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Controlling physical systems and their dynamics on the level of individual quanta propels both fundamental science and quantum technologies. Trapped atomic and molecular systems, neutral and charged, are at the forefront of quantum science. Their extraordinary level of control is evidenced by numerous applications in quantum information processing and quantum metrology. Studying the long-range interactions between these systems when combined in a hybrid atom-ion trap has lead to landmark results. Reaching the ultracold regime, however, where quantum mechanics dominates the interaction, e.g., giving access to controllable scattering resonances, has been elusive so far. Here we demonstrate Feshbach resonances between ions and atoms, using magnetically tunable interactions between $^{138}$Ba$^{+}$ ions and $^{6}$Li atoms. We tune the experimental parameters to probe different interaction processes - first, enhancing three-body reactions and the related losses to identify the resonances, then making two-body interactions dominant to investigate the ion's sympathetic cooling in the ultracold atomic bath. Our results provide deeper insights into atom-ion interactions, giving access to complex many-body systems and applications in experimental quantum simulation., 13 pages, 7 figures

Understanding the sources of losses and chemical reactions of ultracold alkali-metal molecules is among the critical elements needed for their application in precision measurements and quantum technologies. Recent experiments with nonreactive systems have reported unexpectedly large loss rates, posing a challenge for theoretical explanation. Here, we examine the dynamics of intermediate four-atom complexes formed in bimolecular collisions. We calculate the nuclear spin--rotation, spin--spin, and quadrupole coupling constants for bialkali tetramers using ab intio quantum-chemical methods. We show that the nuclear spin--spin and quadrupole couplings are strong enough to couple different rotational manifolds to increase the density of states and lifetimes of the collision complexes, which is consistent with experimental results. We propose further experiments to confirm our predictions., Comment: 6 pages, 3 plots

State-of-the-art experiments using Rydberg atoms can now operate with large numbers of trapped particles with tunable geometry and long coherence time. We propose a way to utilize this in a hybrid setup involving neutral ground state atoms to efficiently simulate condensed matter models featuring electron-phonon coupling. Such implementation should allow for controlling the coupling strength and range as well as the band structure of both the phonons and atoms, paving the way towards studying both static and dynamic properties of extended Hubbard-Holstein models.

The presence of strong interactions in a many-body quantum system can lead to a variety of exotic effects. Here we show that even in a comparatively simple setup consisting of a charged impurity in a weakly interacting bosonic medium the competition of length scales gives rise to a highly correlated mesoscopic state. Using quantum Monte Carlo simulations, we unravel its vastly different polaronic properties compared to neutral quantum impurities. Moreover, we identify a transition between the regime amenable to conventional perturbative treatment in the limit of weak atom-ion interactions and a many-body bound state with vanishing quasi-particle residue composed of hundreds of atoms. In order to analyze the structure of the corresponding states we examine the atom-ion and atom-atom correlation functions which both show nontrivial properties. Our findings are directly relevant to experiments using hybrid atom-ion setups that have recently attained the ultracold regime., Comment: published version, 10 pages, 5 figures, 1 table

We investigate transport dynamics of a single low-energy ionic impurity in a Bose-Einstein condensate. The impurity is implanted into the condensate starting from a single Rydberg excitation, which is ionized by a sequence of fast electric field pulses aiming to minimize the ion's initial kinetic energy. Using a small electric bias field, we study the subsequent collisional dynamics of the impurity subject to an external force. The fast ion-atom collision rate, stemming from the dense degenerate host gas and the large ion-atom scattering cross section, allows us to study a regime of frequent collisions of the impurity within only tens of microseconds. Comparison of our measurements with stochastic trajectory simulations based on sequential Langevin collisions indicate diffusive transport properties of the impurity and allows us to measure its mobility. Furthermore, working with a free and untrapped ion provides unique means to distinguish single realizations, where the impurity is subject to inelastic molecular-ion formation via three-body recombination. We study the cold chemistry of these events and find evidence for subsequent rovibrational quenching collisions of the produced molecule. Our results open a novel path to study dynamics of charged quantum impurities in ultracold matter., Comment: 10 pages, 9 figures

We study the beyond-mean-field corrections to the energy of a dipolar Bose gas confined to two dimensions by a box potential with dipoles oriented in plane such that their interaction is anisotropic in the two unconfined dimensions. At a critical strength of the dipolar interaction the system becomes unstable on the mean field level. We find that the ground state of the gas is strongly influenced by the corrections, leading to formation of a self-bound droplet, in analogy to the free space case. Properties of the droplet state can be found by minimizing the extended Gross–Pitaevskii energy functional. In the limit of strong confinement we show analytically that the correction can be interpreted as an effective three-body repulsion which stabilizes the gas at finite density.

