Quantum Control Landscapes Beyond the Dipole Approximation: Controllability, Singular Controls, and Resources

We investigate the control landscapes of closed n-level quantum systems beyond the dipole approximation by including a polarizability term in the Hamiltonian. The latter term is quadratic in the control field. Theoretical analysis of singular controls is presented, which are candidates for producing landscape traps. The results for considering the presence of singular controls are compared to their counterparts in the dipole approximation (i.e., without polarizability). A numerical analysis of the existence of traps in control landscapes for generating unitary transformations beyond the dipole approximation is made upon including the polarizability term. An extensive exploration of these control landscapes is achieved by creating many random Hamiltonians which include terms linear and quadratic in a single control field. The discovered singular controls are all found not to be local optima. This result extends a great body of recent work on typical landscapes of quantum systems where the dipole approximation is made. We further investigate the relationship between the magnitude of the polarizability and the fluence of the control resulting from optimization. It is also shown that including a polarizability term in an otherwise uncontrollable dipole coupled system removes traps from the corresponding control landscape by restoring controllability. We numerically assess the effect of a polarizability term on a known example of a particular three-level Λ-system with a second order trap in its control landscape. It is found that the addition of the polarizability removes the trap from the landscape. The general practical control implications of these simulations are discussed.

The potential role of aerial pesticide applications to control landscape-scale outbreaks of pests and diseases in British forestry with a focus on dothistroma needle blight

British forestry is threatened by numerous pests and diseases. This study investigated the potential for re-introduction of aerial pesticide applications for landscape-scale disease management. In North Scotland in 2013 and 2015, copper oxychloride was applied to Pinus sylvestris L. stands infected with Dothistroma septosporum (Dorogin) Morelet. Helicopters distributed ultra-low-volume (ULV) applications of product via Micronair rotary atomisers, following methods used against D. septosporum in P. radiata D. Don stands in New Zealand. Product deposition was quantified on paper catchers and in foliage, soil and water. Catchers 100 m beyond the plot boundaries intercepted 0.5 per cent of within-plot mean deposition. Foliar analysis revealed slightly elevated copper concentrations (+0.07 μg g−1 dw) 250 m outside plot boundaries. Copper in foliage and needle litter remained above background levels for 109 and 157 weeks after application, respectively, longer than recorded during New Zealand operations. Concentrations in the soil increased over 3 years’ monitoring, whilst deposition into water traps resulted in copper concentrations well within limits set by the Scottish Environmental Protection Agency. No deleterious impacts on vascular and non-vascular ground and canopy flora were recorded. Copper fungicide applications significantly reduced foliar infection at both sites but did not affect needle retention. Further ground-based trials will investigate the efficacy of other actives. In Britain, such aerial operations have not occurred for two decades: this study demonstrated aerial and ground teams have the necessary expertise for their re-introduction, whilst highlighting areas needing further optimization.

Common foundations of optimal control across the sciences: evidence of a free lunch

A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favourable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide-ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond the laboratory set-up overhead). The full scope and implications of this observed common control behaviour pose an open question for assessment in further work. This article is part of the themed issue ‘Horizons of cybernetical physics’.