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Escaping From an Ultracold Inferno: Classical and Semiclassical Mechanics Near Threshold

Micheline B. Soley

Published Nov 26, 2019• 2 citations
OpenAlex

Abstract

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.

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Abstract A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanokelvin. Here we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. We map out an accurate ab initio ground-state potential energy surface of the K 2 Rb complex in full dimensionality and report numerically-exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome.

Nature Communications•Jul 19, 2017•81 citations
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 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.
Studying ultracold chemical reactions with quantum state resolution reveals details of the reaction processes, especially with single quantum state preparation of the reactants and state-selective detection of reaction products. In this thesis, we investigate two main processes: KRb + KRb → K2 + Rb2 reactions, and Rb and KRb atom-molecule collisions. In the KRb bimolecular reaction, we demonstrate the preservation of quantum coherence in bimolecular reactions for the first time, which is surprising in a reaction considered to be largely chaotic. Additionally, we proposed a coherent control scheme to manipulate product yields across different product channels. These results represent a critical step toward probing quantum coherence and entanglement in the chemical reaction. In atom-molecule collisions between Rb and KRb, we discovered an exceptionally long-lived intermediate complex, KRb2, which can be photo-excited by trapping light. The observed complex lifetime was orders of magnitude longer than theoretical predictions, underscoring the limitations of the current theory. We further explored the dependence of complex lifetimes on the initial quantum states and external electric and magnetic fields, providing additional experimental benchmarks to guide future theoretical work. Separately, we found that inelastic collisions between hyperfine-excited Rb atoms and KRb molecules can lead to rotation excitation of KRb post-collision. By probing the product state distribution, the result suggests that mechanical angular momentum is coupled to the spins. Such couplings are too weak in the current theory models to explain the result. Moreover, our result contradicts state-of-the-art coupled-channel calculations. These suggest that some subtle effects, such as molecular vibration and conical intersections, play a critical role in the reaction dynamics. The final piece of the thesis describes the observation of resonant interaction between a Rydberg atom and an ensemble of polar molecules. Such hybrid quantum systems have been proposed for a wide range of applications. Our work provides an experimental demonstration of resonant dipolar interactions between Rydberg atoms and ultracold polar molecules, paving the way for the realization of hybrid systems for quantum computation and simulation.
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.
Abstract Chemical reactions represent a class of quantum problems that challenge both the current theoretical understanding and computational capabilities1. Reactions that occur at ultralow temperatures provide an ideal testing ground for quantum chemistry and scattering theories, because they can be experimentally studied with unprecedented control2, yet display dynamics that are highly complex3. Here we report the full product state distribution for the reaction 2KRb → K2 + Rb2. Ultracold preparation of the reactants allows us complete control over their initial quantum degrees of freedom, whereas state-resolved, coincident detection of both products enables the probability of scattering into each of the 57 allowed rotational state-pairs to be measured. Our results show an overall agreement with a state-counting model based on statistical theory4–6, but also reveal several deviating state-pairs. In particular, we observe a strong suppression of population in the state-pair closest to the exoergicity limit as a result of the long-range potential inhibiting the escape of products. The completeness of our measurements provides a benchmark for quantum dynamics calculations beyond the current state of the art.
A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanoKelvin. In this work we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. For the first time we map out an accurate ab initio ground state potential energy surface of the KRbK complex in full dimensionality and report numerically exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome. We compare this with a lighter system with a smaller density of states (here the LiYbLi trimer) which displays random, and not chaotic, behavior.
Abstract A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanokelvin. Here we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. We map out an accurate ab initio ground-state potential energy surface of the K 2 Rb complex in full dimensionality and report numerically-exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome.