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arXiv:2005.13148 · Physical Review A

Unified model of ultracold molecular collisions

James F. E. Croft, John L. Bohn, Goulven Quéméner

Published Sep 8, 2020• 33 citations
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Abstract

A scattering model is developed for ultracold molecular collisions, which allows inelastic processes, chemical reactions, and complex formation to be treated in a unified way. All these scattering processes and various combinations of them are possible in ultracold molecular gases, and as such this model will allow the rigorous parametrization of experimental results. In addition we show how, once extracted, these parameters can be related to the physical properties of the system, shedding light on fundamental aspects of molecular collision dynamics.

DOI
10.1103/physreva.102.033306

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A scattering model is developed for ultracold molecular collisions, which allows inelastic processes, chemical reactions, and complex formation to be treated in a unified way. All these scattering processes and various combinations of them are possible in ultracold molecular gases, and as such this model will allow the rigorous parametrization of experimental results. In addition we show how, once extracted, these parameters can be related to the physical properties of the system, shedding light on fundamental aspects of molecular collision dynamics.
The investigation of ultracold atomic or molecular collision is important for us to understand the essence of a chemical reaction. We present a simple analytical model of arbitrary-order partial-wave scatterings for ultracold molecular collision in the threshold regime. The threshold formulas of the transmission and reflection coefficients are given. For high-partial-wave collision, shape resonance will take place because of the existence of a centrifugal barrier. We investigate the effect of shape resonance and short-range interaction on molecular collisions. Moreover, we find a method to fit the loss parameter from the experimental data of ultracold bosonic molecular collision. As an applied example, we calculate the thermally average loss rate for the ultracold 87Rb133Cs+87Rb133Cs^{87}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{133}\mathrm{Cs}+^{87}\mathrm{Rb}\phantom{\rule{0.16em}{0ex}}^{133}\mathrm{Cs}87Rb133Cs+87Rb133Cs collision, our results are consistent with the recent experimental and theoretical results of Gregory et al. [Nat. Commun. 10, 3104 (2019)].
Over the past decade, and particularly the past five years, a quiet revolution has been building at the border between atomic physics and experimental quantum chemistry. The rapid development of techniques for producing cold and even ultracold molecules without a perturbing rare-gas cluster shell is now enabling the study of chemical reactions and scattering at the quantum scattering limit with only a few partial waves contributing to the incident channel. Moreover, the ability to perform these experiments with nonthermal distributions comprising one or a few specific states enables the observation and even full control of state-to-state collision rates in this computation-friendly regime: This is perhaps the most elementary study possible of scattering and reaction dynamics.
Recent years have seen tremendous progress in research on cold and controlled molecular collisions, both in theory and in experiment. The advent of techniques to prepare cold and ultracold molecules and ions, to store them in optical lattices or in charged quasicristalline structures, and to use them in crossed or merged beam experiments have opened many new possibilities to study the most fundamental aspects of molecular interactions. At the same time, theoretical work has made progress in tackling these problems and accurately describing quantum effects in complex systems, and in proposing viable options to control chemical reactions at ultralow energies. Through tutorials on both the theoretical and experimental aspects of research in cold and ultracold molecular collisions, this book provides advanced undergraduate students, graduate students and researchers with the foundations needed to understand this exciting field.
Collision physics plays a key role in understanding the properties of ultracold gases. First, collisions ensure thermalization in trapped atomic samples, which is essential for the success of evaporative cooling. Second, interactions between atoms determine the equilibrium shape and the dynamics of the condensate once it is formed. Finally collisions limit the achievable spatial densities via inelastic processes, which ultimately determine whether a given atomic species may lead to Bose-Einstein condensation. The purpose of the following lectures is to give a basic introduction to collision physics with a special emphasis on the low temperature aspect of these interactions. We will consider here only binary interactions between atoms since one of the remarkable prop-erties of the physics of ultra-cold dilute gases is that all the macroscopic properties of the system can be directly deduced from the two-body interaction potential. In particular the essential concept of scattering length will be introduced and developped for some simple potentials, using as practical examples experimental results obtained on atomic cesium and rubidium. The present lectures are complementary to the ones given by D. Heinzen where a detailed comparison between the collisional properties of the various alkali atoms will be found, together with explanations of the spectroscopic approaches used in the precise determination of interatomic potentials. 1. – Scattering theory: a brief reminder 1.1. Collision between two particles. – We consider here an elementary collision process between two particles 1 and 2 with the same mass M, interacting through the potential
II. Inelastic atom -molecule collisions 2 A. Vibrational and rotational relaxation 2 1. Collisions at cold and ultracold temperatures 2 2. Shape resonances in molecular collisions 6 3. Feshbach resonances in molecular collisions 6 B. Quasi-resonant transitions 7 C. Atom -molecular ion collisions 8 III.Chemical Reactions at ultracold temperatures 9 A. Tunneling dominated reactions 9 1.Reactions at zero temperature 10 2. Feshbach resonances in reactive scattering 12 B. Barrierless reactions 14 1.Collision systems of three alkali metal atoms 14 2. Role of PES in determining ultracold reactions 16 3.Relaxation of vibrationally excited alkali metal dimers 18 4. Reactions of heteronuclear and isotopically substituted alkali-metal dimer systems 19 IV.Inelastic molecule -molecule collisions 20 A. Molecules in the ground vibrational state 20 B. Vibrationally inelastic transitions 22 V. Summary and outlook 24 References 24 I. A. Vibrational and rotational relaxation 1. Collisions at cold and ultracold temperatures
Ultracold atoms and molecules provide an unprecedented view into the role of quantum effects in chemical reactions. However, these same quantum effects make ultracold chemical reactions notoriously difficult to simulate. Contrary to conventional wisdom that ultracold systems necessitate quantum approaches, with classical mechanics offering a rough approximation at best, the past three decades have seen an explosion in classical, quasiclassical, and semiclassical approaches that yield near-exact results for ultracold systems─including in cases where today's quantum methods would be computationally intractable. This review illustrates the power of these approaches with 30 years' worth of numerical and experimental evidence. The review provides a comprehensive account of the successes of universal classical post-threshold laws for low-energy atomic and molecular scattering systems, as well as the cutting edge in quasiclassical approaches that unravel the ongoing controversy surrounding long-lived collision complex lifetimes in ultracold collisions. Special attention is placed on atomic systems where classical scaling laws hold directly at zero Kelvin, which underline the predictive power classical methods can offer even in the most extreme quantum chemical environments. The review culminates with a discussion of broader implications for classically inspired approaches to prototypically quantum chemistry in the second quantum revolution.