Ab initio calculation of the spectrum of Feshbach resonances in NaLi + Na collisions

We present a combined experimental and theoretical study of the spectrum of magnetically tunable Feshbach resonances in NaLi $(a^3\Sigma^+)$ $+$ Na collisions. In the accompanying paper, we observe experimentally 8 and 17 resonances occur between $B=0$ and $1400$~G in upper and lower spin-stretched states, respectively. Here, we perform ab initio calculations of the NaLi $+$ Na interaction potential and describe in detail the coupled-channel scattering calculations of the Feshbach resonance spectrum. The positions of the resonances cannot be predicted with realistic uncertainty in the state-of-the-art ab initio potential, but our calculations yield a typical number of resonances that is in near-quantitative agreement with experiment. We show that the main coupling mechanism results from spin-rotation and spin-spin couplings in combination with the anisotropic atom-molecule interaction. The calculations furthermore explain the qualitative difference between the numbers of resonances in either spin state

Cold hybrid ion-atom systems

Hybrid systems of laser-cooled trapped ions and ultracold atoms combined in a single experimental setup have recently emerged as a new platform for fundamental research in quantum physics. This paper reviews the theoretical and experimental progress in research on cold hybrid ion-atom systems which aim to combine the best features of the two well-established fields. A broad overview is provided of the theoretical description of ion-atom mixtures and their applications, and a report is given on advances in experiments with ions trapped in Paul or dipole traps overlapped with a cloud of cold atoms, and with ions directly produced in a Bose-Einstein condensate. This review begins with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and nonradiative charge-transfer processes and their control with magnetically tunable Feshbach resonances. Then the relevant experimental techniques and the intrinsic properties of hybrid systems are described. In particular, the impact is discussed of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, a review of recent proposals is given for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. The last part focuses on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. Applications and prospects are discussed of cold molecular ions for cold controlled chemistry and precision spectroscopy