Optimally controlled quantum molecular dynamics: A perturbation formulation and the existence of multiple solutions

High-NA achromatic metalenses by inverse design

We use inverse design to discover metalens structures that exhibit broadband, achromatic focusing across low, moderate, and high numerical apertures. We show that standard unit-cell approaches cannot achieve high-efficiency high-NA focusing, even at a single frequency, due to the incompleteness of the unit-cell basis, and we provide computational upper bounds on their maximum efficiencies. At low NA, our devices exhibit the highest theoretical efficiencies to date. At high NA-of 0.9 with translation-invariant films and of 0.99 with "freeform" structures-our designs are the first to exhibit achromatic high-NA focusing.

Theoretical Prediction of the Creation and Observation of a Ghost Trilobite Chemical Bond

The "trilobite"-type of molecule, predicted in 2000 and observed experimentally in 2015, arises when a Rydberg electron exerts a weak attractive force on a neutral ground state atom. Such molecules have bond lengths exceeding 100 nm. The ultralong-range chemical bond between the two atoms is a nonperturbative linear combination of the many degenerate electronic states associated with high principal quantum numbers, and the resulting electron probability distribution closely resembles a fossil trilobite from antiquity. We show how to coherently engineer this same long-range orbital through a sequence of electric and magnetic field pulses even when the ground-state atom is not present and propose several methods to observe the resulting orbital. The existence of such a ghost chemical bond in which an electron reaches out from one atom to a nonexistent second atom is a consequence of the high level degeneracy.

Active control of the dynamics of atoms and molecules

There has been much progress in the control of chemical reactions since methods of active control were first proposed by Brumer & Shapiro and by Tannor & Rice ten years ago. This chapter reviews both theoretical and experimental advances in the field. Control schemes based on quantum mechanical interference between competing paths and the manipulation of wave packets with tailored laser pulses are discussed. The theory of optimal control, the limitations of control theory applied to many-body dynamics, and the effects of constraints on the trajectory of the controlled observable are presented. Experimental progress in controlling the population of specific quantum states, in manipulating the dynamics of bound wave packets, and in the control of chemical reactions are reviewed, and current problems in the field are summarized.

Quantum Optimally Controlled Transition Landscapes

A large number of experimental studies and simulations show that it is surprisingly easy to find excellent quality control over broad classes of quantum systems. We now prove that for controllable quantum systems with no constraints placed on the controls, the only allowed extrema of the transition probability landscape correspond to perfect control or no control. Under these conditions, no suboptimal local extrema exist as traps that would impede the search for an optimal control. The identified landscape structure is universal for all controllable quantum systems of the same dimension when seeking to maximize the same transition probability, regardless of the detailed nature of the system Hamiltonian. The presence of weak control field noise or environmental decoherence is shown to preserve the general structure of the control landscape, but at lower resolution.

Generalized monotonically convergent algorithms for solving quantum optimal control problems

A wide range of cost functionals that describe the criteria for designing optimal pulses can be reduced to two basic functionals by the introduction of product spaces. We extend previous monotonically convergent algorithms to solve the generalized pulse design equations derived from those basic functionals. The new algorithms are proved to exhibit monotonic convergence. Numerical tests are implemented in four-level model systems employing stationary and/or nonstationary targets in the absence and/or presence of relaxation. Trajectory plots that conveniently present the global nature of the convergence behavior show that slow convergence may often be attributed to "trapping" and that relaxation processes may remove such unfavorable behavior.

Optimal control theory for a target state distributed in time: Optimizing the probe-pulse signal of a pump-probe-scheme

Optimal control theory (OCT) is formulated for the case of a two-color pump-probe experiment. The approach allows to calculate the pump-pulse shape in such a way that the probe-pulse absorption signal is maximized. Since the latter quantity is given by the time-averaged expectation value of a time dependent operator (the probe-pulse field-strength times the dipole operator) a version of OCT has to be used where the target state is distributed in time. The method is applied to a molecular three-level system with the pump-pulse driving the transition from the electronic ground state into the first-excited electronic state and the probe-pulse connecting the first-excited state with a higher lying electronic state. Depending on the probe-pulse duration, the vibrational wave packet becomes localized or at least highly concentrated in the Franck-Condon window for the transition into the higher-excited state. The dependence on the probe-pulse duration and on the delay time between the optimized pump-pulse and the probe-pulse is discussed in detail. The whole study demonstrates the feasibility of laser pulse induced temporal wave packet localization and the use of spectroscopic quantities as target states in experiments on femtosecond laser pulse control.

Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulses

We used strong-field laser pulses that were tailored with closed-loop optimal control to govern specified chemical dissociation and reactivity channels in a series of organic molecules. Selective cleavage and rearrangement of chemical bonds having dissociation energies up to approximately 100 kilocalories per mole (about 4 electron volts) are reported for polyatomic molecules, including (CH3)2CO (acetone), CH3COCF3 (trifluoroacetone), and C6H5COCH3 (acetophenone). Control over the formation of CH(3)CO from (CH3)2CO, CF3 (or CH3) from CH3COCF3, and C6H5CH3 (toluene) from C6H5COCH3 was observed with high selectivity. Strong-field control appears to have generic applicability for manipulating molecular reactivity because the tailored intense laser fields (about 10(13) watts per square centimeter) can dynamically Stark shift many excited states into resonance, and consequently, the method is not confined by resonant spectral restrictions found in the perturbative (weak-field) regime.