We investigate inelastic collision dynamics of a single cold ion in a Bose-Einstein condensate. We observe rapid ion-atom-atom three-body recombination leading to formation of weakly bound molecular ions followed by secondary two-body molecule-atom collisions quenching the rovibrational states towards deeper binding energies. In contrast to previous studies exploiting hybrid ion traps, we work in an effectively field-free environment and generate a free low-energy ionic impurity directly from the atomic ensemble via Rydberg excitation and ionization. This allows us to implement an energy-resolved field-dissociation technique to trace the relaxation dynamics of the recombination products. Our observations are in good agreement with numerical simulations based on Langevin capture dynamics and provide complementary means to study stability and reaction dynamics of ionic impurities in ultracold quantum gases., Comment: 5 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2007.00309

Feshbach resonances are among the essential control tools used in ultracold atom experiments. However, for complex atomic species the theoretical characterization of resonances becomes challenging. For closely spaced resonances, the measurement of three-body losses does not provide sufficient resolution to discriminate them. For this reason, resonance spectroscopy of trapped isolated atoms is becoming the state of the art. Here we show that trapping the atoms in a double well potential such as an optical lattice or a pair of optical tweezers enables precise characterization of not only the resonance position and width, but also its pole strength, giving valuable information about the atomic structure relevant for subsequent many-body studies.

We present results from a joint theoretical and experimental study of the low-energy Penning ionization of NH3, CH3F, and CHF3 by metastable Ne(P-3(2)) and He(S-3(1)) atoms. We combine the merged neutral beams experiment, covering a range of collision energies between 0.1-150K, with multichannel quantum defect theory calculations based on interaction potentials from symmetry-adapted perturbation theory. The three symmetric tops provide several distinct properties that make them interesting targets for cold chemistry studies. Of these three, only NH3 has a lone electron pair that leads to a strong binding with rare gas atoms. The CHF3 molecule has much smaller rotational constants than both NH3 and CH3F, and thus has a considerably higher density of rotational states already at low energies. Their presence opens inelastic collision channels that reduce the observed reactive cross section. We show that this effect dominates the total rate coefficient in heavy molecules already at relatively low collision energies but is much less prominent for lighter molecules

Recent experiments with ultracold lanthanide atoms which are characterized by a large magnetic moment have revealed the crucial importance of beyond-mean-field corrections in understanding the dynamics of the gas. We study how the presence of an external optical lattice modifies the structure of the corrections. We find that deep in the superfluid regime the equation of state is well described by introducing an anisotropic effective mass. However, for a deep lattice we find terms with anomalous density dependence which do not arise in free space. For a one-dimensional lattice, the relative orientation of the dipole axis with respect to the lattice plays a crucial role and the beyond-mean-field corrections can be either enhanced or suppressed.

Hybrid ion&ndash, atom systems provide an excellent platform for studies of state-resolved quantum chemistry at low temperatures, where quantum effects may be prevalent. Here we study theoretically the process of vibrational relaxation of an initially weakly bound molecular ion due to collisions with the background gas atoms. We show that this inelastic process is governed by the universal long-range part of the interaction potential, which allows for using simplified model potentials applicable to multiple atomic species. The product distribution after the collision can be estimated by making use of the distorted wave Born approximation. We find that the inelastic collisions lead predominantly to small changes in the binding energy of the molecular ion.

We study a quasi-two dimensional gas of bosonic dipoles, calculating the beyond mean field corrections to the ground state energy and chemical potential neglecting the transverse mode structure. We show that the corrections are sensitive to the high momentum part of the interaction and cannot be expressed solely in terms of the scattering length and the dipole strength. While nonuniversal, the correction is found to be negative, which provides an additional attractive term in the extended Gross-Pitaevskii equation, enhancing the roton instability.

