A recent rejuvenation of experimental and theoretical interest in the physics of few-body systems has provided deep, fundamental insights into a broad range of problems. Few-body physics is a cross-cutting discipline not restricted to conventional subject areas such as nuclear physics or atomic or molecular physics. To a large degree, the recent explosion of interest in this subject has been sparked by dramatic enhancements of experimental capabilities in ultracold atomic systems over the past decade, which now permit atoms and molecules to be explored deep in the quantum mechanical limit with controllable two-body interactions. This control, typically enabled by magnetic or electromagnetically dressed Fano-Feshbach resonances, allows, in particular, access to the range of universal few-body physics, where two-body scattering lengths far exceed all other length scales in the problem. The Efimov effect, where three particles experiencing short-range interactions can counterintuitively exhibit an infinite number of bound or quasibound energy levels, is the most famous example of universality. Tremendous progress in the field of universal Efimov physics has taken off, driven particularly by a combination of experimental and theoretical studies in the past decade, and prior to the first observation in 2006, by an extensive set of theoretical studies dating back to 1970. Because experimental observations of Efimov physics have usually relied on resonances or interference phenomena in three-body recombination, this connects naturally with the processes of molecule formation in a low-temperature gas of atoms or nucleons, and more generally with $N$-body recombination processes. Some other topics not closely related to the Efimov effect are also reviewed in this article, including confinement-induced resonances for explorations of lower-dimensionality systems, and some chemically interesting systems with longer-range forces such as the ion-atom-atom recombination problem.

Engineering molecules with a tunable bond length and defined quantum states lies at the heart of quantum chemistry. The unconventional binding mechanism of Rydberg molecules makes them a promising candidate to implement such tunable molecules. A very peculiar type of Rydberg molecules are the so-called butterfly molecules, which are bound by a shape resonance in the electron–perturber scattering. Here we report the observation of these exotic molecules and employ their exceptional properties to engineer their bond length, vibrational state, angular momentum and orientation in a small electric field. Combining the variable bond length with their giant dipole moment of several hundred Debye, we observe counter-intuitive molecules which locate the average electron position beyond the internuclear distance.

Within a dense environment ($\rho \approx {10}^{14}\mathrm{atoms}/{\mathrm{cm}}^3$) at ultracold temperatures ($T<1\mu \mathrm{K}$), a single atom excited to a Rydberg state acts as a reaction center for surrounding neutral atoms. At these temperatures, almost all neutral atoms within the Rydberg orbit are bound to the Rydberg core and interact with the Rydberg atom. We have studied the reaction rate and products for $nS$ ${}^{87}\mathrm{Rb}$ Rydberg states, and we mainly observe a state change of the Rydberg electron to a high orbital angular momentum $l$, with the released energy being converted into kinetic energy of the Rydberg atom. Unexpectedly, the measurements show a threshold behavior at $n\approx 100$ for the inelastic collision time leading to increased lifetimes of the Rydberg state independent of the densities investigated. Even at very high densities ($\rho \approx 4.8\times {10}^{14}{\mathrm{cm}}^{-3}$), the lifetime of a Rydberg atom exceeds $10\mu \mathrm{s}$ at $n>140$ compared to $1\mu \mathrm{s}$ at $n=90$. In addition, a second observed reaction mechanism, namely, ${\mathrm{Rb}}_2^{+}$ molecule formation, was studied. Both reaction products are equally probable for $n=40$, but the fraction of ${\mathrm{Rb}}_2^{+}$ created drops to below 10% for $n\ge 90$.

We present spectroscopy of a single Rydberg atom excited within a Bose-Einstein condensate. We not only observe the density shift as discovered by Amaldi and Segrè in 1934, but a line shape that changes with the principal quantum number $n$. The line broadening depends precisely on the interaction potential energy curves of the Rydberg electron with the neutral atom perturbers. In particular, we show the relevance of the triplet $p$-wave shape resonance in the $e^{-}\text{−}\mathrm{Rb}(5S)$ scattering, which significantly modifies the interaction potential. With a peak density of $5.5\times {10}^{14}{\mathrm{cm}}^{-3}$, and therefore an interparticle spacing of $1300a_0$ within a Bose-Einstein condensate, the potential energy curves can be probed at these Rydberg ion-neutral atom separations. We present a simple microscopic model for the spectroscopic line shape by treating the atoms overlapped with the Rydberg orbit as zero-velocity, uncorrelated, pointlike particles, with binding energies associated with their ion-neutral separation, and good agreement is found.

We study three-body recombination of ${\mathrm{Ba}}^{+}+\mathrm{Rb}+\mathrm{Rb}$ in the mK regime where a single ${{}^{138}\mathrm{Ba}}^{+}$ ion in a Paul trap is immersed into a cloud of ultracold ${}^{87}\mathrm{Rb}$ atoms. We measure the energy dependence of the three-body rate coefficient $k_3$ and compare the results to the theoretical prediction, $k_3\propto E_{\mathrm{col}}^{-3/4}$, where $E_{\mathrm{col}}$ is the collision energy. We find agreement if we assume that the nonthermal ion energy distribution is determined by at least two different micromotion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed in an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the $s$-wave regime.