Rydberg Molecules Research Articles

Observation of mixed singlet-tripletRb2Rydberg molecules

We present high-resolution spectroscopy of Rb$_\text{2}$ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. \cite{Anderson2014b}. Our experimental data enables the determination of the effective zero-energy singlet $s$-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the $p$-wave contribution and all orders in the relative momentum $k$, and compare the obtained molecular binding energies to the experimental data.

Quantum state control of ultracold plasma fission

Double-resonant transitions excite nitric oxide in a seeded supersonic molecular beam, yielding a state-selected Rydberg gas that evolves to form an ultracold plasma. This plasma propagates in z with the molecular beam over a variable distance as great as 600 mm to strike an imaging detector, which records the charge distribution in the dimensions, x and y. The laser-crossed molecular beam excitation geometry convolutes an axial Gaussian distribution of NO about z with the Gaussian intensity distribution of the laser beam about x to create an ellipsoidal volume of Rydberg gas. Plasma images provide evidence for the relaxation of this Rydberg gas volume in an electron impact avalanche that breaks the ellipsoidal symmetry in x to form repelling plasma volumes. We find that the energy deposited in the recoil velocity of mass transport, Vx depends systematically on the initially selected Rydberg gas principal quantum number, n0, and the initial density of the Rydberg gas, ρ0. These quantities combine to determine ρe, the initial density of electrons formed by the prompt Penning ionization of closely spaced pairs of Rydberg molecules. Above a threshold density of Penning electrons, we find that Vx depends linearly on ρe. We argue that this bifurcation occurs as a consequence of the initial geometry of the Rydberg gas. Ambipolar electron expansion accelerates initially formed core ions. Resonant charge transfer redistributes this ion energy to the column of Rydberg molecules on the long axis of the ellipsoid. The equalized velocities in each direction give rise to a ±x streaming motion that concentrates density in opposing plasma volumes, causing the symmetric gas volume to split like a rotating liquid drop. Significantly, these dynamics reduce electron temperature with little decrease in the ion density or increase in the ion temperature. This appears to facilitate the formation of a strongly coupled plasma.

Lifetimes of ultra-long-range strontium Rydberg molecules

The lifetimes of the lower-lying vibrational states of ultralong-range strontium Rydberg molecules comprising one ground-state 5s2 1S0 atom and one Rydberg atom in the 5s38s 3S1 state are reported. The molecules are created in an ultracold gas held in an optical dipole trap and their numbers determined using field ionization, the product electrons being detected by a microchannel plate. The measurements show that, in marked contrast to earlier measurements involving rubidium Rydberg molecules, the lifetimes of the low-lying molecular vibrational states are very similar to those of the parent Rydberg atoms. This results because the strong p-wave resonance in low-energy electronrubidium scattering, which plays an important role in determining the molecular lifetimes, is not present for strontium. The absence of this resonance offers advantages for experiments involving strontium Rydberg atoms as impurities in quantum gases and for testing theories of molecular formation and decay.

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.

Ultralong-Range Rb-KRb Rydberg Molecules: Selected Aspects of Electronic Structure, Orientation and Alignment

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 ≥ 3) Rydberg degenerate manifold and the energetically closest neighboring levels with principal quantum numbers n' > n and orbital quantum number l ≤ 2. We focus here on the adiabatic electronic potentials evolving from the Rb(n,l ≥ 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.

Dynamically probing ultracold lattice gases via Rydberg molecules

We show that the excitation of long-range Rydberg molecules in a three-dimensional optical lattice can be used as a position- and time-sensitive probe for doubly occupied sites in the system. To this end, we detect the ions which are continuously generated by the decay of the formed Rydberg molecules. While a superfluid gas shows molecule formation for all parameters, a Mott insulator with n = 1 filling reveals a strong suppression of the number of formed molecules. In the limit of weak probing, the technique can be used to probe the superfluid to Mott-insulator transition in real-time. Our method can be extended to higher fillings and has various applications for the real-time diagnosis and manipulation of ultracold lattice gases.

Ultralong-Range Rydberg Cs2 Molecules Investigated at the Ab Initio Level of Theory

Vibrational properties of ultralong Rydberg Cs$_2$ molecules are investigated on corresponding potential curves obtained by perturbation theory. The Rydberg Cs$_2$ molecules are associated by a Rydberg Cs($nS/nP$) atom $(n=30-70)$ and a ground state Cs($6s$) atom. The starting point for the perturbation treatment of corresponding Rydberg molecular potential curves is to generate accurate atomic Rydberg states from realistic {\it ab initio} effective core potential. The calculated results have similar characteristics with available experimental and theoretical investigations on Rydberg Rb$_2$ molecules. And this is the first time that Rydberg molecules are studied at the {\it ab initio} level.

