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. We provide a broad overview of the theoretical description of ion-atom mixtures and their applications, and report 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. We start with microscopic models describing the electronic structure, interactions, and collisional physics of ion-atom systems at low and ultralow temperatures, including radiative and non-radiative charge transfer processes and their control with magnetically tunable Feshbach resonances. Then we describe the relevant experimental techniques and the intrinsic properties of hybrid systems. In particular, we discuss the impact of the micromotion of ions in Paul traps on ion-atom hybrid systems. Next, we review recent proposals for using ions immersed in ultracold gases for studying cold collisions, chemistry, many-body physics, quantum simulation, and quantum computation and their experimental realizations. In the last part we focus on the formation of molecular ions via spontaneous radiative association, photoassociation, magnetoassociation, and sympathetic cooling. We discuss applications and prospects of cold molecular ions for cold controlled chemistry and precision spectroscopy.

Analytical potential energy surface for the NH3+HNH2+H2 reaction: Application of variational transition-state theory and analysis of the equilibrium constants and kinetic isotope effects using curvilinear and rectilinear coordinates J. Chem. Phys. 106, 4013 (1997) product ions, respectively. The cross sections for both reactions were found to increase with decreasing collision energy, E coll , in the range 8 μeV < E coll < 20 meV. The measured rate constant exhibits a curvature in a log(k)-log(E coll ) plot from which it is concluded that the Langevin capture model does not properly describe the Ne * + NH 3 reaction in the entire range of collision energies covered here. Calculations based on multichannel quantum defect theory were performed to reproduce and interpret the experimental results. Good agreement was obtained by including long range van der Waals interactions combined with a 6-12 Lennard-Jones potential. The branching ratio between the two reactive channels, =, is relatively constant, ≈ 0.3, in the entire collision energy range studied here. Possible reasons for this observation are discussed and rationalized in terms of relative time scales of the reactant approach and the molecular rotation. Isotopic differences between the Ne * + NH 3 and Ne * + ND 3 reactions are small, as suggested by nearly equal branching ratios and cross sections for the two reactions. © 2014 AIP Publishing LLC.

We develop a general quantum theory for reactive collisions involving power-law potentials (−1/r n ) valid from the ultracold up to the high-temperature limit. Our quantum defect framework extends the conventional capture models to include the non-universal case when the short-range reaction probability P re < 1. We present explicit analytical formulas as well as numerical studies for the van der Waals (n = 6) and polarization (n = 4) potentials. Our model agrees well with recent merged beam experiments on Penning ionization, spanning collision energies from 10mK to 30K [Henson et al, Science 338, 234(2012)].PACS numbers: 34.50. Cx, 03.65.Nk, 34.10.+x, 34.50.Lf Much recent work involves the inelastic and reactive collisions of cold atoms or molecules with one another [1][2][3][4] or with ions in hybrid traps [5][6][7]. These could involve the ultracold regime with translational temperature on the order of µK or less or the cold regime between a few mK and a few K. Systematic theoretical principles for understanding the quantum dynamics of such collisions are needed. Much work has already been done in this area, as reviewed by Ref. [8]. One class of theories based on Quantum Defect Theory (QDT) allows us to systematize and develop tools for understanding such collisions [9][10][11][12][13][14][15]. One special limiting case is that of highly reactive collisions, where simple classical trajectory capture models known as the Langevin (n = 4) [16] or Gorin (n = 6) [17] models apply when the long range potential takes on the form −C n /r n (n > 3). These familiar models assume that every classical trajectory contributes to the collision cross section that is captured by the long range potential so the particles spiral in to short distance where they react or relax with probability P re . We use the term "universal" to describe capture models with P re = 1, since they do not depend on any details of the strong short-range chemical interactions.In the cold and ultracold regimes, it is essential to build in quantum corrections to these classical models due to quantum threshold laws [18][19][20]. This has been done using QDT for both the Langevin [21,22] and Gorin [23,24] universal models where P re = 1. Here, we will follow the formalism by Idziaszek et al. [22,23] and generalize the previous results to the nonuniversal regime with P re < 1, and to the arbitrary collision energy. In the limiting cases of low and high temperatures we give analytic formulas that are valid for power-law potentials (−1/r n ). We apply our theory to interpret the ionization rate constants measured by recent merged beam experiments in the cold regime [25]. Using a single complex QDT parameter found by fitting low energy data only, we are able to reproduce the experimental data over four orders of magnitude in energy including about twenty partial waves in the calculation.Generalized complex scattering length. We consider reactive collisions of particles interacting via power-law potential V (r) = −C n /r n (n > 3) at large distances r R 0 ...

We report on the observation of weakly-bound dimers of bosonic Dysprosium with a strong universal s-wave halo character, associated with broad magnetic Feshbach resonances. These states surprisingly decouple from the chaotic backgound of narrow resonances, persisting across many such narrow resonances. In addition they show the highest reported magnetic moment µ 20 µ B of any ultracold molecule. We analyze our findings using a coupled-channel theory taking into account the short range van der Waals interaction and a correction due to the strong dipole moment of Dysprosium. We are able to extract the scattering length as a function of magnetic field associated with these resonances and obtain a background scattering length a bg = 91(16) a 0 . These results offer prospects of a tunability of the interactions in Dysprosium, which we illustrate by observing the saturation of three-body losses.

Resonances are among the clearest quantum mechanical signatures of scattering processes. Previously, shape resonances and Feshbach resonances have been observed in inelastic and reactive collisions involving atoms or diatomic molecules. Structure in the integral cross section has been observed in a handful of elastic collisions involving polyatomic molecules. The present paper presents the observation of shape resonances in the reactive scattering of a polyatomic molecule, NH3. A merged-beam study of the gas phase He((3)S1) + NH3 Penning ionization reaction dynamics is described in the collision energy range 3.3 μeV < Ecoll < 10 meV. In this energy range, the reaction rate is governed by long-range attraction. Peaks in the integral cross section are observed at collision energies of 1.8 meV and 7.3 meV and are assigned to ℓ = 15,16 and ℓ = 20,21 partial wave resonances, respectively. The experimental results are well reproduced by theoretical calculations with the short-range reaction probability Psr = 0.035. No clear signature of the orbiting resonances is visible in the branching ratio between NH3 (+) and NH2 (+) formation.

Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled channels calculations for several cases of overlapping resonances in the collisions of two $^7$Li atoms or two Cs atoms.Comment: 8 page

We study a system of three photons in an atomic medium coupled to Rydberg states near the conditions of electromagnetically induced transparency. Based on the analytical analysis of the microscopic set of equations in the far-detuned regime, the effective three-body interaction for these Rydberg polaritons is derived. For slow light polaritons, we find a strong three-body repulsion with the remarkable property that three polaritons can become essentially noninteracting at short distances. This analysis allows us to derive the influence of the three-body repulsion on bound states and correlation functions of photons propagating through a one-dimensional atomic cloud.

We consider a general problem of inelastic collision of particles interacting with power-law potentials. Using quantum defect theory we derive an analytical formula for the energy-dependent complex scattering length, valid for arbitrary collision energy, and use it to analyze the elastic and reactive collision rates. Our theory is applicable for both universal and non-universal collisions. The former corresponds to the unit reaction probability at short range, while in the latter case the reaction probability is smaller than one. In the high-energy limit we present a method that allows to incorporate quantum corrections to the classical reaction rate due to the shape resonances and the quantum tunneling.