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We present a novel binding mechanism where a neutral Rydberg atom and an atomic ion form a molecular bound state at a large internuclear distance. The binding mechanism is based on Stark shifts and level crossings that are induced in the Rydberg atom due to the electric field of the ion. At particular internuclear distances between the Rydberg atom and the ion, potential wells occur that can hold atom–ion molecular bound states. Apart from the binding mechanism, we describe important properties of the long-range atom–ion Rydberg molecule, such as its lifetime and decay paths, its vibrational and rotational structure, and its large dipole moment. Furthermore, we discuss methods of how to produce and detect it. The unusual properties of the long-range atom–ion Rydberg molecule give rise to interesting prospects for studies of wave packet dynamics in engineered potential energy landscapes., publishedVersion

Thirty eight doublet electronic states of the Rydberg molecule NaHe are studied by means of numerical solution of the Schrodinger equation using the finite element method. Twelve of these 38 electronic states are studied for the first time. It is confirmed that potential-energy curves (PECs) of high Rydberg Σ–states have several wells and barriers at large internuclear distances due to radial oscillations of the electron density in the Rydberg states of the sodium atom.

Measurements of ultralong-range Rydberg molecule formation in cold gases of fermionic 87Sr atoms are presented. Measurements undertaken using polarised and unpolarised cold atom samples demonstrate...

The adiabatic potential energy curves of ${\mathrm{Rb}}_{2}$ in the long-range Rydberg electronic states are calculated using the two-electron $R$-matrix method [M. Tarana and R. \ifmmode \check{C}\else \v{C}\fi{}ur\'{\i}k, Phys. Rev. A 95, 042515 (2017)] for the intermediate internuclear separations between 37 and 200 a.u. The results are compared with the zero-range models to find a region of the internuclear distances where Fermi's pseudopotential approach provides accurate energies. A finite-range potential model of the atomic perturber is used to calculate the wave functions of the Rydberg electron and their features specific for the studied range of internuclear distances are identified.

A detailed theoretical framework for highly excited Rydberg molecules is developed based on the generalized local frame transformation. Our approach avoids the use of pseudopotentials and yields analytical expressions for the body-frame reaction matrix. The latter is used to obtain the molecular potential energy curves, but equally it can be employed for photodissociation, photoionization, or other processes. To illustrate the reliability and accuracy of our treatment we consider the Rb$^*-$Rb Rydberg molecule and compare our treatment with state-of-the-art alternative approaches. As a second application, the present formalism is used to re-analyze the vibrational spectra of Sr$^*-$Sr molecules, providing additional physical insight into their properties and a comparison of our results with corresponding measurements., 13 pages, 8 figures and 1 table

We propose a scheme to realize a heavy Rydberg system (HRS), a bound pair of oppositely charged ions, from a gas of ultracold atoms. The intermediate step to achieve large internuclear separations is the creation of a unique class of ultra-long-range Rydberg molecules bound in a stairwell potential energy curve. Here, a ground-state atom is bound to a Rydberg atom in an oscillatory potential emerging due to attractive singlet $p$-wave electron scattering. The utility of our approach originates in the large electronic dipole transition element between the Rydberg- and the ionic molecule, while the nuclear configuration of the ultracold gas is preserved. The Rabi coupling between the Rydberg molecule and the heavy Rydberg system is typically in the MHz range and the permanent electric dipole moments of the HRS can be as large as one kilo-Debye. We identify specific transitions which place the creation of the heavy Rydberg system within immediate reach of experimental realization., Comment: 14 pages, 5 figures

We report on a new measurement of the A+ 2ΠΩ′=1/2,3/2←X+ 2Σ+ electronic transition of MgAr+. The experiment relied on the resonance-enhanced multiphoton dissociation of the isolated ionic core of Rydberg MgAr molecules. The dissociation mechanism leading to the production of Mg atoms in high Rydberg states was used to separate the dissociation signal from the background and record background-free spectra. The rotational structure of the measured vibrational bands was partially resolved, and values of the rotational constants and band origins were extracted from the spectra. ISSN:0026-8976 ISSN:1362-3028

We predict the existence of a universal class of ultralong-range Rydberg molecular states whose vibrational spectra form trimmed Rydberg series. A dressed ion-pair model captures the physical origin of these exotic molecules, accurately predicts their properties, and reveals features of ultralong-range Rydberg molecules and heavy Rydberg states with a surprisingly small Rydberg constant. The latter is determined by the small effective charge of the dressed anion, which outweighs the contribution of the molecule's large reduced mass. This renders these molecules the only known few-body systems to have a Rydberg constant smaller than $R_\infty/2$., Comment: 6 pages, 3 figures and supplemental material (4 pages and 4 figures)

