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arXiv:1904.12119 · Physical Review Research

Magnetic tuning of ultracold barrierless chemical reactions

Timur V. Tscherbul, Jacek Kłos

Published Feb 3, 2020• 15 citations
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Abstract

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.

DOI
10.1103/physrevresearch.2.013117

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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 demonstrate that it is possible to efficiently control ultracold chemical reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers in their metastable triplet states by choosing the internal hyperfine and rovibrational states of the reactants as well as by inducing magnetic Feshbach resonances with an external magnetic field. We base these conclusions on coupled-channel statistical calculations that include the effects of hyperfine contact and magnetic-field-induced Zeeman interactions on ultracold chemical reactions of hyperfine-resolved ground-state Na and the triplet NaLi(a^{3}Σ^{+}) producing singlet Na_{2}(^{1}Σ_{g}^{+}) and a Li atom. We find that the reaction rates are sensitive to the initial hyperfine states of the reactants. The chemical reaction of fully spin-polarized, high-spin states of rotationless NaLi(a^{3}Σ^{+},v=0,N=0) molecules with fully spin-polarized Na is suppressed by a factor of 10-100 compared to that of unpolarized reactants. We interpret these findings within the adiabatic state model, which treats the reaction as a sequence of nonadiabatic transitions between the initial nonreactive high-spin state and the final low-spin states of the reaction complex. In addition, we show that magnetic Feshbach resonances can similarly change reaction rate coefficients by several orders of magnitude. Some of these resonances are due to resonant trimer bound states dissociating to the N=2 rotational state of NaLi(a^{3}Σ^{+},v=0) and would thus exist in systems without hyperfine interactions.
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)].
This article reviews the current state of the art in the field of cold and ultracold molecules and demonstrates that chemical reactions, inelastic collisions and dissociation of molecules at subkelvin temperatures can be manipulated with external electric or magnetic fields. The creation of ultracold molecules may allow for spectroscopy measurements with extremely high precision and tests of fundamental symmetries of nature, quantum computation with molecules as qubits, and controlled chemistry. The probability of chemical reactions and collisional energy transfer can be very large at temperatures near zero kelvin. The collision energy of ultracold atoms and molecules is much smaller than perturbations due to interactions with external electric or magnetic fields available in the laboratory. External fields may therefore be used to induce dissociation of weakly bound molecules, stimulate forbidden electronic transitions, suppress the effect of centrifugal barriers in outgoing reaction channels or tune Feshbach resonances that enhance chemical reactivity.
We demonstrate a method for controlling the outcome of an ultracold chemical few-body reaction by redirecting a tunable fraction of reaction flux from one selected product channel to another one. In the reaction, three ultracold atoms collide to form a diatomic molecule. This product molecule can be produced in various internal states, characterizing the different product channels of the reaction. Our scheme relies on the coupling between two such product channels at an avoided molecular energy level crossing in the presence of an external magnetic field. The degree of coupling can be set by the magnetic field strength and allows for a widely tunable flux control between the two channels. This scheme is quite general and also holds great promise for a large variety of chemical processes with diverse species, since molecular energy level crossings are ubiquitous in molecular systems and are often easily accessible by standard laboratory equipment.
We show that isotope-exchange reactions between ground-state alkali-metal, alkaline-earth-metal, and lanthanide heteronuclear dimers consisting of two isotopes of the same atom are exothermic with an energy change in the range of 1-8000 MHz, thus resulting in cold or ultracold products. For these chemical reactions, there are only one rovibrational and at most several hyperfine possible product states. The number and energetics of open and closed reactive channels can be controlled by the laser and magnetic fields. We suggest a laser-induced isotope- and state-selective Stark shift control to tune the exothermic isotope-exchange reactions to become endothermic, thus providing the ground for testing models of the chemical reactivity. The present proposal opens the way for studying the state-to-state dynamics of ultracold chemical reactions beyond the universal limit with a meaningful control over the quantum states of both reactants and products.
We present a multichannel finite-range three-body scattering theoretical model used for investigating the magnetically tuned atom-dimer collision reaction. We take the $^{6}\mathrm{Li}\text{\ensuremath{-}}^{6}\mathrm{Li}_{2}$ system as an example to calculate the atom-dimer scattering length and dimer relaxation rate steered by a magnetic field. When the reactants are prepared in three shallow atom-dimer hyperfine channels, our calculation results agree with two experimental measurements [S. Nakajima et al., Phys. Rev. Lett. 105, 023201 (2010); T. Lompe et al., Phys. Rev. Lett. 105, 103201 (2010)]. We find that the two-body ppp-wave interaction has a significant influence on the atom-dimer collision reaction in the three hyperfine channels. By including the hyperfine and Zeeman interactions, we calculate the hyperfine state-to-state transition probability from the reactant channel to the deep atom-dimer hyperfine channel. We find a universality in the atom-dimer collision reaction, i.e., the universality of deep dimer product. The universality of deep dimer product in the $^{6}\mathrm{Li}\text{\ensuremath{-}}^{6}\mathrm{Li}_{2}$ collision reaction is more robust at magnetic field B>620B>620B>620 G than that at B<620B<620B<620 G.