Quantum control of molecular rotation

The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian with only a few accurately known parameters, and transitions between rotational levels can be driven by external fields from various parts of the electromagnetic spectrum. Control over the rotational motion can be exerted in one-, two- and many-body scenarios, thereby allowing to probe Anderson localization, target stereoselectivity of bimolecular reactions, or encode quantum information, to name just a few examples. The corresponding approaches to quantum control are pursued within separate, and typically disjoint, subfields of physics, including ultrafast science, cold collisions, ultracold gases, quantum information science, and condensed matter physics. It is the purpose of this review to present the various control phenomena, which all rely on the same underlying physics, within a unified framework. To this end, we recall the Hamiltonian for free rotations, assuming the rigid rotor approximation to be valid, and summarize the different ways for a rotor to interact with external electromagnetic fields. These interactions can be exploited for control --- from achieving alignment, orientation, or laser cooling in a one-body framework, steering bimolecular collisions, or realizing a quantum computer or quantum simulator in the many-body setting.Comment: 52 pages, 11 figures, 607 reference

Dissipative Quantum Dynamics and Optimal Control using Iterative Time Ordering: An Application to Superconducting Qubits

We combine a quantum dynamical propagator that explicitly accounts for quantum mechanical time ordering with optimal control theory. After analyzing its performance with a simple model, we apply it to a superconducting circuit under so-called Pythagorean control. Breakdown of the rotating-wave approximation is the main source of the very strong time-dependence in this example. While the propagator that accounts for the time ordering in an iterative fashion proves its numerical efficiency for the dynamics of the superconducting circuit, its performance when combined with optimal control turns out to be rather sensitive to the strength of the time-dependence. We discuss the kind of quantum gate operations that the superconducting circuit can implement including their performance bounds in terms of fidelity and speed.Comment: 16 pages, 11 figure

Monotonically convergent optimization in quantum control using Krotov's method

The non-linear optimization method developed by Konnov and Krotov [Automation and Remote Control 60, 1427 (1999)] has been used previously to extend the capabilities of optimal control theory from the linear to the non-linear Schr\"odinger equation [Sklarz and Tannor, Phys. Rev. A 66, 053619 (2002)]. Here we show that based on the Konnov-Krotov method, monotonically convergent algorithms are obtained for a large class of quantum control problems. It includes, in addition to non-linear equations of motion, control problems that are characterized by non-unitary time evolution, non-linear dependencies of the Hamiltonian on the control, time-dependent targets and optimization functionals that depend to higher than second order on the time-evolving states. We furthermore show that the non-linear (second order) contribution can be estimated either analytically or numerically, yielding readily applicable optimization algorithms. We demonstrate monotonic convergence for an optimization functional that is an eighth-degree polynomial in the states. For the 'standard' quantum control problem of a convex final-time functional, linear equations of motion and linear dependency of the Hamiltonian on the field, the second-order contribution is not required for monotonic convergence but can be used to speed up convergence. We demonstrate this by comparing the performance of first and second order algorithms for two examples

Quantum Effects in Cold and Controlled Molecular Dynamics

This chapter discusses three examples of quantum effects that can be observed in state-of-the-art experiments with molecular beams—scattering resonances as a probe of interparticle interactions in cold collisions, the protection of Fano-Feshbach resonances against decay despite resonant coupling to a scattering continuum, and a circular dichroism in photoelectron angular distributions arising in the photoionization of randomly oriented chiral molecules. The molecular beam setup provides molecules in well-defined quantum states. This, together with a theoretical description based on first principles, allows for excellent agreement between theoretical prediction and experimental observation and thus a rigorous understanding of the observed quantum effects