Atom-dimer exchange and dissociation reaction rates are predicted for different combinations of two
4He atoms and one of the alkaline species among
6Li,7Li, and
23Na, by using three-body scattering formalism with short-range two-body interactions. Our study was concerned with low-energy reaction rates in which the
s-,
p-, and
d-wave contributions are the relevant ones. The
4He is chosen as one of the atoms in the binary mixture, in view of available previous investigations and laboratory accessibilities. Focusing on possible experimental cold-atom realizations with two-atomic mixtures, in which information on atom-dimer reaction rates can be extracted, we predict the occurrence of a dip in the elastic reaction rate for colliding energies smaller than 20 mK, when the dimer is the
4He23Na molecule. We are also anticipating a zero in the elastic
p-wave contribution for the
4He+4He7Li and
4He+4He23Na reaction processes. With weakly bound molecules reacting with atoms at very low colliding energies, we interpret our results in the light of Efimov physics which supports model independence and robustness of our predictions. Specific sensitivities on the effective range were evidenced, highlighted by the particular inversion role of the
p- and
d-waves in the atom exchange and dissociation processes.
The quantum world within an atom or molecule that once attracted explorations only by academic physicists now provides fertile sustenance for chemists seeking control of chemical reactions and for engineers developing ever smaller electronic devices or tools for processing information with greater security. Whereas the first pioneers could only discover the most elementary properties – the discrete energy levels that characterize the internal structures of atoms and the radiative transitions that link these structures to our external world – it is now possible to alter that structure at will, albeit briefly. Objective This monograph presents the physical principles that describe such deliberately crafted changes, namely how single atoms or molecules (or other simple quantum systems) are affected by coherent interactions, primarily laser light – a subject that has been regarded first as a part of quantum electronics and then quantum optics but is most generally described as coherent atomic excitation [Sho90]. This physics has relevance to such basic concerns as the detection and quantitative analysis of trace amounts of chemicals, the catalysis or control of chemical reactions, the alignment of molecules, and the processing of quantum information. The physics necessarily involves elementary quantum mechanics, but it has many associations to the classical dynamics that governs macroscopic objects – waves and particles. The mathematics that quantifies the changes is that of differential equations, specifically coupled ordinary differential equations (ODEs), whose parameters incorporate the controls of experimenters and whose solutions, appropriately interpreted, quantify the resulting changes.
We consider ultracold, chemically reactive scattering collisions of the diatomic molecules KRb. When two such molecules collide in an ultracold gas, we find that they are energetically forbidden from reacting to form the trimer species
K2Rb or
Rb2K, and hence can only react via the bond-swapping reaction $2\mathrm{KRb}\ensuremath{\rightarrow}{\mathrm{K}}_{2}+{\mathrm{Rb}}_{2}$. Moreover, the tiny energy released in this reaction can in principle be set to zero by applying electric or microwave fields, implying a means of controlling the available reaction channels in a chemical reaction.