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Chemical Reviews

Ultracold Molecular Collisions: Quasiclassical, Semiclassical, and Classical Approaches in the Quantum Regime

Micheline B. Soley, Eric J. Heller

Published Jun 25, 2025• 7 citations
Publisher

Abstract

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.

DOI
10.1021/acs.chemrev.4c01014

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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.
In the past two decades, the revolutionary technologies of creating cold and ultracold molecules have provided cutting-edge experiments for studying the fundamental phenomena of collision physics. To a large degree, the recent explosion of interest in the molecular collisions has been sparked by dramatic progress of experimental capabilities and theoretical methods, which permit molecular collisions to be explored deep in the quantum mechanical limit. Tremendous experimental advances in the field have already been achieved, and the authors, from an experimental perspective, provide a review of these studies for exploring the nature of molecular collisions occurring at temperatures ranging from the Kelvin to the nanoKelvin regime, as well as for applications of producing ultracold molecules.
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.
Inspired by Wannier's threshold law, we recognize that collision-complex decay meets the requirements of quantum-classical correspondence in sufficiently exothermic ultracold reactions. We make use of this correspondence to elucidate the classical foundations of ultracold reactions and to help bring calculations currently beyond the capabilities of quantum mechanics within reach. A classical method with a simplified model of many-body interactions is provided for the determination of the collision-complex lifetime and demonstrated for a reduced-dimensional system, as preliminary to the calculation of collision-complex lifetimes in the full-dimensional system.
Ultracold chemistry, the science of chemical reactions below one milliKelvin, has the potential to expedite technologies from controlled reactions to quantum computation. Experimental investigation of the ultracold KRb dimer reaction (2KRb → [K2Rb2]⋆ → K2 + Rb2) has been central to the field. Despite recent experimental and theoretical work on the reaction, it remains an open question how cold products (14 K) are formed from the hot collision complex (4,000 K). The answer to this question has been obstructed by the computational intensity of quantum mechanical simulations at cold temperatures. This dissertation makes use of the analogy of an “ultracold inferno” to circumvent the computationally intensive quantum mechanical treatments typically applied near threshold. The thesis reveals that, unexpectedly, classical mechanics is expected to be exact for elements of the ultracold KRb dimer reaction and many threshold processes previously thought to be the sole province of quantum mechanics. Classical behaviors can thus be observed in certain systems at extremely low temperatures, and classical mechanics can be employed to bring computational simulation of many threshold systems within reach. To identify when classical mechanics is valid near threshold, two semiclassical criteria of quantum-classical correspondence are presented. The criteria are then put into practice to calculate the rate of product formation in a reduced-dimensional model with the essence of the ultracold KRb dimer reaction via classical analytic phase-space counting and classical numerical dynamics simulations. A hybrid semiclassical-quantum method is also proposed to bring simulation of many full-dimensional exothermic ultracold reactions within reach. Classical “post-threshold” laws are derived and shown to operate in a plethora of cold and ultracold systems. Quantum and classical threshold behavior is unified from across physics and chemistry to emphasize the wide-reaching importance of classical mechanics near threshold. This thesis concludes classical mechanics has broad applications in threshold phenomena in fields such as ultracold and cold physics and chemistry, intense laser science, plasma science, nuclear physics, positron and positronium scattering, electron detachment and attachment, and astrochemistry. Classical techniques can be used to facilitate calculations and to better understand the mechanisms behind these threshold processes. These findings illustrate the power of time-honored classical mechanics in the age of the quantum leap.
Ultracold polar molecular quantum gases promise to open new research directions ranging from the study of ultra-cold chemistry, precision measurements to novel quantum phase transitions. Based on the preparation of high-phase space density gases of polar KRb molecules [1–3], I will discuss the control of dipolar collisions and chemical reactions of polar molecules in a regime where quantum statistics, single scattering partial waves, and quantum threshold laws play a dominant role [4]. In particular, I will point out the crucial role of electric dipole-dipole interactions [5] and external confinement [6] in determining the chemical reaction rate. Finally, I will discuss prospects of reaching quantum degeneracy in bialkali samples of polar molecules and prospects for these systems as novel dipolar quantum many-body systems.
At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.