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Three-body recombination, or ternary association, is a termolecular reaction in which three particles collide, forming a bound state between two, whereas the third escapes freely. Three-body recombination reactions play a significant role in many systems relevant to physics and chemistry. In particular, they are relevant in cold and ultracold chemistry, quantum gases, astrochemistry, atmospheric physics, physical chemistry, and plasma physics. As a result, three-body recombination has been the subject of extensive work during the last 50 years, although primarily from an experimental perspective. Indeed, a general theory for three-body recombination remains elusive despite the available experimental information. Our group recently developed a direct approach based on classical trajectory calculations in hyperspherical coordinates for three-body recombination to amend this situation, leading to a first principle explanation of ion-atom-atom and atom-atom-atom three-body recombination processes. This review aims to summarize our findings on three-body recombination reactions and identify the remaining challenges in the field., 33 pages, 14 figures and 5 tables. Submitted to International Reviews in Physical Chemistry

We present Python Quasi-classical atom-molecule scattering (PyQCAMS), a new Python package for atom-molecule scattering within the quasi-classical trajectory approach. The input consists of mass, collision energy, impact parameter, and pair-wise interactions to choose between Buckingham, generalized Lennard-Jones, and Morse potentials. As the output, the code provides the vibrational quenching, dissociation, and reactive cross sections along with the rovibrational energy distribution of the reaction products. Furthermore, we treat H$_2$ + Ca $\rightarrow$ CaH + H reactions as a prototypical example to illustrate the properties and performance of the software. Finally, we study the parallelization performance of the code by looking into the time per trajectory as a function of the number of CPUs used.

We have studied the general aspects of the dynamics of an ion trapped in an ideal multipolar radiofrequency trap while interacting with a dense cold atomic gas. In particular, we have explored the dynamical stability, the energy relaxation and the characteristic harmonic motion exhibited by a trapped Yb$^{+}$ ion in different multipolar potentials and immersed in various cold atomic samples (Li, Na, Rb, Yb). For this purpose, we used two different molecular dynamics simulations; one based on a time-event drive algorithm and the other based on the stochastic Langevin equation. Relevant values for experimental realizations, such as the associated ion's lifetimes and observable distributions, are presented along with some analytical expressions which relate the ion's dynamical properties with the trap parameters., Comment: 12 pages, 11 figures

We show that two seemingly unrelated problems - the trapping of an atom in an optical superlattice (OSL) and the libration of a planar rigid rotor in combined electric and optical fields - have isomorphic Hamiltonians. Formed by the interference of optical lattices whose spatial periods differ by a factor of two, OSL gives rise to a periodic potential that acts on atomic translation via the AC Stark effect. The latter system, also known as the generalized planar pendulum (GPP), is realized by subjecting a planar rigid rotor to combined orienting and aligning interactions due to the coupling of the rotor's permanent and induced electric dipole moments with the combined fields. The mapping makes it possible to establish correspondence between concepts developed for the two eigenproblems individually, such as localization on the one hand and orientation/alignment on the other. Moreover, since the GPP problem is conditionally quasi-exactly solvable (C-QES), so is atomic trapping in an OSL. We make use of both the correspondence and the quasi-exact solvability to treat ultracold atoms in an optical superlattice as a semifinite-gap system. The band structure of this system follows from the eigenenergies and their genuine and avoided crossings obtained previously for the GPP as analytic solutions of the Whittaker-Hill equation. These solutions characterize both the squeezing and the tunneling of atoms trapped in an optical superlattice and pave the way to unraveling their dynamics in analytic form., 25 pages, 12 figures, 2 tables, Submitted to the New Journal of Physics

Nuclear scattering events with large momentum transfer in atomic, molecular, or solid-state systems may result in electronic excitations. In the context of atomic scattering by dark matter (DM), this is known as the Migdal effect, but the same effect has also been studied in molecules in the chemistry and neutron scattering literature. Here we present two distinct Migdal-like effects from DM scattering in molecules, which we collectively refer to as the molecular Migdal effect: a center-of-mass recoil, equivalent to the standard Migdal treatment, and a non-adiabatic coupling resulting from corrections to the Born-Oppenheimer approximation. The molecular bonds break spherical symmetry, leading to large daily modulation in the Migdal rate from anisotropies in the matrix elements. Our treatment reduces to the standard Migdal effect in atomic systems but does not rely on the impulse approximation or any semiclassical treatments of nuclear motion, and as such may be extended to models where DM scatters through a long-range force. We demonstrate all of these features in a few simple toy models of diatomic molecules, namely ${\rm H}_2^+$, N$_2$, and CO, and find total molecular Migdal rates competitive with those in semiconductors for the same target mass. We discuss how our results may be extended to more realistic targets comprised of larger molecules which could be deployed at the kilogram scale., v1: 15+2 pages, 7 figures

We study the evolution of a single BaRb$^+$ molecule while it continuously collides with ultracold Rb atoms. The initially weakly-bound molecule can undergo a sequence of elastic, inelastic, reactive, and radiative processes. We investigate these processes by developing methods for discriminating between different ion species, electronic states, and kinetic ion energy ranges. By comparing the measurements to model calculations we obtain a consistent description of the typical trajectory of the ion through the manifold of available atomic and molecular states. As a further result, we determine rates for collisional and radiative relaxation as well as photodissociation, spin-flip collisions, and chemical reactions., 19 pages, 17 figures, 2 tables

We study ultracold long-range collisions of heteronuclear alkali-metal dimers with a reservoir gas of alkali-metal Rydberg atoms in a two-photon laser excitation scheme. In a low density regime where molecules remain outside the Rydberg orbits of the reservoir atoms, we show that the two-photon photoassociation (PA) of the atom-molecule pair into a long-range bound trimer state is efficient over a broad range of atomic Rydberg channels. As a case study, we obtain the PA lineshapes for the formation of trimers composed of KRb molecules in the rovibrational ground state and excited Rb atoms in the asymptotic Rydberg levels $n^{2}S_j$ and $n^{2}D_j$, for $n=20-80$. We predict atom-molecule binding energies in the range $10-10^3$ kHz for the first vibrational state below threshold. The average trimer formation rate is order $10^8\, {\rm s}^{-1}$ at 1.0 $\mu$K, and depends weakly on the principal quantum number $n$. Our results set the foundations for a broader understanding of exotic long range collisions of dilute molecules in ultracold atomic Rydberg reservoirs., Comment: 7 pages, 4 figures

We propose a novel direct detection concept to search for dark matter with 100~keV to 100~MeV masses. Such dark matter can scatter off molecules in a gas and transfer an $\mathcal{O}(1)$ fraction of its kinetic energy to excite a vibrational and rotational state. The excited ro-vibrational mode relaxes rapidly and produces a spectacular multi-infrared-photon signal, which can be observed with ultrasensitive photodetectors. We discuss in detail a gas target consisting of carbon monoxide molecules, which enable efficient photon emission even at a relatively low temperature and high vapor pressure. The emitted photons have an energy in the range 180~meV to 265~meV. By mixing together carbon monoxide molecules of different isotopes, including those with an odd number of neutrons, we obtain sensitivity to both spin-independent interactions and spin-dependent interactions with the neutron. We also consider hydrogen fluoride, hydrogen bromide, and scandium hydride molecules, which each provide sensitivity to spin-dependent interactions with the proton. The proposed detection concept can be realized with near-term technology and allows for the exploration of orders of magnitude of new dark matter parameter space.