Bound and autoionizing potential energy curves in the CH molecule.

This article presents a method of computing bound state potential curves and autoionizing curves using fixed-nuclei R-matrix data extracted from the Quantemol-N software suite. It is a method based on two related multichannel quantum-defect theory approaches. One is applying bound-state boundary conditions to closed-channel asymptotic solution matrices, and the other is searching for resonance positions via eigenphase shift analysis. We apply the method to the CH molecule to produce dense potential-curve datasets presented as graphs and supplied as tables in the publication supplement.

Triatomic Photoassociation in an Ultracold Atom-Molecule Collision.

Ultracold collisions of neutral atoms and molecules have been of great interest since experimental advances enabled the cooling and trapping of such species. This study develops a simplified theoretical treatment of a low-energy collision between an alkali atom and a diatomic molecule accompanied by absorption of a photon from an external electromagnetic field. The long-range interaction between the two species is treated, including the atomic spin-orbit interaction. The long-range potential energy curves for the triatomic complex are calculated in realistic detail, while effects of the short-range behavior are mimicked by applying different boundary conditions at the van der Waals length. For neutral colliding species, the leading interaction term is the dipole-dipole interaction. In the case of nonpolar dimers like Cs2, the second leading term is the quadrupole-quadrupole interaction. However, there is also a strong dipole-quadrupole interaction for dimers with a large permanent dipole moment such as NaCs, making the dipole-quadrupole interaction the second leading term for an atom colliding with a polar dimer. Our applications of the simplified treatment show a higher density of trimer states for a polar dimer compared to the case of a nonpolar dimer like Cs2. This is a consequence of the strong quadrupole-dipole coupling between the atom and the dimer dipole moment.

Differential Measurement of Electron Ejection after Two-Photon Two-Electron Excitation of Helium.

We report the measurement of the photoelectron angular distribution of two-photon single-ionization near the 2p^{2} ^{1}D^{e} double-excitation resonance in helium, benchmarking the fundamental nonlinear interaction of two photons with two correlated electrons. This observation is enabled by the unique combination of intense extreme ultraviolet pulses, delivered at the high-repetition-rate free-electron laser in Hamburg (FLASH), ionizing a jet of cryogenically cooled helium atoms in a reaction microscope. The spectral structure of the intense self-amplified spontaneous emission free-electron laser pulses has been resolved on a single-shot level to allow for post selection of pulses, leading to an enhanced spectral resolution, and introducing a new experimental method. The measured angular distribution is directly compared to state-of-the-art theory based on multichannel quantum defect theory and the streamlined R-matrix method. These results and experimental methodology open a promising route for exploring fundamental interactions of few photons with few electrons in general.

Observation of Wigner-Dyson level statistics in a classically integrable system.

Resonances in particle transmission through a 1D finite lattice are studied in the presence of a finite number of impurities. Although this is a one-dimensional system that is classically integrable and has no chaos, studying the statistical properties of the spectrum such as the level spacing distribution and the spectral rigidity shows the same statistics as the one obtained for chaotic systems. Using a dimensionless parameter that reflects the degree of state localization, we demonstrate how the transition from Poisson-level statistics to the Wigner-Dyson is affected by state localization. The resonance positions are calculated using both the Wigner-Smith time delay and a Siegert state method, which are in good agreement. Our results show the dependence of the level statistics on the localization length as it evolves from a Poisson distribution to Wigner-Dyson.

Nonresonant Density of States Enhancement at Low Energies for Three or Four Neutrons.

The low energy systems of three or four neutrons are treated within the adiabatic hyperspherical framework, yielding an understanding of the low energy quantum states in terms of an adiabatic potential energy curve. The dominant low energy potential curve for each system, computed here using widely accepted nucleon-nucleon interactions with and without the inclusion of a three-nucleon force, shows no sign of a low energy resonance. However, both systems exhibit a low energy enhancement of the density of states, or of the Wigner-Smith time delay, which derives from long-range universal physics analogous to the Efimov effect. That enhancement could be relevant to understanding the low energy excess of correlated four-neutron ejection events observed experimentally in a nuclear reaction by Kisamori et al. [Phys. Rev. Lett. 116, 052501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.052501].

Dissociative Recombination of Cold HeH

The HeH^{+} cation is the simplest molecular prototype of the indirect dissociative recombination (DR) process that proceeds through electron capture into Rydberg states of the corresponding neutral molecule. This Letter develops the first application of our recently developed energy-dependent frame transformation theory to the indirect DR processes. The theoretical model is based on the multichannel quantum-defect theory with the vibrational basis states computed using exterior complex scaling of the nuclear Hamiltonian. The ab initio electronic R-matrix theory is adopted to compute quantum defects as functions of the collision energy and of the internuclear distance. The resulting DR rates are convolved over the beam energy distributions relevant to a recent experiment at the Cryogenic Storage Ring, giving good agreement between the experiment and the theory.

