Look Out for Traps

Abstract

Chemistry The intricate glassware notwithstanding, chemistry at the molecular level has traditionally been a passive activity. Trillions upon trillions of molecules are mixed together somewhat crudely, and then they are left to their own devices in the (often informed) hope that they will collide with one another in just the right way to rearrange into a desired product. With the increasing sophistication of laser technology, however, schemes have been proposed over the past several decades to manipulate the process more actively. The idea is to tailor a laser pulse in fine enough detail to steer atoms or molecules precisely along a landscape of quantum-mechanical energy states, and thereby to direct their behavior. And what should such a control pulse look like? To find out, it's often simplest to try out a few at the outset, and then keep tuning the most effective ones iteratively until the optimal outcome is attained. Analysis of this approach suggested that, if there were an optimum pulse, the iterations would proceed cleanly toward it, without becoming trapped around a local maximum in the ensemble of possible pulses. Pechen and Tannor now show mathematically that the situation is more complicated. They draw a distinction between kinematic and dynamic critical points, dealing respectively with the time evolution operator of the system subjected to the control parameter and the control parameter itself. Even when kinematic traps are absent, second-order dynamic traps can arise, as the authors demonstrate using a three-level model system. Phys. Rev. Lett. 106 , 120402 (2011).