Having only three electrons, He₂⁺ represents a system for which highly accurate ab initio calculations are possible. The latest calculation of rovibrational energies in He₂⁺ do not include relativistic or QED corrections but claim an accuracy of about 120 MHzW.-C. Tung, M. Pavanello, L. Adamowicz, J. Chem. Phys. 136, 104309 (2012). The available experimental data on He₂⁺, though accurate to 300 MHz, are not precise enough to rigorously test these calculations or reveal the magnitude of the relativistic and QED corrections. We have performed high-resolution Rydberg spectroscopy of metastable He₂ molecules and employed multichannel-quantum-defect-theory extrapolation techniquesD. Sprecher, J. Liu, T. Krähenmann, M. Schäfer, and F. Merkt, J. Chem. Phys. 140, 064304 (2014).o determine the rotational energy-level structure in the He₂⁺ ion. To this end we have produced samples of helium molecules in the a ³Σ_u⁺ state in supersonic beams with velocities tunable down to 100 m/s by combining a cryogenic supersonic-beam source with a multistage Zeeman deceleratorM. Motsch, P. Jansen, J. A. Agner, H. Schmutz, and F. Merkt, Phys. Rev. A 89, 043420 (2014). The metastable He₂ molecules are excited to np Rydberg states using the frequency doubled output of a pulse-amplified ring dye laser. Although the bandwidth of the laser systems is too large to observe the reduction of the Doppler width resulting from deceleration, the deceleration greatly simplifies the spectral assignments because of its spin-rotational state selectivity. Our approach enabled us to determine the rotational structure of He₂⁺ with unprecedented accuracy, to determine the size of the relativistic and QED corrections by comparison with the results of Ref. a and to precisely measure the rotational structure of the metastable state for comparison with the results of Focsa et al.C. Focsa, P. F. Bernath, and R. Colin, J. Mol. Spectrosc. 191, 209 (1998).

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Footnotes:

W.-C. Tung, M. Pavanello, L. Adamowicz, J. Chem. Phys. 136, 104309 (2012).. D. Sprecher, J. Liu, T. Krähenmann, M. Schäfer, and F. Merkt, J. Chem. Phys. 140, 064304 (2014).t M. Motsch, P. Jansen, J. A. Agner, H. Schmutz, and F. Merkt, Phys. Rev. A 89, 043420 (2014).. C. Focsa, P. F. Bernath, and R. Colin, J. Mol. Spectrosc. 191, 209 (1998)..

We use a delayed field ionization technique to observe the microwave transitions of calcium Rydberg states, from the 4snf states to the 4s(n+1)d, 4sng, 4snh, 4sni, and 4snk states for 18 ≤ n ≤ 23. We analyze the observed intervals between the l and (l+1), l ≥ 5, states of the same n to determine the Ca⁺ 4s dipole and quadrupole polarizabilities. We show that the adiabatic core polarization model is not adequate to extract the Ca⁺ 4s dipole and quadrupole polarizabilities and a non adiabatic treatment is required. We use the non adiabatic core polarization model to determine the ionic dipole and quadrupole polarizabilities to be α_d=76.9(3)  a₀³ and α_q=206(9)  a₀⁵, respectively.

l0pt Figure Exciting an atom with high-frequency radiation in the presence of a low frequency field can result in energy transfer between the photoelectron and the low frequency field, depending on the phase of the low frequency field when the excitation occurs. We excite Li atoms with IR lasers in the presence of a microwave field. In a previous experiment, detection of highly excited states with excitation by a ps laser tuned above the limit clearly showed a phase dependence. The variation of the signal due to a phase change reach 0.1% of the total excitation in that case. We are using a new excitation scheme with a CW amplitude modulated laser, the modulation being phase locked to the microwaves. We now observe a signal variation of 10% of the total excitation. The ps pulses spreads the population over a broad energy spectrum while the modulated excitation keeps it in narrow bands. The modulated laser frequency can be tuned to couple one band to the highly excited states, enhancing the collection efficiency, additionally it is closer to the limit. Furthermore, the modulated laser allows the observation of phase dependent transfer to both higher and lower energies. The observations can be described with relatively simple models.

Microwave transitions between pair states composed of two Rb Rydberg atoms in a magneto-optical trap are investigated. Our current interest is the transition from ndnd to (n+1)d(n-2)f states. This transition is allowed because the dipole-dipole induced configuration interaction between the ndnd state and the energetically close (n+2)p(n-2)f state admixes some of the latter state into the former. The resonance frequencies of the ndnd-(n+1)d(n-2)f transitions for n=35 to 42 have been measured and found to agree well with the calculated values. In addition, the power shifts of the resonance frequencies have been measured for n=35 to 42. The dependence of the fractional population transfer from the ndnd to (n+1)d(n-2)f states on the microwave field strength and atomic density has been measured and can be compared to a simple theoretical model. This work has been supported by the Air Force Office of Scientific Research.

