Permanent electric dipole moments in molecules require a breaking of parity symmetry. Conventionally, this symmetry breaking relies on the presence of heteronuclear constituents. We report the observation of a permanent electric dipole moment in a homonuclear molecule in which the binding is based on asymmetric electronic excitation between the atoms. These exotic molecules consist of a ground-state rubidium (Rb) atom bound inside a second Rb atom electronically excited to a high-lying Rydberg state. Detailed calculations predict appreciable dipole moments on the order of 1 Debye, in excellent agreement with the observations.

We observe that when an ultracold ground state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit, ultralong-

We observe ultralong-range blueshifted Cs(2) molecular states near ns(1/2) Rydberg states in an optical dipole trap, where 31≤n≤34. The accidental near degeneracy of (n-4)l and ns Rydberg states for l>2 in Cs, due to the small fractional ns quantum defect, leads to nonadiabatic coupling among these states, producing potential wells above the ns thresholds. Two important consequences of admixing high angular momentum states with ns states are the formation of large permanent dipole moments, ~15-100 Debye, and accessibility of these states via two-photon association. The observed states are in excellent agreement with theory.

We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green's function in d-dimensions is derived. The resulting LippmannSchwinger equation is solved for the case of three-particles with s-wave zero-range interactions. Identical particle symmetry is incorporated in a general and intuitive way. Complete semi-analytic expressions for the nonadiabatic channel couplings are derived. Finally, a model to describe the atom-loss due to three-body recombination for a three-component fermi-gas of 6 Li atoms is presented.

The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behaviour of superconductors, fermionic superfluids and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulae that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including its implications for the famous BCS-BEC crossover problem. Derivations and relevant formulae are also included for the calculation of challenging few-body processes such as recombination.

We predict the existence of a class of ultracold giant molecules formed from trapped ultracold Rydberg atoms and polar molecules. The interaction which leads to the formation of such molecules is the anisotropic, long-range charge-dipole interaction. We show that prominent candidate molecules such as deuterated hydroxyl (OD) and KRb should bind to Rydberg rubidium atoms, with energies E(b)≃5-25  GHz at distances R≃0.1-1  μm. These molecules form in double wells, mimicking chiral molecules, with each well containing a particular dipole orientation. We prepare a set of correlated dressed electron-dipole eigenstates which are used in an on-resonance Raman scheme to coherently control the molecular dipole orientation.

Ultracold molecules formed from association of a single Rydberg atom with surrounding atoms or molecules and those from double Rydberg excitations are discussed in this review. Ultralong-range Rydberg molecules possess a novel molecular bond resulting from scattering of the Rydberg electron from the perturber atoms or molecules. The strong interactions between Rydberg atoms in ultracold gases may lead to formation of macroscopic Rydberg macrodimers. The exquisite control over the properties of the Rydberg electron means that interesting and unusual few-body and quantum many-body features can be realized in such systems.

Formulas for the cross section and event rate constant describing recombination of N particles are derived in terms of general S-matrix elements. Our result immediately yields the generalized Wigner threshold scaling for the recombination of N bosons. A semianalytical formula encapsulates the overall scaling with energy and scattering length, as well as resonant modifications by the presence of N-body states near the threshold collision energy in the entrance channel. We then apply our model to the case of four-boson recombination into an Efimov trimer and a free atom.