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.

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 k3 and compare the results to the theoretical prediction, k3 ∝ E −3/4 col where E col is the collision energy. We find agreement if we assume that the non-thermal ion energy distribution is determined by at least two different micro-motion 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 into an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.When three atoms collide, a diatomic molecule can form in a three-body recombination (TBR) process. In cold neutral atomic gases, TBR was investigated for spinpolarized hydrogen as well as alkalis (see e.g. [1][2][3]). In the context of Bose-Einstein condensation, TBR plays a crucial role as a main loss mechanism. By now, the scaling of TBR as a function of collision energy and scattering lengths in neutral ultracold gases has been investigated in detail [4]. When considering TBR in atom-ion systems, one can expect three-body interactions to be more pronounced due to the underlying longer-range r −4 polarization potential. Energy scaling of TBR in charged gases was studied at temperatures down to a few K, especially for hydrogen and helium due to their relevance in plasmas and astrophysics (e.g. [5,6]). Depending on the studied temperature range a variety of power laws was found but not a common threshold law. The recent development of novel hybrid traps for both laser cooled atoms and ions has opened the possibility to investigate cold atom-ion interactions and chemical reactions in the mK-regime and below. First experiments in such setups studied elastic and reactive two-body collisions (e.g. [7][8][9][10][11][12][13][14]). In accordance with the well-known Langevin theory, the corresponding reactive rates were measured to be independent of the collision energy [8,10]. Very recently we predicted a theoretical threshold law on the scaling properties for cold atom-atom-ion three-body collisions [15]. Understanding the scaling of reaction rates with quantities such as the collision energy is crucial for fundamentally understanding TBR and for the prospects of the experimental realization of ultracold s-wave atom-ion collisions. Furthermore, as we will show here, studying TBR allows for insights into the kinetics of an ion immersed in a cloud of atoms. This letter reports on the combined theoretical and experimental investigation of the energy scaling of threebody atom-atom-ion collisions in the mK regime. We measure the TBR rate coefficient k 3 of Ba + in an ultracold Rb cloud as a function of the mean collision energy of the ion, E col , which we control via the excess micromotion (eMM) of the Paul trap...

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 [1], but a line shape which 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 inter-particle 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, point-like particles, with binding energies associated with their ion-neutral separation, and good agreement is found.A Rydberg atom excited in a dense background gas of atoms provides a testbed of Rydberg electron-neutral atom collisions. Spectroscopy has always been a sensitive technique for studying these collisions and in particular spectroscopy performed in a cold, dense atom sample eliminates most other line broadening mechanisms, thereby isolating the effects of elastic and inelastic electron-neutral atom collisions on the line shape. The realization of ultralong-range Rydberg molecules via elastic electronneutral collisions [2] relies on cold, dense atom samples. Since the first observation [3], Rydberg molecules continue to be realized with increasing experimental control in various potential energy landscapes and atomic species [3][4][5][6][7][8][9][10], where the neutral atom ground state wavefunction is typically bound in the outer one or two potential wells of the electron-atom potential energy curves (PECs). By applying an electric field [11] or by exciting nS states with nearly integer quantum defects, as in Cs [12], more deeply bound trilobite Rydberg molecules [2] are realized. With higher densities of cold atom samples, many neutral atoms overlap with the Rydberg orbit and the bound states become unresolvable [13,14]. By utilizing the high densities of a Bose-Einstein condensate (BEC), the neutral atoms within the Rydberg orbit provide a probe of elastic and inelastic electron-neutral collisions for a large range of ion-neutral separations. We show in this paper that Rydberg spectroscopy in a BEC allows us to probe, with high resolution, the scattering resonance directly for the first time in this temperature regime.In a completely different temperature regime (> 400 K) than the work presented here (< 1 µK), Rydberg spectroscopy done during the 1980s in unpolarized thermal vapors investigated the line shift and line broadening of Rydberg atoms excited in a background gas of the same species atoms at similar densities [15,16]. Subsequent theory work [17][18][19][20] modeled the line shapes b...

Within a dense environment (ρ ≈ 10 14 atoms=cm 3 ) at ultracold temperatures (T < 1 μK), a single atom excited to a Rydberg state acts as a reaction center for surrounding neutral atoms. At these temperatures, almost all neutral atoms within the Rydberg orbit are bound to the Rydberg core and interact with the Rydberg atom. We have studied the reaction rate and products for nS 87 Rb Rydberg states, and we mainly observe a state change of the Rydberg electron to a high orbital angular momentum l, with the released energy being converted into kinetic energy of the Rydberg atom. Unexpectedly, the measurements show a threshold behavior at n ≈ 100 for the inelastic collision time leading to increased lifetimes of the Rydberg state independent of the densities investigated. Even at very high densities (ρ ≈ 4.8 × 10 14 cm −3 ), the lifetime of a Rydberg atom exceeds 10 μs at n > 140 compared to 1 μs at n ¼ 90. In addition, a second observed reaction mechanism, namely, Rb þ 2 molecule formation, was studied. Both reaction products are equally probable for n ¼ 40, but the fraction of Rb þ 2 created drops to below 10% for n ≥ 90.