A ground state atom immersed in the wave function of the valence electron of a Rydberg atom can generate a long-range Rydberg molecule (LRRM). In this work, using the multipole expansion of the electrostatic interaction in prolate spheroidal coordinates, approximate and compact expressions of the electrostatic potential that determine the chemistry of trilobite and butterfly LRRM are explored. It is shown that even the spheroidal monopole term can be used to describe general features of the potential generated by a LRRM at short distances. It is also shown that even at long separations that allow a perturbative description of the intermolecular interaction between two LRRM, the convergence of the multipole spheroidal expansion is faster than that of its spherical analogue., Comment: 17 pages, 9 figures

Present nuclear detection techniques prevents us from determining if the analogue of a Rydberg molecule exists for the nuclear case. But nothing in nature disallows their existence. As in the atomic case, Rydberg nuclear molecules would be a laboratory for new aspects and applications of nuclear physics. We propose that Rydberg nuclear molecules, which represent the exotic, halo nuclei version, such as 11Be + 11Be, of the well known quasimolecules observed in stable nuclei such as 12C + 12C, might be common structures that could manifest their existence along the dripline. A study of possible candidates and the expected structure of such exotic clustering of two halo nuclei: the Rydberg nuclear molecules, is made on the basis of three diferent methods. It is shown that such cluster structures might be stable and unexpectedly common., 6 pages, 4 figures, revised text, accepted for publication in Physics Letters B

The level structure of negative-ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system which is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so far unobserved fine structure of the $^3P_J$ triplet of Rb$^-$ and allow us to extract parameters of the associated $p$-wave scattering resonances which deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion., 11 pages, 6 figures

We report on a new measurement of the A + 2 Π Ω ′ = 1 / 2 , 3 / 2 ← X + 2 Σ + electronic transition of MgAr + . The experiment relied on the resonance-enhanced multiphoton dissociation of the isola...

We present experimental evidence for spin-orbit interaction of an electron as it scatters from a neutral atom. The scattering process takes place within a Rb$_2$ ultralong-range Rydberg molecule, consisting of a Rydberg atomic core, a Rydberg electron, and a ground state atom. The spin-orbit interaction leads to characteristic level splittings of vibrational molecular lines which we directly observe via photoassociation spectroscopy. We benefit from the fact that molecular states dominated by resonant $p$-wave interaction are particularly sensitive to the spin-orbit interaction. Our work paves the way for studying novel spin dynamics in ultralong-range Rydberg molecules. Furthermore, it shows that the molecular setup can serve as a microlaboratory to perform precise scattering experiments in the low-energy regime of a few meV., Comment: 13 pages, 10 figures, 2 tables

We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules which form in an ultra-cold gas of Cs atoms. We account for the partial-wave scattering of the Rydberg electrons from the Cs perturber atoms by including the full set of spin-resolved 1,3 S_J and 1,3 P_J scattering phase shifts, and allow for the mixing of singlet (S = 0) and triplet (S = 1) spin states through Rydberg electron spinorbit and ground state electron hyperfine interactions. Excellent agreement with observed data in Sasmannshausen et al. [Phys. Rev. Lett. 113, 133201(2015)] in line positions and profiles is obtained. We also determine the spin- dependent permanent electric dipole moments for these molecules. This is the first such calculation of ultralong-range Rydberg molecules for which all of the relativisticcontributions are accounted.

We present a comprehensive study of the diverse properties of heteronuclear Rydberg molecules, placing a special emphasis on those composed of the light alkali atoms, Li, Na, and K. Electron-atom scattering phase shifts, which determine the strength of the molecular bond, are calculated at very low energy and then used in a spin-dependent theoretical model to calculate accurate Rydberg molecule potential energy curves. The wide parameter range accessible by combining the various properties of different alkali atoms often leads to hybridized electronic states accessible via one or two photon excitation schemes. This analysis of heteronuclear molecules leads to a prediction that the relative densities and spatial distributions of atoms in an ultracold mixture can be probed at controllable length scales via spectroscopic detection of these molecules., Comment: 12 pages, 9 figures, 2 tables

We explore the electronic structure of ultralong-range pentaatomic Rydberg molecules from a merger of a Rydberg atom and two ground state heteronuclear diatomic molecules. Our focus is on the interaction of Rb($23s$) and Rb($n=20$, $l\ge 3$) Rydberg states with ground and rotationally excited KRb diatomic polar molecules. For symmetric and asymmetric configurations of the pentaatomic Rydberg molecule, we investigate the metamorphosis of the Born-Oppenheimer potential curves, essential for the binding of the molecule, with varying distance from the Rydberg core and analyze the alignment and orientation of the polar diatomic molecules., 12 pages, 12 figures

