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.

Scalable local control over gate operations is an outstanding challenge in the field of quantum computing and programmable quantum simulation with Rydberg-atom arrays. One approach is to use a global field to excite atoms to the Rydberg state and tune individual atoms in and out of resonance via local light shifts. In this work, we point out that photon-scattering errors from light shifts can be significantly reduced if the light shift is applied to the Rydberg state instead of the ground state, which can be realized in Rydberg states of alkaline-earth atoms using optical transitions in the ion core. As a proof of concept, we experimentally demonstrate global control of Rydberg excitations in an $\mathrm{Yb}$ optical-tweezer array via light shifts induced by a laser tuned near the $\mathrm{Yb}$${}^{+}6s\to 6p_{1/2}$ transition. We also perform detailed spectroscopy of the induced light shift and scattering rates of the $6sns{}^3{\mathrm{S}}_1$ Rydberg states and reveal the existence of satellite lines where losses from autoionization are strongly suppressed. This work can be readily extended to implement local gate operations in Rydberg-atom arrays.

We investigate theoretically and experimentally the heteronuclear Efimov scenario for a three-body system that consists of two bosons and one distinguishable particle with positive intraspecies scattering lengths. The three-body parameter at the three-body scattering threshold and the scaling factor between consecutive Efimov resonances are found to be controlled by the scattering length between the two bosons, approximately independent of short-range physics. We observe two excited-state Efimov resonances in the three-body recombination spectra of an ultracold mixture of fermionic ${}^6\mathrm{Li}$ and bosonic ${}^{133}\mathrm{Cs}$ atoms close to a Li-Cs Feshbach resonance, where the Cs-Cs interaction is positive. Deviation of the obtained scaling factor of 4.0(3) from the universal prediction of 4.9 and the absence of the ground state Efimov resonance shed new light on the interpretation of the universality and the discrete scaling behavior of heteronuclear Efimov physics.

Neutral alkaline earth(like) atoms have recently been employed in atomic arrays with individual readout, control, and high-fidelity Rydberg-mediated entanglement. This emerging platform offers a wide range of new quantum science applications that leverage the unique properties of such atoms: ultranarrow optical “clock” transitions and isolated nuclear spins. Specifically, these properties offer an optical qubit ($o$) as well as ground ($g$) and metastable ($m$) nuclear spin qubits, all within a single atom. We consider experimentally realistic control of this omg architecture and its coupling to Rydberg states for entanglement generation, focusing specifically on ytterbium-171 (${}^{171}\mathrm{Yb}$) with nuclear spin $I=\frac{1}{2}$. We analyze the $S$-series Rydberg states of ${}^{171}\mathrm{Yb}$, described by the three spin-$\frac{1}{2}$ constituents (two electrons and the nucleus). We confirm that the $F=\frac{3}{2}$ manifold, a unique spin configuration, is well suited for entangling nuclear spin qubits. Further, we analyze the $F=\frac{1}{2}$ series, described by two overlapping spin configurations, using a multichannel quantum defect theory. We study the multilevel dynamics of the nuclear spin states when driving the clock or Rydberg transition with Rabi frequency ${\mathrm{\Omega }}_c=2\pi \times 200\text{kHz}$ or ${\mathrm{\Omega }}_R=2\pi \times 6\text{MHz}$, respectively, finding that a modest magnetic field ($\approx 200\text{G}$) and feasible laser polarization intensity purity ($\lesssim 0.99$) are sufficient for gate fidelities exceeding 0.99. We also study single-beam Raman rotations of the nuclear spin qubits and identify a “magic” linear polarization angle with respect to the magnetic field at which purely ${\sigma }_x$ rotations are possible.

We calculate the $\text{L=0}$ ground and excited state energies for the rare gas trimers ${\mathrm{He}}_3,$ ${\mathrm{Ne}}_3,$ and ${\mathrm{Ar}}_3.$ An adiabatic representation is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B splines. We compare results obtained in a strict adiabatic approximation with nonperturbative coupled-adiabatic-channel calculations. Structural properties such as the pair and angle distributions are monitored as functions of the hyper-radius. These structural studies pinpoint the locus of configurational changes that occur as the trimer fragments into a diatom plus an atom. Analysis of the angular channel functions and their associated radial components permits an approximate classification of the vibrational spectrum.

Sufficiently high densities in Bose–Einstein condensates provide favorable conditions for the production of ultralong-range polyatomic molecules consisting of one Rydberg atom and a number of neutral ground state atoms. The chemical binding properties and electronic wave functions of these exotic molecules are investigated analytically via hybridized diatomic states. The effects of the molecular geometry on the system’s properties are studied through comparisons of the adiabatic potential curves and electronic structures for both symmetric and randomly configured molecular geometries. General properties of these molecules with increasing numbers of constituent atoms and in different geometries are presented. These polyatomic states have spectral signatures that lead to non-Lorentzian line-profiles.