The adiabatic potential energy curves of Rb$_2$ in the long-range Rydberg electronic states are calculated using the two-electron \textit{R}-matrix method [M. Tarana, R. Čurík, Phys. Rev. A \textbf{93}, 012515 (2016)] for the intermediate internuclear separations between 35 a.u. and 200 a.u. The results are compared with the zero-range models to find a region of the internuclear distances where the 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.
We investigate the impact of an electric field on the structure of ultralong-range polar diatomic Rydberg molecules. Both the s-wave and p-wave interactions of the Rydberg electron and the neutral ground state atom are taken into account. In the presence of the electric field the angular degree of freedom between the electric field and the internuclear axis acquires vibrational character and we encounter two-dimensional oscillatory adiabatic potential energy surfaces with an antiparallel equilibrium configuration. The electric field allows to shift the corresponding potential wells in such a m…
We present a novel binding mechanism where a neutral Rydberg atom and an atomic ion form a molecular bound state at large internuclear distance. The binding mechanism is based on Stark shifts and level crossings which are induced in the Rydberg atom due to the electric field of the ion. At particular internuclear distances between Rydberg atom and ion, potential wells occur which 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 rotati…
We report the observation of cold Cs Rydberg atom molecules bound at internuclear separations of R~3-9 um. The bound states result from avoided crossings between Rydberg atom pair interaction potentials in an applied electric field. The molecular states can be modified by changing the applied electric field. The molecules are observed by mapping the radial separation of the two Rydberg atoms as a function of time delay between excitation and detection using the Coulomb repulsion of the ions after pulsed field ionization. Measurements were performed for 63D+65D, 64D+66D, 65D+67D, and 66D+68D pa…
We observe ultralong-range blue-shifted Cs$_{2}$ molecular states near $ns_{1/2}$ Rydberg states in an optical dipole trap, where $31\leq n\leq34$. The accidental near degeneracy of $(n-4)l$ and $ns$ Rydberg states for $l>2$ in Cs, due to the small fractional $ns$ quantum defect, leads to non-adiabatic coupling among these states, producing potential wells above the $ns$ thresholds. Two important consequences of admixing high angular momentum states with $ns$ states are the formation of large permanent dipole moments, $\sim 15-100\,$Debye, and accessibility of these states via two-photon assoc…
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 …
We investigate triatomic molecules that consist of two ground state atoms and a highly excited Rydberg atom, bound at large internuclear distances of thousands of Ångstroms. In the molecular state the Rydberg electron is in a superposition of high angular momentum states whose probability densities resemble the form of trilobite fossils. The associated potential energy landscape has an oscillatory shape and supports a rich variety of stable geometries with different bond angles and bond lengths. Based on an electronic structure investigation we analyze the molecular geometry systematically and…
Electrostatic multipole interactions generate long-range Rydberg-Rydberg macrodimer. We calculate the adiabatic potentials of cesium $(nD_{J})_2$ Rydberg macrodimers for principal quantum numbers $n$ ranging from 56 to 62, for $J=3/2$ and $5/2$, and for the allowed values of the conserved sum of the atomic angular-momentum components along the internuclear axis, $M$. For most combinations $(n, M, J)$ exactly one binding potential exists, which should give rise to Rydberg macrodimer states. We study the dependence of the adiabatic potentials on the size of the two-body basis sets used in the ca…
We investigate the quantum dynamics of ultra-long-range trilobite molecules exposed to homogeneous electric fields. A trilobite molecule consists of a Rydberg atom and a ground-state atom, which is trapped at large internuclear distances in an oscillatory potential due to scattering of the Rydberg electron off the ground-state atom. Within the Born-Oppenheimer approximation, we derive an analytic expression for the two-dimensional adiabatic electronic potential energy surface in weak electric fields valid up to 500 V/m. This is used to unravel the molecular quantum dynamics employing the Multi…
We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. Only diatomic molecules are considered. The method is based on a two-electron \rmath approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via multichannel version of the Coulomb Green's function. This approach is put into a test by its application to a study of Rydberg states of the hydrogen molecule for internuclear distances…
Rydberg molecules, often exemplified by long-range "trilobite" molecules, are a subject of much recent interest at high principal quantum number $n$. States that use the same bonding mechanism can exist at much lower $n$ and less-extreme internuclear separations that are still quite long range. We use a high-resolution pulsed amplifier to study previously-detected transitions to a low-$n$ Rydberg molecular state near the $5s+7p$ asymptote in $^{85}$Rb$_2$. The observed line structure is modeled using precise ground-state positions and a lower bound of $τ> 1.1 \times 10^{-9}$ s is set on the ex…
We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the …
We measure the angular dependence of the resonant dipole-dipole interaction between two individual Rydberg atoms with controlled relative positions. By applying a combination of static electric and magnetic fields on the atoms, we demonstrate the possibility to isolate a single interaction channel at a Förster resonance, that shows a well-defined angular dependence. We first identify spectroscopically the Förster resonance of choice and we then perform a direct measurement of the interaction strength between the two atoms as a function of the angle between the internuclear axis and the quantiz…
Rates of depopulation by blackbody radiation (BBR) and effective lifetimes of alkali-metal \textit{nS}, \textit{n}P and \textit{nD} Rydberg states have been calculated in a wide range of principal quantum numbers $n \le 80$ at the ambient temperatures of 77, 300 and 600 K. Quasiclassical formulas were used to calculate the radial matrix elements of the dipole transitions from Rydberg states. Good agreement of our numerical results with the available theoretical and experimental data has been found. We have also obtained simple analytical formulas for estimates of effective lifetimes and BBR-in…
We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole-dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in $50S_{1/2}$ states in the blockade regime. For…
We investigate the interaction between three rubidium atoms in highly excited ($58p$) Rydberg states lying along a common axis and calculate the potential energy surfaces (PES) between the three atoms. We find that three-body long-range potential wells exist in some of these surfaces, indicating the existence of very extended bound states that we label \textit{macrotrimers}. We calculate the lowest vibrational eigenmodes and the resulting energy levels and show that the corresponding vibrational periods are rapid enough to be detected spectroscopically.