We propose a novel experimental method to extend the investigation of ion-atom collisions from the so far studied cold, essentially classical regime to the ultracold, quantum regime. Key aspect of this method is the use of Rydberg molecules to initialize the ultracold ion-atom scattering event. We exemplify the proposed method with the lithium ion-atom system, for which we present simulations of how the initial Rydberg molecule wavefunction, freed by photoionization, evolves in the presence of the ion-atom scattering potential. We predict bounds for the ion-atom scattering length from ab initio calculations of the interaction potential. We demonstrate that, in the predicted bounds, the scattering length can be experimentally determined from the velocity of the scattered wavepacket in the case of $^\textsf{6}\textsf{Li}^\textsf{+}$ - $^\textsf{6}\textsf{Li}$, and from the molecular ion fraction in the case of $^\textsf{7}\textsf{Li}^\textsf{+}$ - $^\textsf{7}\textsf{Li}$. The proposed method to utilize Rydberg molecules for ultracold ion-atom scattering, here particularized for the lithium ion-atom system, is readily applicable to other ion-atom systems as well., Comment: 12 pages, 7 figures

The interaction between a Rydberg electron and a neutral atom situated inside its extended orbit is described via contact interactions for each atom-electron scattering channel. In ultracold environments, these interactions lead to ultra-long-range molecular states with binding energies typically ranging from $10$-$10^4$MHz. These energies are comparable to the relativistic and hyperfine structure of the separate atomic components. Studies of molecular formation aiming to reproduce observations with spectroscopic accuracy must therefore include the hyperfine splitting of the neutral atom and the spin-orbit splittings of both the Rydberg atom and the electron-atom interaction. Adiabatic potential energy curves that fully include these additional effects are presented for Rb$_2$ and Cs$_2$. The influence of spin degrees of freedom on the potential energy curves and molecular multipole moments probed in recent experimental work is elucidated and contrasted with other recent theoretical effort in this direction., 14 pages, 10 figures

We report on an ion-optical system that serves as a microscope for ultracold ground state and Rydberg atoms. The system is designed to achieve a magnification of up to 1000 and a spatial resolution in the 100 nm range, thereby surpassing many standard imaging techniques for cold atoms. The microscope consists of four electrostatic lenses and a microchannel plate in conjunction with a delay line detector in order to achieve single particle sensitivity with high temporal and spatial resolution. We describe the design process of the microscope including ion-optical simulations of the imaging system and characterize aberrations and the resolution limit. Furthermore, we present the experimental realization of the microscope in a cold atom setup and investigate its performance by patterned ionization with a structure size down to 2.7 {\mu}m. The microscope meets the requirements for studying various many-body effects, ranging from correlations in cold quantum gases up to Rydberg molecule formation., Comment: 11 pages, 11 figures

We study the impact of Rydberg molecule formation on the storage and retrieval of Rydberg polaritons in an ultracold atomic medium. We observe coherent revivals appearing in the retrieval efficiency of stored photons that originate from simultaneous excitation of Rydberg atoms and Rydberg molecules in the system with subsequent interference between the possible storage paths. We show that over a large range of principal quantum numbers the observed results can be described by a two-state model including only the atomic Rydberg state and the Rydberg dimer molecule state. At higher principal quantum numbers the influence of polyatomic molecules becomes relevant and the dynamics of the system undergoes a transition from coherent evolution of a few-state system to an effective dephasing into a continuum of molecular states., Submitted to PRA

We have performed high resolution photoassociation spectroscopy of rubidium ultra long-range Rydberg molecules in the vicinity of the 25$P$ state. Due to the hyperfine interaction in the ground state perturber atom, the emerging mixed singlet-triplet potentials contain contributions from both hyperfine states. We show that this can be used to induce remote spin-flips in the perturber atom upon excitation of a Rydberg molecule. When furthermore the spin-orbit splitting of the Rydberg state is comparable to the hyperfine splitting in the ground state, the orbital angular momentum of the Rydberg electron is entangled with the nuclear spin of the perturber atom. Our results open new possibilities for the implementation of spin-dependent interactions for ultracold atoms in bulk systems and in optical lattices., 6 pages, 3 figures

We investigate the electronic structure of a triatomic Rydberg molecule formed by a Rydberg atom and two neutral ground-state atoms. Taking into account the $s$-wave and $p$-wave interactions we perform electronic structure calculations and analyze the adiabatic electronic potentials evolving from the Rb$(n=35, l\ge 3)$ Rydberg degenerate manifold. We hereby focus on three different classes of geometries of the Rydberg molecules, including symmetric, asymmetric and planar configurations. The metamorphosis of these potential energy surfaces in the presence of an external electric field is explored., 8 pages, 8 figures

