Classical and quantum rotation numbers of asymmetric-top molecules

Hamraoui, K.; Damme, L. Van; Mardešić, Pavao; Sugny, Dominique

doi:10.1103/physreva.97.032118

Cited by 12 publications

(14 citation statements)

References 49 publications

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“…A large number of studies have shown the advantage of classical analysis for revealing the properties of quantum molecular spectra. This aspect has been investigated for the free molecular rotation [47,60,61,62,63,64,65], but also for molecules subject to a constant electric field [66,67,68]. Take Hamiltonian monodromy [57] as an example, which is the simplest topological obstruction to the existence of global action angle variables in classical integrable systems.…”

Section: Geometric Description Of Rotational Dynamicsmentioning

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: Geometric Description Of Rotational Dynamicsmentioning

confidence: 99%

Quantum control of molecular rotation

2019

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“…Clusters consisting of 2 and 3 nanotori were able to change their position twice during the considered period of time. Such a consistent change of positions has similar features to the flip effect of one body, which is described by the intermediate axis theorem [35][36][37][38]. Note that the classical intermediate axis theorem explains the case of unstable rotational motion of a body around an axis with an intermediate moment of inertia.…”

Section: Collective Behavior Of the Nanotori Clustermentioning

confidence: 78%

Molecular Dynamics Study of Collective Behavior of Carbon Nanotori in Columnar Phase

et al. 2021

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Supramolecular interaction of carbon nanotori in a columnar phase is described using the methods of classical molecular dynamics. The collective behavior and dynamic properties of toroidal molecules arising under the action of the van der Waals forces are studied. The conditions under which columnar structures based on molecular tori become unstable and rearrange into another structure are investigated. The reasons for the appearance of two types of directed rotational motion from the chaotic motion of molecules are discussed.

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“…Different molecular systems could show traces of this effect at the quantum scale [20]. An example is given by asymmetric top molecules, such as the water molecule, which are the microscopic equivalent of asymmetric rigid bodies [21]. Another field of applications is the control of quantum systems by external electromagnetic fields [22] using, e.g., the analogy between Bloch and Euler equations [23].…”

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confidence: 99%

Geometric Origin of the Tennis Racket Effect

Mardesic,

Van Damme,

Guillen

et al. 2020

Preprint

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The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a result of the Picard-Lefschetz formula. We prove that a perfect twist of the racket is achieved in the limit of an ideal asymmetric object. We give upper and lower bounds to the twist defect for any rigid body, which reveals the robustness of the effect. A similar study allows us to explore in which conditions the Monster flip, an almost impossible skate board trick, can be realized.

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Classical and quantum rotation numbers of asymmetric-top molecules

Cited by 12 publications

References 49 publications

Quantum control of molecular rotation

Quantum control of molecular rotation

Molecular Dynamics Study of Collective Behavior of Carbon Nanotori in Columnar Phase

Geometric Origin of the Tennis Racket Effect

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