Control of quantum phenomena: Past, present, and future

Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. The current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. The two most critical theoretical insights were (1) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (2) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control, which is a laboratory procedure employing measurement-driven, closed-loop optimization to identify the best shapes of femtosecond laser control pulses for steering quantum dynamics towards the desired objective. Optimization in adaptive feedback control experiments is guided by a learning algorithm, with stochastic methods proving to be especially effective. Adaptive feedback control of quantum phenomena has found numerous applications in many areas of the physical and chemical sciences, and this paper reviews the extensive experiments. Other subjects discussed include quantum optimal control theory, quantum control landscapes, the role of theoretical control designs in experimental realizations, and real-time quantum feedback control. The paper concludes with a prospective of open research directions that are likely to attract significant attention in the future.Comment: Review article, final version (significantly updated), 76 pages, accepted for publication in New J. Phys. (Focus issue: Quantum control

Searching for quantum optimal controls in the presence of singular critical points

Quantum optimal control has enjoyed wide success for a variety of theoretical and experimental objectives. These favorable results have been attributed to advantageous properties of the corresponding control landscapes, which are free from local optima if three conditions are met: (1) the quantum system is controllable, (2) the Jacobian of the map from the control field to the evolution operator is full rank, and (3) the control field is not constrained. This paper explores how gradient searches for globally optimal control fields are affected by deviations from assumption (2). In some quantum control problems, so-called singular critical points, at which the Jacobian is rank-deficient, may exist on the landscape. Using optimal control simulations, we show that search failure is only observed when a singular critical point is also a second-order trap, which occurs if the control problem meets additional conditions involving the system Hamiltonian and/or the control objective. All known second-order traps occur at constant control fields, and we also show that they only affect searches that originate very close to them. As a result, even when such traps exist on the control landscape, they are unlikely to affect well-designed gradient optimizations under realistic searching conditions.Comment: 14 pages, 2 figure