Combining ultracold atomic gases with the peculiar properties of Rydberg excited atoms gained a lot of theoretical and experimental attention in recent years. Embedded in the ultracold gas, an interaction between the Rydberg atom and the surrounding ground state atoms arises through the scattering of the Rydberg electron from an intruding perturber atom. This peculiar interaction gives rise to a plenitude of previously unobserved effects. Within the framework of the present thesis, this interaction is studied in detail for Rydberg \(P\)-states in rubidium. Due to their long lifetime, atoms in Rydberg states are subject to scattering with the surrounding ground state atoms in the ultracold cloud. By measuring their lifetime as a function of the ground state atom flux, we are able to obtain the total inelastic scattering cross section as well as the partial cross section for associative ionisation. The fact that the latter is three orders of magnitude larger than the size of the formed molecular ion indicates the presence of an efficient mass transport mechanism that is mediated by the Rydberg–ground state interaction. The immense acceleration of the collisional process shows a close analogy to a catalytic process. The increase of the scattering cross section renders associative ionisation an important process that has to be considered for experiments in dense ultracold systems. The interaction of the Rydberg atom with a ground state perturber gives rise to a highly oscillatory potential that supports molecular bound states. These so-called ultralong-range Rydberg molecules are studied with high resolution time-of-flight spectroscopy, where we are able to determine the binding energies and lifetimes of the molecular states between the two fine structure split \(25P\)-states. Inside an electric field, we observe a broadening of the molecular lines that indicates the presence of a permanent electric dipole moment, induced by the mixing with high angular momentum states. Due to the mixing of the ground state atom’s hyperfine states by the molecular interaction, we are able to observe a spin-flip of the perturber upon creation of a Rydberg molecule. Furthermore, an incidental near-degeneracy in the underlying level scheme of the \(25P\)-state gives rise to highly entangled states between the Rydberg fine structure state and the perturber’s hyperfine structure. These mechanisms can be used to manipulate the quantum state of a remote particle over distances that exceed by far the typical contact interaction range. Apart from the ultralong-range Rydberg molecules that predominantly consist of only one low angular momentum state, a class of Rydberg molecules is predicted to exist that strongly mixes the high angular momentum states of the degenerate hydrogenic manifolds. These states, the so-called trilobite- and butterfly Rydberg molecules, show very peculiar properties that cannot be observed for conventional molecules. Here we present the first experimental observation of butterfly Rydberg molecules. In addition to an extensive spectroscopy that reveals the binding energy, we are also able to observe the rotational structure of these exotic molecules. The arising pendular states inside an electric field allow us, in comparison to the model of a dipolar rotor, to extract the precise bond length and dipole moment of the molecule. With the information obtained in the present study, it is possible to photoassociate butterfly molecules with a selectable bond length, vibrational state, rotational state, and orientation inside an electric field. By shedding light on various previously unrevealed aspects, the experiments presented in this thesis significantly deepen our knowledge on the Rydberg–ground state interaction and the peculiar effects arising from it. The obtained spectroscopic information on Rydberg molecules and the changed reaction dynamics for molecular ion creation will surely provide valuable data for quantum chemical simulations and provide necessary data to plan future experiments. Beyond that, our study reveals that the hyperfine interaction in Rydberg molecules and the peculiar properties of butterfly states provide very promising new ways to alter the short- and long-range interactions in ultracold many-body systems. In this sense the investigated Rydberg–ground state interaction not only lies right at the interface between quantum chemistry, quantum many-body systems, and Rydberg physics, but also creates many new and fascinating possibilities by combining these fields. Die Kombination ultrakalter Gase mit den außergewöhnlichen Eigenschaften hochangeregter Rydbergatome hat in den letzten Jahren große Aufmerksamkeit von theoretischer und experimenteller Seite erhalten. In dieser Kombination kommt es innerhalb eines ultrakalten Gases zur Wechselwirkung zwischen dem Rydbergatom und den umgebenden Grundzustandsatomen, welche