We present analysis of low-n long-range molecular Rydberg states in ⁸⁵Rb₂, based on high-resolution spectra. The weakly bound states are accessed by bound-bound transitions from high-v levels of the a  ³ Σ_u⁺ state, which are prepared by photoassociation of laser-cooled atoms. Single-photon transitions to target states near the 5s + 7p asymptote are excited by a frequency-doubled pulse-amplified CW laser with a narrow linewidth, under 200 MHz. The long-range portion of the bonding potential is dominated by the elastic scattering interaction of the Rydberg electron of a perturbed 7p atom and a nearby ground-state atom, in much the same manner as trilobite states. We use time of flight to selectively measure molecular ions, which are formed via autoionization. This technique gives a two orders-of-magnitude improvement in linewidth over our previous work, reported in Ref. [1]. We also present calculations of a proposed scheme for STIRAP transfer from the current v"=35 level of the a  ³ Σ_u⁺ state to the v"=39 level. The long-range states accessible to us are defined in large part by the Franck-Condon factors, which are dominated by the outer lobe of the wavefunction. Thus, choosing a v" sets R, and determines the Franck-Condon window. The proposed v" = 39 level has a classical outer turning point at  ∼ 72  a₀, and will provide access to higher-n states with longer-range wells. This work is supported by the NSF and AFOSR.
[1] M. A. Bellos et al., Phys. Rev. Lett. 111, 053001 (2013)

We have studied the ν=1 Rydberg states of BaF in the energy region E=38800-39100 cm⁻¹(n*=15-25) via optical-optical double resonance spectroscopy. Rydberg states excited above the first ionization potential spontaneously autoionize and ¹³⁸Ba¹⁹F⁺ ions are detected by TOF-MS. In addition, BaF possesses a particularly low ionization potential, which allows for the study of autoionization dynamics in the absence of predissociative decay. This work extends the assignments of core-penetrating Rydberg states of BaF (Jakubek and Field, 2000) for applications to state-selective ion production schemes. Polarization and Stark spectroscopy techniques will be discussed in the context of accurate and efficient assignment of spectra.

Free induction decay detected chirped pulse millimeter wave spectroscopy of Rydberg-Rydberg transitions in atoms and molecules is a powerful and flexible method for characterizing the electronic structure of Rydberg states and determining the structure and dynamics of the ion-core. Complicating the use of this technique are the difficulties in reliably and repeatedly accessing not just the most information rich core-nonpenetrating states, but also the low-l core-penetrating Rydberg states in the area of principal quantum number n^* > 35. Small transition moments and narrow linewidths for transitions between valence electronic states and high Rydberg states are the primary limiting factor. We demonstrate a simple method to avoid the problem entirely by using chirped pulse technology operating in the frequency range of 260-295 GHz, which allows us to sample a lower range of n^* values than before with comparable frequency resolution and accuracy as our previous W-band experiments. Further improvements to our experiment in order to accurately capture details of Stark demolition, a technique that provides rapid differentiation between core-penetrating and core-nonpenetrating states, will also be discussed.

Rydberg states of atoms or molecules for which the inner turning point of the Rydberg electron on the radial plus centrifugal potential lies outside the bulk of the ion core electron density are known as core-non-penetrating states. Interpretation of Rydberg spectroscopic data for polar molecules makes use of effective potentials that include ionic bonding and polarizability in order to represent electric properties of the ion core. We examine the accuracy and convergence properties of single-center polarization potentials and show that the center of charge representation, for which the core dipole moment is zero so that first-order l-mixing can be neglected, is excluded by the convergence sphere for use with l-states that can be treated by an expansion about the center or mass, the center of dipole or a newly-defined center of polarizability. The potential expansion converges only outside a sphere enclosing the charge distribution, and the sphere is much larger when the center of charge is used. For higher l-states of the rotating molecule (turning points defined in center of mass), the sphere required for convergence is much smaller for an origin within the charge distribution, so that lower l states are modeled correctly.

We use ab-initio calculations to examine the electronic structure of CaF⁺,making comparison to the available experimental data and effective potential models. An electron-density-difference plot comparing isolated Ca⁺² and F⁻ ions with the CaF⁺ ab-initio density shows s-d mixing at Ca, and maintenance of near spherical symmetry at F. This unexpected result is interpreted in terms of the electronic states of Ca⁺. Calculation of the effective charge on F spanning the region of the transition from ionic to dissociating Ca⁺ F⁰ locates the transition very near the crossing of the Ca⁺² F⁻ and Ca⁺ F⁰ curves and additionally determines the width of the ionic-bonding transition region. An accurate non-relativistic long or intermediate range effective potential for the CaF Rydberg electron is obtained by choice of origin at the center of polarizability, with inclusion of multipoles through octopole and the use of anisotropic polarizability. The estimates of CaF⁺ polarizability from ab-initio and effective potential models predict high anisotropy, with the parallel dipole polarizability, where the atomic dipoles are mutually enhancing, predicted to be about double the perpendicular polarizability, where the atomic dipoles are mutually antagonistic.