Hybrid systems of ultracold atoms and trapped ions or Rydberg atoms can be useful for quantum simulation purposes. By tuning the geometric arrangement of the impurities, it is possible to mimic solid-state and molecular systems. Here, we study a single trapped atom interacting with a set of arbitrarily arranged static impurities and show that the problem admits an analytical solution. We analyze in detail the case of two impurities, finding multiple trap-induced resonances which can be used for entanglement generation. Our results serve as a building block for the studies of quantum dynamics of complex systems.

We present a detailed analysis of the usefulness of ultracold atomic collisions for sensing the strength of an external magnetic field as well as its spatial gradient. The core idea of the sensor, which we recently proposed in K. Jachymski \emph{et al.}, Phys. Rev. Lett. {\bf 120}, 013401 (2018), is to probe the transmission of the atoms through a set of quasi-one-dimensional waveguides that contain an impurity. Magnetic field-dependent interactions between the incoming atoms and the impurity naturally lead to narrow resonances that can act as sensitive field probes since they strongly affect the transmission. We illustrate our findings with concrete examples of experimental relevance, demonstrating that a sensitivity of the order of 1 nT for the field strength and $100\,\mathrm{nT}/\mathrm{mm}$ for the gradient can be reached using our scheme.

Ultracold atoms placed in a tight cigar-shaped trap are usually described in terms of the Lieb-Liniger model. We study the extensions of this model which arise when van der Waals interaction between atoms is taken into account. We find that the corrections induced by the finite range of interactions can become especially important in the vicinity of narrow Feshbach resonances and suggest realistic schemes of their experimental detection. The interplay of confinement and interactions can lead to effective transparency where the one-dimensional interactions are weak in a wide range of parameters.

We examine the possibility to study the statistical properties of trapped ultracold bosons with light scattering. We derive general effective hamiltonian and show that the spectrum of scattered photons contains information about density-density correlations. As a specific example we discuss light scattering as a potential tool to probe the Mott transition in optical lattice and Anderson localization in incommensurate superlattice.

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., Comment: Review article. 63 pages, 49 figures, over 400 references

Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections with respect to Born approximation arise, and derive modified pseudopotential using realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagram. Our results are relevant for recent experiments with erbium and dysprosium atoms., slight corrections & extensions

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 non-interacting 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., Comment: 5+4 pages

Low energy reaction dynamics can strongly depend on the internal structure of the reactants. The role of rotationally inelastic processes in cold collisions involving polyatomic molecules has not been explored so far. Here we address this problem by performing a merged-beam study of the He((3)S1)+CHF3 Penning ionization reaction in a range of collision energies E/kB = 0.5-120 K. The experimental cross sections are compared with total reaction cross sections calculated within the framework of quantum defect theory. We find that the broad range of collision energies combined with the relatively small rotational constants of CHF3 makes rotationally inelastic collisions a crucial player in the total reaction dynamics. Quantitative agreement between theory and experiment is only obtained if the energy-dependent probability for rotational excitation is included in the calculations, in stark contrast to previous experiments where classical scaling laws were able to describe the results.

We present results from a joint theoretical and experimental study of the low-energy Penning ionization of NH

Overlapping Feshbach resonances are commonly observed in experiments with ultracold atoms and can influence the molecule production process. We derive an effective approach to describe magnetoassociation in an external trap in the presence of multiple overlapping resonances. We study how the strength and shape of the trap affects the energy level structure and demonstrate the existence of a regime in which the conventional two-channel Landau-Zener description of the molecule production process breaks down., Comment: 7 pages, 5 figures

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 background of narrow resonances, persisting across many such narrow resonances. In addition they show the highest reported magnetic moment $\ensuremath{\mu}\ensuremath{\simeq}20{\ensuremath{\mu}}_{\mathrm{B}}$ 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 ${a}_{\mathrm{bg}}=91(16)\phantom{\rule{0.16em}{0ex}}{a}_{0}$. These results offer prospects of a tunability of the interactions in dysprosium, which we illustrate by observing the saturation of three-body losses.

Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by random matrix theory. Scattering resonances observed in ultracold atomic and molecular systems exhibit similar features as a consequence of their energy level structure. We study how the overlap between Feshbach resonances affects the distribution of resonance spacings. The spectrum of strongly overlapping resonances turns out to be non-Poisson even when the assumptions of random matrix theory are not fulfilled, but the spectrum is also not completely chaotic and tends towards being semi-Poisson.

We consider low energy threshold reactive collisions of particles interacting via a van der Waals potential at long range in the presence of external confinement and give analytic formulas for the confinement modified scattering in such circumstances. The reaction process is described in terms of the short range reaction probability. Quantum defect theory is used to express elastic and inelastic or reaction collision rates analytically in terms of two dimensionless parameters representing phase and reactivity. We discuss the modifications to Wigner threshold laws for quasi-one-dimensional and quasi-two-dimensional geometries. Confinement-induced resonances are suppressed due to reactions and are completely absent in the universal limit where the short-range loss probability approaches unity., Comment: prepared as a contribution to New Journ. Phys. special issue on cold molecules; v2: minor improvements

We propose a simple idea for realizing a quantum gate with two identical fermions in a double well trap via external optical pulses without addressing the atoms individually. The key components of the scheme are Feshbach resonance and Pauli blocking, which decouple unwanted states from the dynamics. As a physical example we study atoms in the presence of a magnetic Feshbach resonance in a nanoplasmonic trap and discuss the constraints on the operation times for realistic parameters, reaching a fidelity above $99.9\%$ within $42\mu$s., Comment: 5 pages

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., Comment: followup to arXiv:1301.5857

We study polar molecule scattering in quasi-one-dimensional geometries. Elastic and reactive collision rates are computed as a function of collision energy and electric dipole moment for different confinement strengths. The numerical results are interpreted in terms of first order scattering and of adiabatic models. Universal dipolar scattering is also discussed. Our results are relevant to experiments where control of the collision dynamics through one dimensional confinement and an applied electric field is envisioned., Comment: 25 pages, 13 figures

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., 8 pages

We develop a general quantum theory for reactive collisions involving power-law potentials ($\ensuremath{-}1/{r}^{n}$) valid from the ultracold up to the high-temperature limit. Our quantum defect framework extends the conventional capture models to include the nonuniversal case when the short-range reaction probability ${P}^{\mathrm{re}}l1$. 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 10 mK to 30 K [Henson et al., Science 338, 234 (2012)].

We consider a pair of atoms in an arbitrary trapping potential in the presence of magnetically tunable Feshbach resonance. We find the energy levels and occupation of the bound molecular states taking into account possible coupling between center of mass and relative motion induced by the trap. As a specific example we discuss the case of different atomic species in harmonic potential, where each atom feels different trapping frequency., Comment: 4 figures, as published

We consider a gas of bosons in a bichromatic optical lattice at finite temperatures. As the amplitude of the secondary lattice grows, the single-particles eigenstates become localized. We calculate the canonical partition function using exact methods for the noninteracting and strongly interacting limit and analyze the statistical properties of the superfluid phase, localized phase and the strongly interacting gas. We show that those phases may be distinguished in experiment using off-resonant light scattering., Comment: v2: minor corrections to the text

Two isotopic chemical reactions, $\mathrm{Ne}^*$ + NH$_3$, and $\mathrm{Ne}^*$ + ND$_3$, have been studied at low collision energies by means of a merged beams technique. Partial cross sections have been recorded for the two reactive channels, namely $\mathrm{Ne}^*$ + NH$_3$ $\rightarrow$ Ne + NH$_3^+$ + $e^-$, and $\mathrm{Ne}^*$ + NH$_3$ $\rightarrow$ Ne + NH$_2^+$ + H + $e^-$, by detecting the NH$_3^+$ and NH$_2^+$ product ions, respectively. The cross sections for both reactions were found to increase with decreasing collision energy, $E_{coll}$, in the range 8 $\mu$eV$

Feshbach resonances, which allow for tuning the interactions of ultracold atoms with an external magnetic field, have been widely used to control the properties of quantum gases. We propose a scheme for using scattering resonances as a probe for external fields, showing that by carefully tuning the parameters it is possible to reach a ${10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{G}$ (or nT) level of precision with a single pair of atoms. We show that, for our collisional setup, it is possible to saturate the quantum precision bound with a simple measurement protocol.