bedingt ist durch die Streuung des Rydbergelektrons an dem in die Wellenfunktion eindringenden Grundzustandsatom. Im Rahmen dieser Doktorarbeit wird diese außergewöhnliche Wechselwirkung im Detail für Rydberg \(P\)-Zustände in Rubidium untersucht. Bedingt durch ihre lange Lebensdauer sind Atome in Rydbergzuständen in ultrakalten Gasen Stößen mit den umgebenden Grundzustandsatomen ausgesetzt. Durch die Bestimmung ihrer Lebensdauer als Funktion des Flusses von Grundzustandsatomen durch ihre Oberfläche sind wir in der Lage, sowohl den totalen inelastischen Streuquerschnitt als auch den Streuquerschnitt für assoziative Ionisation zu bestimmen. Aufgrund der Tatsache, dass letzterer mehr als drei Größenordnungen größer ist als der geometrische Querschnitt des erzeugten \(\mathrm{Rb}_2^+\)-Molekülions, schließen wir auf die Existenz eines effizienten Massentransports, der durch die Rydberg-Grundzustandswechselwirkung entsteht. Die daraus resultierende enorme Beschleunigung des Kollisionsprozesses weist starke Ähnlichkeiten zur Katalyse auf. Die beobachtete Vergrößerung des Streuquerschnitts macht assoziative Ionisation zu einem relevanten Zerfallsprozess, der in Experimenten an dichten ultrakalten Gasen berücksichtigt werden muss. Die untersuchte Wechselwirkung des Rydbergatoms mit den umgebenden Grundzustandsatomen erzeugt ein stark oszillierendes Potential, in dem gebundene Zustände existieren können. Diese sogenannten ultralong-range Rydbergmoleküle werden in dieser Arbeit mittels einer hochaufgelösten Flugzeitspektroskopie untersucht, die es ermöglicht, die Bindungsenergien und die Lebenszeiten der Molekülzustände rund um die beiden Feinstrukturzustände des \(25P\)-Zustands zu untersuchen. In einem elektrischen Feld beobachten wir eine Verbreiterung der Moleküllinien, was auf ein permanentes elektrisches Dipolmoment der Moleküle hinweist, das durch die Zustandsmischung mit hohen Drehimpulszuständen entsteht. Das Mischen der Hyperfeinzustände des Grundzustandsatoms durch die molekulare Wechselwirkung sorgt dafür, dass wir während der Molekülanregung einen Spinflip im Grundzustandsatom beobachten können. Zudem führt eine Beinahe-Entartung im zugrundeliegenden Niveauschema des \(25P\)-Zustands dazu, dass Zustände entstehen, welche die Feinstruktur des Rydbergatoms mit der Hyperfeinstruktur des Grundzustandsatoms stark verschränken. Diese Effekte könnten eingesetzt werden, um den Quantenzustand von Teilchen zu manipulieren, die sehr viel weiter voneinander entfernt sind als die typische Kontaktwechselwirkungsdistanz. Abgesehen von ultralong-range Rydbergmolekülen, die hauptsächlich aus nur einem Zustand geringen Drehimpulses bestehen, ist eine weitere Klasse an Rydbergmolekülen theoretisch vorhergesagt, welche die hohen Drehimpulszustände der entarteten wasserstoffähnlichen Mannigfaltigkeiten mischt. Diese sogenannten trilobite- und butterfly-Rydbergmoleküle weisen einzigartige Eigenschaften auf, die bei konventionellen Molekülen unmöglich sind. Im Rahmen dieser Arbeit erbringen wir den ersten klaren experimentellen Nachweis für die Existenz von butterfly-Rydbergmolekülen. Zusätzlich zu einer detaillierten Spektroskopie, aus der wir die Bindungsenergie der Zustände bestimmen können, sind wir zum ersten Mal in der Lage, die Rotationsstruktur von Rydbergmolekülen experimentell zu beobachten. In einem externen elektrischen Feld nehmen die butterfly-Moleküle sogenannte pendular states ein. Der Vergleich der Spektroskopie dieser Zustände mit dem Modell eines dipolaren, starren Rotors erlaubt es uns, die Bindungslänge und das Dipolmoment dieser zu bestimmen. Mit den so gewonnenen Informationen ist es möglich, butterfly-Rydbergmoleküle mit wählbarer Bindungslänge, Vibrationszustand, Rotationszustand und Ausrichtung in einem elektrischen Feld anzuregen. Durch das Aufzeigen verschiedener zuvor unbeobachteter Facetten der Rydberg-Grundzustandswechselwirkung trägt die vorliegende Arbeit entscheidend dazu bei, das Wissen über diese außergewöhnliche Wechselwirkung und die aus ihr entstehenden Effekte zu vergrößern. Die gewonnenen spektroskopischen Ergebnissen zu Rydbergmolekülen und der geänderten Reaktionsdynamik bei der Bildung von \(\mathrm{Rb}_2^+\) sind sicher wertvolle Grundlagen für quantenchemische Simulationen sowie für die Planung zukünftiger Experimente. Darüber hinaus zeigt die vorliegende Studie, dass die Hyperfeinwechselwirkung in Rydbergmolekülen und die außergewöhnlichen Eigenschaften von butterfly-Rydbergmolekülen ein großes Potential bergen, um die kurz- und langreichweitigen Wechselwirkungen in ultrakalten Vielteilchensystemen zu beeinflussen. In diesem Sinn liegt die untersuchte Rydberg-Grundzustandswechselwirkung nicht nur in der Schnittmenge zwischen Quantenchemie, Vielteilchenquantensystemen und Rydbergphysik, sondern bereichert jedes dieser Felder durch die faszinierende Physik, die durch ihre Kombination entsteht.