Nonadiabatic Molecular Association in Thermal Gases Driven by Radio-Frequency Pulses.

The molecular association process in a thermal gas of ^{85}Rb is investigated where the effects of the envelope of the radio-frequency field are taken into account. For experimentally relevant parameters our analysis shows that with increasing pulse length the corresponding molecular conversion efficiency exhibits low-frequency interference fringes which are robust under thermal averaging over a wide range of temperatures. This dynamical interference phenomenon is attributed to Stückelberg phase accumulation between the low-energy continuum states and the dressed molecular state which exhibits a shift proportional to the envelope of the radio-frequency pulse intensity.

Coherent Superposition of Feshbach Dimers and Efimov Trimers.

A powerful experimental technique to study Efimov physics at positive scattering lengths is demonstrated. We use the Feshbach dimers as a local reference for Efimov trimers by creating a coherent superposition of both states. Measurement of its coherent evolution provides information on the binding energy of the trimers with unprecedented precision and yields access to previously inaccessible parameters of the system such as the Efimov trimers' lifetime and the elastic processes between atoms and the constituents of the superposition state. We develop a comprehensive data analysis suitable for noisy experimental data that confirms the trustworthiness of our demonstration.

Spin current generation and relaxation in a quenched spin-orbit-coupled Bose-Einstein condensate.

Understanding the effects of spin-orbit coupling (SOC) and many-body interactions on spin transport is important in condensed matter physics and spintronics. This topic has been intensively studied for spin carriers such as electrons but barely explored for charge-neutral bosonic quasiparticles (including their condensates), which hold promises for coherent spin transport over macroscopic distances. Here, we explore the effects of synthetic SOC (induced by optical Raman coupling) and atomic interactions on the spin transport in an atomic Bose-Einstein condensate (BEC), where the spin-dipole mode (SDM, actuated by quenching the Raman coupling) of two interacting spin components constitutes an alternating spin current. We experimentally observe that SOC significantly enhances the SDM damping while reducing the thermalization (the reduction of the condensate fraction). We also observe generation of BEC collective excitations such as shape oscillations. Our theory reveals that the SOC-modified interference, immiscibility, and interaction between the spin components can play crucial roles in spin transport.

Extreme Correlation and Repulsive Interactions in Highly Excited Atomic Alkali Anions.

At high energies, single-photon photodetachment of alkali negative ions populates final states where both the ejected electron and the residual valence electron possess high angular momenta. The photodetached electron interacts strongly with the anisotropic core, and thus the partial cross sections for these channels display non-Wigner threshold behavior reflecting these large, and occasionally repulsive, interactions. Our fully quantum-mechanical theoretical study enables a deeper interpretation of these partial cross sections. Comparisons of the behavior in different channels and between different atomic species-sodium, potassium, and cesium-show the critical role of near degeneracies in the energy spectrum and demonstrate that much of the behavior of the partial photodetachment cross sections stems from the permanent, rather than induced, electric dipole moments of these nearly degenerate channels. This provides a concrete example of a system where negative dispersion forces play a decisive role.

Semiclassical Treatment of High-Lying Electronic States of H2.

We report quantum-mechanical and semiclassical WKB calculations for energies and wave functions of high-lying 2Σ states of H2+ in atomic units. The high-lying states we present lie in an unexplored regime, corresponding asymptotically to H ( n ≤ 146) plus a proton, with R ≤ 120 000 a0. We compare quantum-mechanical energies, spectroscopic constants, dipole matrix elements, and phases with semiclassical results and demonstrate a high level of agreement. Our quantum-mechanical phases were determined by using Milne's phase-amplitude procedure. We compare our semiclassical energies for low-lying states with those of other researchers.

Theoretical Prediction of the Creation and Observation of a Ghost Trilobite Chemical Bond.

The "trilobite"-type of molecule, predicted in 2000 and observed experimentally in 2015, arises when a Rydberg electron exerts a weak attractive force on a neutral ground state atom. Such molecules have bond lengths exceeding 100 nm. The ultralong-range chemical bond between the two atoms is a nonperturbative linear combination of the many degenerate electronic states associated with high principal quantum numbers, and the resulting electron probability distribution closely resembles a fossil trilobite from antiquity. We show how to coherently engineer this same long-range orbital through a sequence of electric and magnetic field pulses even when the ground-state atom is not present and propose several methods to observe the resulting orbital. The existence of such a ghost chemical bond in which an electron reaches out from one atom to a nonexistent second atom is a consequence of the high level degeneracy.

Ultracold Heteronuclear Three-Body Systems: How Diabaticity Limits the Universality of Recombination into Shallow Dimers.

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.

Inelastic low-energy collisions of electrons with HeH+: Rovibrational excitation and dissociative recombination.

