Comparative study of monotonically convergent optimization algorithms for the control of molecular rotation

Ndong, M.; Lapert, M.; Koch, Christiane P.; Sugny, Dominique

doi:10.1103/physreva.87.043416

Cited by 9 publications

(3 citation statements)

References 54 publications

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“…Polarizability and hyperpolarizability terms lead to a non-linear interaction between the molecular system and the control field. Different optimization procedures were proposed for this kind of dynamics [196,197,198]. Other situations with isotope selectivity [199] and control by microwave pulses [200] have also been explored.…”

Section: Optimal Control For Alignment and Orientationmentioning

confidence: 99%

Quantum control of molecular rotation

2019

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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. IntroductionMolecules, unlike atoms, are extended objects that possess a number of different types of internal motion. In particular, the geometric arrangement of their constituent atoms endows molecules with the basic capability to rotate in three-dimensional space. Rotations can couple to vibrations of the atomic nuclei as well as to the orbital and spin angular momentum of the electrons. The resulting complexity of the energy level structure [1,2,3,4] may be daunting. It offers, on the other hand, a variety of knobs for control and thus is at the core of numerous applications, from the classic example of the ammonia maser [5] all the way to recent measurements of the electron's electric dipole moment in a cryogenic molecular beam of thorium monoxide [6].A key advantage of internal degrees of freedom such as rotation is that they occupy the low-energy part of the energy spectrum. Quantization of the rotational motion has been an early hallmark of quantum mechanics due to its connection to selection rules that govern all light-matter interactions [7]. Nowadays, rotational states and rotational molecular dynamics feature prominently in all active areas of AMO physics research as well as in neighbouring fields such as physical chemistry and quantum information science. Control over the rotational motion is crucial in one-body, two-body and many-body scenarios. For example, rotational state-selective excitation could pave the way towards separating left-and right handed enantiomers of chiral molecules [8,9]. Still within the one-body scenar...

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Section: Optimal Control For Alignment and Orientationmentioning

confidence: 99%

Quantum control of molecular rotation

2019

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“…Specifically, provided a number of physically reasonable conditions are satisfied [65], the landscape is free of local optima, i.e., there exist one manifold of global minimum solutions (resulting in F = 0) and one manifold of global maximum solutions (resulting in F = 1), while all other critical points reside on saddle-point manifolds [62][63][64]. Such a favorable landscape topology facilitates easy optimization, as any gradient-based search (various types of which are popular in quantum optimal control [21,[66][67][68][69][70][71][72][73][74][75]) is guaranteed to reach the global maximum [76]. Unfortunately, when uncertainties are present, this landscape topology is not preserved.…”

Section: Introductionmentioning

confidence: 99%

Robust control of quantum gates via sequential convex programming

2013

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Resource tradeoffs can often be established by solving an appropriate robust optimization problem for a variety of scenarios involving constraints on optimization variables and uncertainties. Using an approach based on sequential convex programming, we demonstrate that quantum gate transformations can be made substantially robust against uncertainties while simultaneously using limited resources of control amplitude and bandwidth. Achieving such a high degree of robustness requires a quantitative model that specifies the range and character of the uncertainties. Using a model of a controlled one-qubit system for illustrative simulations, we identify robust control fields for a universal gate set and explore the tradeoff between the worst-case gate fidelity and the field fluence. Our results demonstrate that, even for this simple model, there exist a rich variety of control design possibilities. In addition, we study the effect of noise represented by a stochastic uncertainty model.Comment: 13 pages, 3 figures; published versio

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“…The latter approach comes with the advantage of independence from the specific form of the optimization functional and matterfield interaction [14,16]. A non-linear matter-field interaction is encountered in multi-photon couplings which are important for example in the control of alignment and orientation [17,18,19]. Additional constraints in the optimization functional can be employed to keep the system dynamics within a certain subspace [20] or to restrict the bandwidth of the optimized field [21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%