We propose an approach to detect individual Rydberg molecules with each molecule consisting of two atoms in different Rydberg states. The scheme exploits the movement of atoms in the presence of an external force that exerts only on atoms in one Rydberg state. Since the movement of atoms in the other Rydberg state depends on whether they are bound with atoms directly driven by the applied force, bound atoms can be distinguished from unbound atoms. By utilizing electromagnetically induced transparency, it is possible to non-destructively image the positions of molecules. The scheme is sensitive to a weak force, which is suited to optically detect spatial positions and bond structure of Rydberg molecules., Comment: 5 pages

Obtaining full control over the internal and external quantum states of molecules is the central goal of ultracold chemistry and allows for the study of coherent molecular dynamics, collisions and tests of fundamental laws of physics. When the molecules additionally have a permanent electric dipole moment, the study of dipolar quantum gases and spin-systems with long-range interactions as well as applications in quantum information processing are possible. Rydberg molecules constitute a class of exotic molecules, which are bound by the interaction between the Rydberg electron and the ground state atom. They exhibit extreme bond lengths of hundreds of Bohr radii and giant permanent dipole moments in the kilo-Debye range. A special type with exceptional properties are the so-called butterfly molecules, whose electron density resembles the shape of a butterfly. Here, we report on the photoassociation of butterfly Rydberg molecules and their orientation in a weak electric field. Starting from a Bose-Einstein condensate of rubidium atoms, we fully control the external degrees of freedom and spectroscopically resolve the rotational structure and the emerging pendular states in an external electric field. This not only allows us to extract the bond length, the dipole moment and the angular momentum of the molecule but also to deterministically create molecules with a tunable bond length and orientation. We anticipate direct applications in quantum chemistry, many-body quantum physics and quantum information processing., Comment: 6 pages, 4 figures; Supplementary Material included

In a Rydberg atom, at least one electron is excited into an orbital with a very high principal quantum number that extends the atom's electronic envelope far beyond the nucleus. Based on ideas introduced by Enrico Fermi in 1934, a recent piece of theoretical work predicted that the scattering of such an electron from a second atom in the ground-state could give rise to attractive interactions. This would yield giant molecules with internuclear separations reaching several thousand Bohr radii. The spectroscopic characterization of such ultra-long-range 'Rydberg molecules' is now reported. The molecules, ultracold rubidium dimers, have spectra in good agreement with model predictions. This achievement raises the exciting prospect of realizing other exotic molecular species such as the so-called trilobite molecules in the near future. A Rydberg atom has one electron excited into an orbital with a very high principal quantum number. The scattering of such an electron from a second atom in the ground state gives rise to long-range bonding, yielding giant molecules with internuclear separations reaching several thousand Bohr radii. Using s-state rubidium Rydberg atoms with quantum numbers between 34 and 40, Bendkowsky and colleagues have now spectroscopically characterized such 'Rydberg molecules', and measured their lifetimes and polarizabilities. Rydberg atoms have an electron in a state with a very high principal quantum number, and as a result can exhibit unusually long-range interactions. One example is the bonding of two such atoms by multipole forces to form Rydberg–Rydberg molecules with very large internuclear distances1,2,3. Notably, bonding interactions can also arise from the low-energy scattering of a Rydberg electron with negative scattering length from a ground-state atom4,5. In this case, the scattering-induced attractive interaction binds the ground-state atom to the Rydberg atom at a well-localized position within the Rydberg electron wavefunction and thereby yields giant molecules that can have internuclear separations of several thousand Bohr radii6,7,8. Here we report the spectroscopic characterization of such exotic molecular states formed by rubidium Rydberg atoms that are in the spherically symmetric s state and have principal quantum numbers, n, between 34 and 40. We find that the spectra of the vibrational ground state and of the first excited state of the Rydberg molecule, the rubidium dimer Rb(5s)–Rb(ns), agree well with simple model predictions. The data allow us to extract the s-wave scattering length for scattering between the Rydberg electron and the ground-state atom, Rb(5s), in the low-energy regime (kinetic energy

Making use of the molecular closed-orbit theory and a new model potential for the Rydberg molecule, we have calculated the recurrence spectra of He2+ molecular ion in a magnetic field for different quantum defects. The Fourier transform spectra of He2+ molecular ion may be used to perform a direct comparison between peaks in the spectra and the scaled action values of closed orbits of the excited electron in external fields. We find that the spectral modulations can be analysed in terms of the scattering of the excited electron on the molecular core. Unlike the case of the Rydberg atom where the elastic scattering is predominant, modulations produced by inelastic scattering are also vital to the photoabsorption spectrum of the Rydberg molecule. Our results are in good agreement with the quantum results, which suggests that our method is correct.

We observe the formation of long-range Cs$_2$ Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s$_{1/2}$($F$=3,4)$\rightarrow$np$_{3/2}$ resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enabled the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy electron-Cs collisions., Comment: v2 with corrections and modifications - to appear in Phys. Rev. Lett

We report the creation of ultralong-range Sr$_2$ molecules comprising one ground-state $5s^2$ $^1S_0$ atom and one atom in a $5sns$ $^3S_1$ Rydberg state for $n$ ranging from 29 to 36. Molecules are created in a trapped ultracold atomic gas using two-photon excitation near resonant with the $5s5p$ $^3P_1$ intermediate state, and their formation is detected through ground-state atom loss from the trap. The observed molecular binding energies are fit with the aid of first-order perturbation theory that utilizes a Fermi pseudopotential with effective $s$-wave and $p$-wave scattering lengths to describe the interaction between an excited Rydberg electron and a ground-state Sr atom., 5 pages, 2 figures

Mid-IR lasing has been observed in supersonic plasmas and assigned to d to p transitions in tri-atomic hydrogen Rydberg states. Possible astrophysical implications are discussed.

