantum amplitudes (3 u l, -l, 2, and 3 are found to optimally cooperate with each other indicated by their lining up in the complex plane for an efficient control process, as shown in (b). In contrast, the amplitudes connecting the undesired transition l) — 4 destructively interfere, as indicated by the three contributing pathways in (c). 

---