We propose to use adiabatic rapid passage with a chirped laser pulse in the strong dipole blockade regime to deterministically excite only one Rydberg atom from randomly loaded optical dipole traps or optical lattices. The chirped laser excitation is shown to be insensitive to the random number \textit{N} of the atoms in the traps. Our method overcomes the problem of the $\sqrt {N} $ dependence of the collective Rabi frequency, which was the main obstacle for deterministic single-atom excitation in the ensembles with unknown \textit{N}, and can be applied for single-atom loading of dipole trap…
Ultracold metastable RbCs molecules are observed in a double species MOT through photoassociation near the Rb(5S$_{1/2}$)+Cs(6P$_{3/2}$) dissociation limit followed by radiative stabilization. The molecules are formed in their lowest triplet electronic state and are detected by resonant enhanced two-photon ionization through the previously unobserved $(3)^{3}Π\leftarrow a^{3}Σ^{+}$ band. The large rotational structure of the observed photoassociation lines is assigned to the lowest vibrational levels of the $0^+,0^-$ excited states correlated to the Rb(5P$_{1/2}$)+Cs(6S$_{1/2}$) dissociation l…
We have studied electron-induced ion-pair dissociation dynamics of CO using the state-of-art velocity map imaging technique in combination with a time-of-flight-based two-field mass spectrometer. Extracting the characteristics for O$^-$/CO nascent atomic anionic fragments from the low energy (25 - 45 eV) electron-molecule scattering, first-time, we have directly detected the existence of S-wave resonated Trilobite resembling a novel molecular binding energy mechanism, as predicted by Greene \textit{et al.} \cite{greene2000creation}. The energy balance demands ion-pair dissociation (IPD) lie wi…
We observe long-range $^{85}$Rb and $^{87}$Rb (24$D$+5$S_{1/2}$) Rydberg molecules for eight different spin couplings, with binding energies up to 440~MHz and sub-percent relative uncertainty. Isotopic effects of the molecular binding energies arise from the different masses and nuclear spins. Because the vibrational states involve different spin configurations and cover a wide range of internuclear separations, the states have different dependencies on the $s$-wave and $p$-wave scattering phase shifts for singlet and triplet scattering. Fitting the spectroscopic data, we comprehensively deter…
It is shown that the slope of the repulsive part of the interaction potential between hydrogen atoms above the dissociation limit decreases with decreasing internuclear separation. Such a form of the repulsive potential explains the reduction of the shock and quasi-isentropic compression curve slopes of hydrogen isotopes at megabar pressures obtained in recent experiments [R. F. Trunin, V. D. Urlin, and A. B. Medvedev, Phys.-Usp. \textbf{53}, 577 (2010), R. I. Ilkaev, \textit{et al.}, AIP Conf. Proc. \textbf{706}, 73 (2004)].
Molecular helium represents a benchmark system for testing $\textit{ab initio}$ calculations on few-electron molecules. We report on the determination of the adiabatic ionization energy of the $a\,^3Σ_u^+$ state of He$_2$, corresponding to the energy interval between the $a\,^3Σ_u^+$ ($v''=0$, $N''=1$) state of He$_2$ and the $X^+\,^2Σ_u^+$ ($v^+=0$, $N^+=1$) state of He${_2}^+$, and of the lowest rotational interval of He${_2}^+$. These measurements rely on the excitation of metastable He$_2$ molecules to high Rydberg states using frequency-comb-calibrated continuous-wave UV radiation in a co…
The $5p$ two-photon ionization cross section of xenon in the photon-energy range below the one-photon ionization threshold is calculated within the time-dependent configuration-interaction-singles (TDCIS) method. The TDCIS calculations are compared to random-phase-approximation (RPA) calculations [Wendin \textit{et al.}, J. Opt. Soc. Am. B \textbf{4}, 833 (1987)] and are found to reproduce the energy positions of the intermediate Rydberg states reasonably well. The effect of interchannel coupling is also investigated and found to change the cross section of the $5p$ shell only slightly compare…
The determination of the electron neutrino mass by electron capture in $^{163}$Ho relies on a precise understanding of the deexcitation of a core hole after an electron capture event. We here present an \textit{ab intio} calculation of the electron capture spectrum in $^{163}$Ho, including all intra-atomic decay channels into bound-states. We use theoretical methods developed for the calculation of core level spectroscopy on correlated electron compounds. Our comparison critically tests the reality of these theories. We find that relativistic interactions beyond the Dirac equation, i.e. quantu…
