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arXiv:2111.01453 · Physical Review A

Model for nuclear spin product-state distributions of ultracold chemical reactions in magnetic fields

Goulven Quéméner, Ming-Guang Hu, Yu Liu, Matthew A. Nichols, Lingbang Zhu, Kang-Kuen Ni

Published Nov 29, 2021• 6 citations
arXivHTMLPDF

Abstract

Based on a theoretical model where the nuclear spins remain unchanged during a collision, we provide an analytical and general expression for the nuclear spin state-to-state distribution of an ultracold diatom-diatom chemical reaction in a magnetic field, for given rotational transitions of the molecules. It simply requires knowledge of the field-dependent eigenfunctions of the molecular reactants and products of the chemical reaction. The final state-to-state distribution drastically changes with the magnetic field. When the distribution is summed over all the final products, a simplified expression is found where only the knowledge of the eigenfunctions of the molecular reactants is required. The present theoretical formalism has been successfully used to explain the magnetic field behavior of the product-state distribution in chemical reactions of ultracold KRb molecules [Hu et al., Nat. Chem. 13, 435 (2021)].

DOI
10.1103/physreva.104.052817

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Based on a theoretical model where the nuclear spins remain unchanged during a collision, we provide an analytical and general expression for the nuclear spin state-to-state distribution of an ultracold diatom-diatom chemical reaction in a magnetic field, for given rotational transitions of the molecules. It simply requires knowledge of the field-dependent eigenfunctions of the molecular reactants and products of the chemical reaction. The final state-to-state distribution drastically changes with the magnetic field. When the distribution is summed over all the final products, a simplified expression is found where only the knowledge of the eigenfunctions of the molecular reactants is required. The present theoretical formalism has been successfully used to explain the magnetic field behavior of the product-state distribution in chemical reactions of ultracold KRb molecules [Hu et al., Nat. Chem. 13, 435 (2021)].
Quantum control of reactive systems has enabled microscopic probes of underlying interaction potentials, the opening of novel reaction pathways, and the alteration of reaction rates using quantum statistics. However, extending such control to the quantum states of reaction outcomes remains challenging. In this work, we realize this goal through the nuclear spin degree of freedom, a result which relies on the conservation of nuclear spins throughout the reaction. Using resonance-enhanced multiphoton ionization spectroscopy to investigate the products formed in bimolecular reactions between ultracold KRb molecules, we find that the system retains a near-perfect memory of the reactants nuclear spins, manifested as a strong parity preference for the rotational states of the products. We leverage this effect to alter the occupation of these product states by changing the superposition of initial nuclear spin states with an external magnetic field. The techniques demonstrated here open up the possibility to study ultracold reaction dynamics at the state-to-state level as well as quantum entanglement between reaction products.
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.
This paper develops a theoretical methodology to describe ultracold atom-diatom chemical reactions without a barrier in the presence of external magnetic fields and hyperfine interactions. The authors apply their method to the chemical reaction Li + CaH -> LiH + Ca and show good agreement with previous experimental work, as well as uncover the possibility of controlling ultracold barrierless chemical reactions by tuning selected hyperfine states of the reactants with an external magnetic field.
We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of long-range forces before they ultimately encounter one another, followed by a probability for the reaction to occur once they do. In this way, the electric-field dependence should be readily parametrized in terms of a pair of fitting parameters (along with a C6{C}_{6}C6​ coefficient) for each asymptotic value of partial-wave quantum numbers $|L,{M}_{L}\ensuremath{\rangle}$. From this, the electric-field dependence of the collision rates follows automatically. We present examples for reactive species, such as KRb, and nonreactive species, such as RbCs.
Coherent superpositions and entanglement are hallmarks of quantum mechanics, but they are fragile and can easily be perturbed by their environment. Selected isolated physical systems can maintain coherence and generate entanglement using well-controlled interactions. Chemical reactions, where bonds break and form, are highly dynamic quantum processes. A fundamental question is whether coherence can be preserved in chemical reactions and then harnessed to generate entangled products. Here we investigate this question by studying the 2KRb →\rightarrow→ K2_22​ + Rb2_22​ reaction at 500 nK, focusing on the the nuclear spin degrees of freedom. We prepare the initial nuclear spins in KRb in an entangled state and characterize the preserved coherence in nuclear spin wavefunction after the reaction. The data are consistent with full coherence at the end of the reaction. This suggests that entanglement can be prepared within the reactants, followed by a chemical reaction that produces separate, entangled molecules. We additionally demonstrate control of the reaction product state distribution by deliberately decohering the reactants.
The main limitation of most ultracold chemistry studies to date is the lack of an analysis of reaction products. Here, we discuss a generally tractable, rigorous theoretical framework for computing statistical product-state distributions for ultracold reactions in external fields. We show that fields have two main effects on the products of a statistical reaction, by (1) modifying the product energy levels and thus potentially reshaping the product distributions and/or (2) adding or removing product states by changing the reaction exothermicity. By analyzing these effects and the strength of the formalism to distinguish between different reaction mechanisms in benchmark reactions involving 40K^{40}\mathrm{K}40K and 87Rb^{87}\mathrm{Rb}87Rb species, we argue that statistical predictions will help understanding product formation and control, and lead developments to realize the full potential of ultracold chemistry.