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 ar- eas 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 3 particles experienc- ing short-range interactions can counterintuitively exhibit an infinite number of bound or quasi-bound 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 ...Comment: review articl

A semi-analytical approach to atomic waveguide scattering for harmonic confinement is developed taking into account all partial waves. As a consequence ℓ-wave confinement-induced resonances are formed being coupled to each other due to the confinement. The corresponding resonance condition is obtained analytically using the K-matrix formalism. Atomic scattering is described by transition diagrams which depict all relevant processes the atoms undergo during the collision. Our analytical results are compared to corresponding numerical data and show very good agreement.

We develop a non-perturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory allowing to include accurately long-range anisotropic interactions. Analyzing ultracold dipolar collisions in a harmonic waveguide we predict dipolar confinement-induced resonances (DCIRs) which are attributed to different angular momentum states. The analytically derived resonance condition reveals in detail the interplay of the confinement with the anisotropic nature of the dipole-dipole interactions. The results are in excellent agreement with ab initio numerical calculations confirming the robustness of the presented approach. The exact knowledge of the positions of DCIRs may pave the way for the experimental realization e.g. Tonks-Girardeau-like or super-Tonks-Girardeau-like phases in effective one-dimensional dipolar gases. In low-dimensional geometries due to tightly confining traps, ultracold atomic scattering undergoes crucial modifications yielding the effect of confinement-induced resonances (CIRs) [1,2]. A CIR is a Fano-Feshbach-type of resonance occurring when the scattering length a s and the length of the transversal confinement a ⊥ are comparable, namely a s /a ⊥ ≈ 0.68. Remarkably, the deepened theoretical understanding of CIR physics [3-10] has lead to major achievements in the experimental manipulation [11,12] of interacting gaseous atomic matter. Together with the extensive study of free-space dipolar collisions [13][14][15][16][17][18][19][20], confinement-induced resonant scattering introduces an intriguing perspective for the control of dipolar many-body phases [21,22]. Indeed, reduced dimensionality has lead to the prediction of dipolar crystals [23] and the control of internal and external degrees of freedom of molecules has allowed the realization of dense ultracold polar molecule gases [24]. In view of the substantial theoretical effort made on confined dipolar scattering [25][26][27][28][29][30], the need for a rigorous understanding of the role of anisotropic forces in CIRs becomes evident.In this letter, we analytically derive the resonance condition for s-wave dipolar CIR (DCIR), with explicit dependence on the dipole-dipole interaction (DDI) strength. This is done within an extended K-matrix formalism for harmonic quasi-one-dimensional (Q1D) geometries [10] which incorporates anisotropic forces, i.e. the DDI, and takes into account contributions from higher angular momentum states. These ℓ-wave states are firstly coupled due to the anisotropic nature of the DDI and secondly by the harmonic confinement, which leads to a rich resonance structure of the DCIRs. The ℓ-wave DCIRs appear in the vicinity of shape resonances which are properly taken into account within the K-matrix approach going beyond the effective onedimensional pseudopotential theory [27]. Interestingly, this interplay between the confinement and the DDI leads to an intricate dependence of the s-wave DCIRs positions...

The universal aspects of two-body collisions in the presence of a harmonic confinement are investigated for both bosons and fermions. The main focus of this study are the confinement-induced resonances (CIR) which are attributed to different angular momentum states ℓ and we explicitly show that in alkaline collisions only four universal ℓ-wave CIRs emerge given that the interatomic potential is deep enough. Going beyond the single mode regime the energy dependence of ℓ-wave CIRs is studied. In particular we show that all the ℓ-wave CIRs may emerge even when the underlying two-body potential cannot support any bound state. We observe that the intricate dependence on the energy yields resonant features where the colliding system within the confining potential experiences an effective free-space scattering. Our analysis is done within the framework of the generalized K-matrix theory and the relevant analytical calculations are in very good agreement with the corresponding ab initio numerical scattering simulations.

A rigorous theoretical framework is developed for a generalized local frame transformation theory (GLFT). The GLFT is applicable to the following systems: to Rydberg atoms or molecules in an electric field, or to negative ions in any combination of electric and/or magnetic fields. A first test application to the photoionization spectra of Rydberg atoms in an external electric field demonstrates dramatic improvement over the first version of the local frame transformation theory developed initially by Fano and Harmin. This revised GLFT theory yields non-trivial corrections because it now includes the full on-shell Hilbert space without adopting the truncations in the original theory. Comparisons of the semi-analytical GLFT Stark spectra with ab initio numerical simulations yields errors in the range of a few tens of MHz, an improvement over the original FanoHarmin theory whose errors are 10-100 times larger. Our analysis provides a systematic pathway to precisely describe the corresponding photoabsorption spectra that should be accurate enough to meet most modern experimental standards.

Two-photon ionization of an alkali-metal atom in the presence of a uniform electric field is investigated using a standardized form of the local frame transformation and generalized quantum defect theory. The relevant long-range quantum defect parameters in the combined Coulombic plus Stark potential are calculated with eigenchannel R-matrix theory applied in the downstream parabolic coordinate η. The present formulation permits us to express the corresponding microscopy observables through the local frame transformation, and it gives a critical test of the accuracy of the Harmin-Fano theory.

The mass-imbalanced three-body recombination process that forms a shallow dimer is shown to possess a rich Efimov-Stückelberg landscape, with corresponding spectra that differ fundamentally from the homonuclear case. A semianalytical treatment of the three-body recombination predicts unusual spectra with intertwined resonance peaks and minima and yields in-depth insight into the behavior of the corresponding Efimov spectra. In particular, the patterns of the Efimov-Stückelberg landscape are shown to depend inherently on the degree of diabaticity of the three-body collisions, which strongly affects the universality of the heteronuclear Efimov states.

We observe and analyze d-wave resonant scattering of bosons in tightly confining harmonic waveguides. It is shown that the d-wave resonance emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for the position of the d-wave resonance is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from s-wave to d-wave resonant behavior. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a novel possibility for studying strongly correlated atomic systems beyond s-wave physics.