Rydberg states are studied for H₂, Li₂, HeH, LiH and BeH using the multi-reference configuration interaction (MRCI) method. The systematics and regularities of the physical properties such as potential energies curves (PECs), quantum defect curves, permanent dipole moment and transition dipole moment curves of the Rydberg series are studied. They are explained using united atom perturbation theory by Bingel and Byers-Brown, Fermi model, Stark theory, and Mulliken's theory. Interesting mirror relationships of the dipole moments are observed between l-mixed Rydberg series, indicating that the members of the l-mixed Rydberg series have dipole moments with opposite directions, which are related to the reversal of the polarity of a dipole moment at the avoided crossing points. The assignment of highly excited states is difficult because of the usual absence of the knowledge on the behaviors of potential energy curves at small internuclear separation whereby the correlation between the united atom limit and separated atoms limit cannot be given. All electron MRCI calculations of PECs are performed to obtain the correlation diagrams between Rydberg orbitals at the united-atom and separated atoms limits.

We present results on Cs ultracold Rydberg atom experiments involving trilobite and butterfly molecules. Trilobite molecules are predicted to have giant, body-fixed permanent dipole moments, on the order of 1000 Debye. We present spectra for nS_1/2+6S_1/2 ³Σ⁺ molecules, where n=37, 39 and 40, and measurements of the Stark broadenings of selected trilobite states in Cs due to the application of a constant external electric field. These results show that for Cs, because of its near integer s-state quantum defect, it is possible to photoassociate molecules whose wavefunction is predominantly of trilobite character yielding molecular frame dipole moments of around 2000 Debye. In addition, we have also recently observed states whose spectra show characteristics of p-wave dominated butterfly states. The work on what we believe to be the butterfly states will be compared and contrasted to the measurements of the trilobite states.

A single Rydberg excitation in the high-density and low-temperature environment of a Bose-Einstein condensate (BEC) leads to a fascinating testbed of low-energy electron-neutral and ion-neutral scattering. In particular the small interparticle spacing in a BEC makes it possible to study the role of ion-neutral interactions in l-changing collisions on time scales much shorter than the Rydberg lifetime. We take advantage of the mean field density shift, caused by elastic electron-neutral collisions, to probe density dependent shells of the ⁸⁷Rb BEC and thereby measure the l-changing collision time versus density and principal quantum number. We report on l-changing collisions due to inelastic scattering of the Rydberg electron with a neutral atom located near the Rydberg ionic core. We measure timescales of both the l-changing collision and the Rb₂ molecule formation of less than one microsecond for n < 100 at the highest BEC densities. We extract a change in kinetic energy of the Rydberg atoms that matches well with the energy gap to the next-lowest manifold. We measure Rb₂ signal that decreases with increasing principal quantum number. The mechanism and timescales of the l-changing collision are compared with simulations including the motion of the ionic core and neutral atoms, as well as the Rydberg electron.

We carried out a relatively comprehensive ab-initio study of the electronic structure of O₂ and O₂⁺. We employed the MRD-CI package together with the cc-pV4Z basis set augmented with seven diffuse functions of s, p and d character on each atom. In this contribution we focus on the quintet states. Potential energy curves of about 50 quintet states were computed. The spectroscopic constants of the six valence quintet states (⁵Σ⁺_g, ⁵Σ⁻_g, ⁵Σ⁻_u, ⁵Π_u, ⁵Π_g, ⁵∆_g) dissociating to the first dissociation limit O(³P)+O(³P) are reported. The four ion-pair quintet states (⁵Σ⁻_g, ⁵Σ⁻_u, ⁵Π_g, ⁵Π_u) dissociating into O⁺(⁴S)+O⁻(²P) at 17.28 eV were also computed and their spectroscopic constants will be presented. A number of bound quintet Rydberg states belonging to series converging to the a⁴Π_u, b⁴Σ⁻_g, f⁴Π_g and ⁶Σ⁺_u states of the O₂⁺ cation were identified and attributed. Long-range interactions involving the ion-pair states as they slowly approach their dissociation limit will be shown.

In this presentation we report progress in the computation of superexcited states of O₂, namely, of bound ³Π_u Rydberg states of the neutral molecule converging to the a⁴Π_u state of O₂⁺. Up to twenty ³Π_u potential energy curves were computed. The MRD-CI package together with the cc-pV4Z basis set augmented with seven diffuse functions of s, p and d type on each atom were employed. This study was prompted by the demand of potential curves to try to understand the mechanism of the neutral dissociation of O₂ above the first ionization limit (IP=12.07 eV) where there exists a competition between autoionization and predissociation. This undertaking focuses on the computation of the I, I^′ and I^′′ 3Π_u states that have been postulated as involved in the neutral dissociation of O₂ in the 865-790 Å (14.33-15.69 eV) energy region.