We investigate the structure and features of an ultralong-range triatomic Rydberg molecule formed by a Rb Rydberg atom and a KRb diatomic molecule. In our numerical description, we perform a realistic treatment of the internal rotational motion of the diatomic molecule, and take into account the Rb($n, l\ge 3$) Rydberg degenerate manifold and the energetically closest neighboring levels with principal quantum numbers $n'>n$ and orbital quantum number $l\le2$. We focus here on the adiabatic electronic potentials evolving from the Rb($n, l\ge 3$) and Rb($n=26, l=2$) manifolds. The directional properties of the KRb diatomic molecule within the Rb-KRb triatomic Rydberg molecule are also analyzed in detail., 6 pages, 5 figures

We study angular-momentum couplings in $^{87}\mathrm{Rb}{}_{2}$ Rydberg molecules formed between a Rydberg and $5{S}_{1/2}$ ground-state atom. We use a Fermi model that includes $S$-wave and $P$-wave singlet and triplet scattering of the Rydberg electron with the $5{S}_{1/2}$ atom, along with the fine-structure coupling of the Rydberg atom and hyperfine-structure coupling of the $5{S}_{1/2}$ atom. We discuss the effects of these couplings on the adiabatic molecular potentials. We obtain bound-state energies, lifetimes, and electric and magnetic dipole moments for the vibrational ground states of the $^{87}\mathrm{Rb}(nD+5{S}_{1/2})$ molecules in all adiabatic potentials, with fine and hyperfine structure included. The hyperfine structure gives rise to mixed singlet-triplet potentials. We also study the effect of the hyperfine structure on the deep ${}^{3}S$-wave- and ${}^{3}P$-wave-dominated adiabatic molecular potentials, which support high-$\ensuremath{\ell}$ $^{87}\mathrm{Rb}{}_{2}$ Rydberg molecules.

Ab initio potential energy curves of the Rydberg NeH molecule in the presence of cylindrical spatial confinement were computed by the method of multi-reference configuration interaction with extended basis sets. The influence of the applied potential to the structures and spectra of the ground and excited states of NeH was analysed in terms of perturbation theory. In addition, the phenomenon of field-induced ionization was discussed.

Gerhard Herzberg, Nobel Laureate in Chemistry, had broad interests and achieved supreme accomplishments in physics, chemistry and astrophysics. The high points in his research were many. In physics they were the work on atomic hydrogen and helium, and evaluations of energy levels and constants of molecular hydrogen and its isotopes. His determinations of many molecular structures and discoveries of spectra of the free radicals CH 2 and CH 3 , and of the Rydberg molecule H3, were each outstanding contributions in chemistry. In astrophysics, his reproduction in the laboratory of the spectrum of CH + , proving its presence in the interstellar medium, and of spectra of C 3 and H 2 O + and their presence in comets, his observation of the quadrupole spectrum of H 2 and his discovery of hydrogen in the atmospheres of the planets opened up new applications of spectroscopy for our knowledge of the universe. His classic volumes on molecular spectra and molecular structures remain as encyclopaedias of molecular knowledge for all time. And his famous laboratory, the ‘Temple of spectroscopy’, served as a home for hundreds of scientists around the world, and helped to bring Canadian science to international prominence.

This review considers the spectroscopy and structure of clusters formed by stepwise addition of polar solvent molecules such as NH3, H2O, and CH3OH to effective one-electron chromophores that include the singly-charged alkaline earth cations Mg+, Ca+, and Sr+; atomic sodium; and the Rydberg molecule NH4. The absorption of photons by such species results in initial electronic excitation, followed by energy transfer to vibrational degrees of freedom, ultimately leading to dissociation. Experimental data are presented to support this electronic-to-vibrational energy transfer mechanism. Wavelength-dependent photodissociation signals for all of these species exhibit a similar size-dependence in which large spectral red shifts are observed as the first solvation shell fills. An examination of ab initio calculations on a number of related systems, as well as theoretical models for charge transfer, suggests that non-covalent interactions of solvent molecules with the single valence electron of the cluster core le...

Gerhard Herzberg, Nobel Laureate in Chemistry, had broad interests and achieved supreme accomplishments in physics, chemistry and astrophysics. The high points in his research were many. In physics they were the work on atomic hydrogen and helium, and evaluations of energy levels and constants of molecular hydrogen and its isotopes. His determinations of many molecular structures and discoveries of spectra of the free radicals CH 2 and CH 3 , and of the Rydberg molecule H3, were each outstanding contributions in chemistry. In astrophysics, his reproduction in the laboratory of the spectrum of CH + , proving its presence in the interstellar medium, and of spectra of C 3 and H 2 O + and their presence in comets, his observation of the quadrupole spectrum of H 2 and his discovery of hydrogen in the atmospheres of the planets opened up new applications of spectroscopy for our knowledge of the universe. His classic volumes on molecular spectra and molecular structures remain as encyclopaedias of molecular knowledge for all time. And his famous laboratory, the ‘Temple of spectroscopy’, served as a home for hundreds of scientists around the world, and helped to bring Canadian science to international prominence.