Inelastic low-energy (0-1 eV) collisions of electrons with HeH+ cations are treated theoretically, with a focus on the rovibrational excitation and dissociative recombination (DR) channels. In an application of ab initio multichannel quantum defect theory, the description of both processes is based on the Born-Oppenheimer quantum defects. The quantum defects were determined using the R-matrix approach in two different frames of reference: the center-of-charge and the center-of-mass frames. The results obtained in the two reference systems, after implementing the Fano-Jungen style rovibrational frame-transformation technique, show differences in the rate of convergence for these two different frames of reference. We find good agreement with the available theoretically predicted rotationally inelastic thermal rate coefficients. Our computed DR rate also agrees well with the available experimental results. Moreover, several computational experiments shed light on the role of rotational and vibrational excitations in the indirect DR mechanism that governs the low energy HeH+ dissociation process. While the rotational excitation is several orders of magnitude more probable process at the studied collision energies, the closed-channel resonances described by the high-n, rotationally excited neutral molecules of HeH contribute very little to the dissociation probability. But the situation is very different for resonances defined by the high-n, vibrationally excited HeH molecules, which are found to dissociate with approximately 90% probability.

Heteronuclear Efimov Scenario with Positive Intraspecies Scattering Length.

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}Li and bosonic ^{133}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.

Observation of pendular butterfly Rydberg molecules.

Engineering molecules with a tunable bond length and defined quantum states lies at the heart of quantum chemistry. The unconventional binding mechanism of Rydberg molecules makes them a promising candidate to implement such tunable molecules. A very peculiar type of Rydberg molecules are the so-called butterfly molecules, which are bound by a shape resonance in the electron-perturber scattering. Here we report the observation of these exotic molecules and employ their exceptional properties to engineer their bond length, vibrational state, angular momentum and orientation in a small electric field. Combining the variable bond length with their giant dipole moment of several hundred Debye, we observe counter-intuitive molecules which locate the average electron position beyond the internuclear distance.

Effective Atom-Molecule Conversions Using Radio Frequency Fields.

The present study is inspired by the Wieman group experiment [Phys. Rev. Lett. 2005, 95, 190404], in which they use a slow modulated magnetic field to effectively transfer rubidium atoms into cold molecules near a Feshbach resonance. We develop a time-dependent collision theory based on two channel model potentials to study the atom-molecule population transfer induced by a single-color radio frequency field in an ultracold 87 Rb gas. Wave-packet dynamical simulations allow an investigation of both bound-bound transitions and free-bound transitions. The effects of temperature, detuning and the RF amplitude on the population transfer are discussed in detail. Some of our simulations suggest that oscillatory atom-molecule conversion could originate from the long coherence time of the wave packet. This coherence time is unusually long in ultracold gases because the collision energy is typically quite well-defined.

Energy Scaling of Cold Atom-Atom-Ion Three-Body Recombination.

We study three-body recombination of Ba^{+}+Rb+Rb in the mK regime where a single ^{138}Ba^{+} ion in a Paul trap is immersed into a cloud of ultracold ^{87}Rb atoms. We measure the energy dependence of the three-body rate coefficient k_{3} and compare the results to the theoretical prediction, k_{3}∝E_{col}^{-3/4}, where E_{col} is the collision energy. We find agreement if we assume that the nonthermal ion energy distribution is determined by at least two different micromotion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed in an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.

Probing an Electron Scattering Resonance using Rydberg Molecules within a Dense and Ultracold Gas.

We present spectroscopy of a single Rydberg atom excited within a Bose-Einstein condensate. We not only observe the density shift as discovered by Amaldi and Segrè in 1934, but a line shape that changes with the principal quantum number n. The line broadening depends precisely on the interaction potential energy curves of the Rydberg electron with the neutral atom perturbers. In particular, we show the relevance of the triplet p-wave shape resonance in the e^{-}-Rb(5S) scattering, which significantly modifies the interaction potential. With a peak density of 5.5×10^{14} cm^{-3}, and therefore an interparticle spacing of 1300 a_{0} within a Bose-Einstein condensate, the potential energy curves can be probed at these Rydberg ion-neutral atom separations. We present a simple microscopic model for the spectroscopic line shape by treating the atoms overlapped with the Rydberg orbit as zero-velocity, uncorrelated, pointlike particles, with binding energies associated with their ion-neutral separation, and good agreement is found.

Ultracold Long-Range Rydberg Molecules with Complex Multichannel Spectra.

A generalized class of ultralong-range Rydberg molecules is predicted which consist of a multichannel Rydberg atom whose outermost electron creates a chemical bond with a distant ground state atom. Such multichannel Rydberg molecules exhibit favorable properties for laser excitation, because states exist where the quantum defect varies strongly with the principal quantum number. The resulting occurrence of near degeneracies with states of high orbital angular momentum promotes the admixture of low l into the high l deeply bound "trilobite" molecule states, thereby circumventing the usual difficulty posed by electric dipole selection rules. Such states also can exhibit multiscale binding possibilities that could present novel options for quantum manipulation.