Here we report on spectroscopic measurements of the aluminum monofluoride molecule (AlF) that are relevant to laser cooling and trapping experiments. We measure the detailed energy level structure of AlF in the X 1 Σ + electronic ground state, in the A 1 Π state, and in the metastable a 3 Π state. We determine the rotational, vibrational and electronic branching ratios from the A 1 Π state. We also study how the rotational levels split and shift in external electric and magnetic fields. We find that AlF is an excellent candidate for laser cooling on any Q-line of the A 1 Π -X 1 Σ + transition and for trapping at high densities.The energy levels in the X 1 Σ + , v = 0 state and within each Ω-manifold in the a 3 Π, v = 0 state are determined with a relative accuracy of a few kHz, using laser-radio-frequency multiple resonance and ionization detection schemes in a jet-cooled, pulsed molecular beam. To determine the hyperfine and Λ-doubling parameters we measure transitions throughout the 0.1 MHz -66 GHz range, between rotational levels in the X 1 Σ + , v = 0 state and between rotational and Λ-doublet levels in all three spin-orbit manifolds of the a 3 Π, v = 0 state. We measure the hyperfine splitting in the A 1 Π state using continuous wave (CW) laser-induced fluorescence spectroscopy of the A 1 Π, v = 0 ← X 1 Σ + , v = 0 band. The resolution is limited by the short radiative lifetime of the A 1 Π, v = 0 state, which we experimentally determine to be 1.90 ± 0.03 ns. The hyperfine mixing of the lowest rotational levels in the A 1 Π state causes a small loss from the the main laser cooling transition of 10 −5 . The off-diagonal vibrational branching from the A 1 Π, v = 0 state is measured to be (5.60 ± 0.02) × 10 −3 in good agreement with theoretical predictions. The strength of the spin-forbidden A 1 Π, v = 0 → a 3 Π, v = 0 transition is measured to be seven orders of magnitude lower than the strength of the A 1 Π, v = 0 → X 1 Σ + , v = 0 transition. We determine the electric dipole moments µ(X) = 1.515 ± 0.004 Debye, µ(a) = 1.780 ± 0.003 Debye and µ(A) = 1.45 ± 0.02 Debye in X 1 Σ + , v = 0, a 3 Π, v = 0 and A 1 Π, v = 0, respectively, by recording CW laser excitation spectra in electric fields up to 150 kV/cm.

A general method to study classical scattering in n-dimension is developed. Through classical trajectory calculations, the three-body recombination is computed as a function of the collision energy for helium atoms, as an example. Quantum calculations are also performed for the J(Π) = 0(+) symmetry of the three-body recombination rate in order to compare with the classical results, yielding good agreement for E ≳ 1 K. The classical threshold law is derived and numerically confirmed for the Newtonian three-body recombination rate. Finally, a relationship is found between the quantum and classical three-body hard hypersphere elastic cross sections which is analogous to the well-known shadow scattering in two-body collisions.

We show that an ensemble of 2 Σ molecules in the rotationally ground state trapped on an optical lattice exhibits collective spin excitations that can be controlled by applying superimposed electric and magnetic fields. In particular, we show that the lowest energy excitation of the molecular ensemble at certain combinations of electric and magnetic fields leads to the formation of a magnetic Frenkel exciton. The exciton bandwidth can be tuned by varying the electric or magnetic fields.We show that the exciton states can be localized by creating vacancies in the optical lattice. The localization patterns of the magnetic exciton states are sensitive to the number and distribution of vacancies, which can be exploited for engineering many-body entangled spin states. We consider the dynamics of magnetic exciton wavepackets and show that the spin excitation transfer between molecules in an optical lattice can be accelerated or slowed down by tuning an external magnetic or electric field.

Sufficiently high densities in Bose-Einstein condensates provide favorable conditions for the production of ultralong-range polyatomic molecules consisting of one Rydberg atom and a number of neutral ground state atoms. The chemical binding properties and electronic wave functions of these exotic molecules are investigated analytically via hybridized diatomic states. The effects of the molecular geometry on the system's properties are studied through comparisons of the adiabatic potential curves and electronic structures for both symmetric and randomly configured molecular geometries. General properties of these molecules with increasing numbers of constituent atoms and in different geometries are presented. These polyatomic states have spectral signatures that lead to non-Lorentzian line-profiles. arXiv:1601.06881v1 [physics.atom-ph]