When an excited atomic electron interacts with a neutral perturbing atom or molecule that possesses a shape resonance, it generates a characteristic class of Born-Oppenheimer potential curves that rise with internuclear distance. We document this effect, and predict the existence of a diverse class of stable, strongly bound atom-atom and atom-molecule states that result from this phenomenon. For the specific case in which Rb is the perturbing atom, we show that such states should be observable in the spectroscopy of an ultracold gas or condensate.

Adiabatic wavefunctions and dipole moments of Rydberg states perturbed by a neutral atom have been investigated. Wavefunctions are equal to sums of products of Coulomb wavefunctions and differ very substantially from any single Coulomb wavefunction. Using the Kirchhoff-integral method (Fabrikant I I 1993 J. Phys. B: At. Mol. Opt. Phys. 26 2533) we calculate the potential curves of two adiabatic Rydberg states for the Rb*(n30) + Rb(5s) system: one dominated by the 3S symmetry near the ground-state Rb atom, and the other dominated by the 3P symmetry.

A one-electron model is developed which is able to describe the electronic structure and potential-energy (PE) surface of the Rydberg molecule H3O, in particular the Rydberg-to-valence transition of the singly occupied orbital along the H3O→H2O+H reaction path. An analytic PE function for the unpaired electron is obtained by numerical inversion of the one-particle Schrodinger equation and a least-squares fitting using a Thomas–Fermi-type model. Application of this procedure to H5O2 indicates the transferability of the model parameters from H 3 O to H 3 O–water clusters in a good approximation. The long-term goal of this work is the development of an accurate pseudopotential which can be employed in computer simulations of excess electrons and excess protons in liquid water.

We report on the formation of ultralong-range Rydberg D-state molecules via photoassociation in an ultracold cloud of rubidium atoms. By applying a magnetic offset field on the order of 10 G and high resolution spectroscopy, we are able to resolve individual rovibrational molecular states. A full theory, using the Born-Oppenheimer approximation including s- and p-wave scattering, reproduces the measured binding energies. The calculated molecular wavefunctions show that in the experiment we can selectively excite stationary molecular states with an extraordinary degree of alignment or anti-alignment with respect to the magnetic field axis., Comment: 10 pages and 8 figures including supplementary

We observe that when an ultracold ground state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit, ultralong-range molecules with giant (kilo-Debye) permanent electric dipole moments form. Large molecular permanent electric dipole moments are challenging to experimentally realize. Meeting this challenge has garnered significant interest because permanent electric dipole moments are important for understanding symmetry breaking in molecular physics, control of chemical reactions and realization of strongly correlated many-body quantum systems. These new hybrid class of `trilobite' molecules are predominated with degenerate Rydberg manifolds, making them difficult to produce with conventional optical association. Their behavior is quantitatively reproduced with detailed coupled-channel calculations., Comment: 18 pages, 3 figures, submitted to Science on 2014-09-03; v2: "One-sentence summary" removed from title

We review recent studies on negative ion formation and studies in other areas that are relevant to the role of high-Rydberg states of H2 and H3 in hydrogen negative ion sources. Possible mechanisms for the formation of these excited states are discussed, including the formation of long-lived superexcited (core-excited) Rydberg states. Experimental evidence for negative ion formation via electron attachment to core-excited Rydberg states in a glow discharge apparatus is presented. An expression for the dissociative electron attachment rate constant for Rydberg molecules is derived based on electron capture by a Rydberg molecule due to polarization interaction.

Chemical bonding between the Rydberg molecule NH4 and three alkali atoms Li, Na, and K, via their 2s, 3s, or 4s valence orbitals, is examined using flexible atomic orbital basis sets and high level...

We report the first clear evidence of dissociative electron attachment involving electron capture by a Rydberg molecule from another Rydberg molecule. We observed the formation of O− from excimer-laser-irradiated O2 in the presence of toluene (or benzene). Results indicate that O− is formed via electron capture by Rydberg states of O2 molecules from high Rydberg states of the hydrocarbon molecules.

We observe "trilobite-like" states of ultracold 85Rb2 molecules, in which a ground-state atom is bound by the electronic wavefunction of its Rydberg-atom partner. We populate these states through the ultraviolet excitation of weakly-bound molecules, and access a regime of trilobite-like states at low principal quantum numbers and with vibrational turning points around 35 Bohr radii. This demonstrates that, unlike previous studies that used free-to-bound transitions, trilobite-like states can also be excited through bound-to-bound transitions. This approach provides high excitation probabilities without requiring high-density samples, and affords the ability to control the excitation radius by selection of the initial-state vibrational level., Comment: 4 pages, 3 figures

Oscillator strengths for the H 3 Rydberg molecule have been calculated using a modified quantum defect orbital (QDO) method. The accuracy of this approach has been estimated by comparing its results with the data derived from more sophisticated ab initio methods and from an earlier, simplified, molecular version of the QDO method.