Production of ultra-long-range Rydberg molecules in a divalent atomic system

SynopsisSr2 Rydberg molecules are created through two-photon excitation in an ultracold strontium gas contained in an optical dipole trap and are detected through atom loss from the trap. First order perturbation theory employing the Fermi pseudopotential and effective s-wave and p-wave scattering lengths is used to evaluate the binding energies of the molecular levels.

Hybridization of Rydberg Electron Orbitals by Molecule Formation.

The formation of ultralong-range Rydberg molecules is a result of the attractive interaction between a Rydberg electron and a polarizable ground-state atom in an ultracold gas. In the nondegenerate case, the backaction of the polarizable atom on the electronic orbital is minimal. Here we demonstrate how controlled degeneracy of the respective electronic orbitals maximizes this backaction and leads to stronger binding energies and lower symmetry of the bound dimers. Consequently, the Rydberg orbitals hybridize due to the molecular bond.

Observation of singlet-scattering channels in long-range Rydberg dimers

SynopsisWe report on the observation of long-range Cs2 Rydberg molecules consisting of a p-state Rydberg atom and a ground-state atom. Two types of molecular states are visible in the photoassociation spectra: states bound purely by triplet s-wave scattering and states bound by mixed singlet-triplet s-wave scattering. 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 reproduces the experimental observations. The detailed analysis reveals the important role of singlet scattering in long-range Rydberg molecules and yields an effective singlet s-wave scattering length for low-energy e−-Cs collisions.

Polyatomic ultralong-range Rydberg molecules in external fields

SynopsisWe consider an ultralong-range polytonic Rydberg molecule formed by a Rydberg atom and two heteronuclear diatomic molecules. We focus here on the interaction of a Rb(n = 24, l ≥ 3) Rydberg atom with two KRb diatomic polar molecules in their rotational ground state. The polar diatomic molecules are allowed to rotate in the electric fields generated by the Rydberg electron and core. We investigate the electronic structure of this ultralong-range polytomic Rydberg molecule, and rovibrational properties of the two polar dimers as an additional external field is applied.

A comparative analysis of binding in ultralong-range Rydberg molecules

We perform a comparative analysis of different computational approaches employed to explore the electronic structure of ultralong-range Rydberg molecules. Employing the Fermi pseudopotential approach, where the interaction is approximated by an s-wave bare delta function potential, one encounters a non-convergent behavior in basis set diagonalization. Nevertheless, the energy shifts within the first order perturbation theory coincide with those obtained by an alternative approach relying on Green’s function calculation with the quantum defect theory. A pseudopotential that yields exactly the results obtained with the quantum defect theory, i.e. beyond first order perturbation theory, is the regularized delta function potential. The origin of the discrepancies between the different approaches is analytically explained.

Rydberg excitation of neutral nitric oxide molecules in strong UV and near-IR laser fields**Project supported by the National Basic Research Program of China (Grant No. 2013CB922200) and the National Natural Science Foundation of China (Grant Nos. 11034003 and 11274140).

Rydberg state excitations of neutral nitric oxide molecules are studied in strong ultraviolet (UV) and near-infra-red (IR) laser fields using a linear time-of-flight (TOF) mass spectrometer with the pulsed electronic field ionization method. The yield of Rydberg molecules is measured as a function of laser intensity and ellipticity, and the results in UV laser fields are compared with those in near-IR laser fields. The present study provides the first experimental evidence of neutral Rydberg molecules surviving in a strong laser field. The results indicate that a rescattering-after-tunneling process is the main contribution to the formation of Rydberg molecules in strong near-IR laser fields, while multi-photon excitation may play an important role in the strong UV laser fields.

Ultrafast electronic dynamics in helium nanodroplets

Helium nanodroplets have emerged as a test bed for the study of isolated quantum liquids and as an ideal matrix for trapping atoms and molecules in a weakly interacting, cryogenic environment. Their high transparency at visible and infrared wavelengths facilitates the study of dissolved species with traditional spectroscopy techniques. At photon energies above ~21 eV, however, the droplets themselves begin to absorb to form complex excited states that have proven a challenge for both experiment and theory. A variety of frequency- and time-domain methods have been used to characterise electronically excited droplet states and their relaxation channels. This review focuses on a recent series of time-domain experimental studies that have revealed several phenomena such as interband relaxation dynamics within the droplet environment, and provided deeper insight into previously detected relaxation channels, including the ejection of Rydberg atoms (He*) and molecules (), the dynamics of highly excited droplet states, and photoassociation to produce strongly-bound excimer species (such as ). A brief outline of corresponding ab initio efforts for the theoretical description of electronically excited He droplet states and their relaxation dynamics will also be given.

Production of trilobite Rydberg molecule dimers with kilo-Debye permanent electric dipole moments

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. However, large molecular permanent electric dipole moments are challenging to realize experimentally. We report the observation of ultralong-range Rydberg molecules with bond lengths of ~100 nanometers and kilo-Debye permanent electric dipole moments that form when an ultracold ground-state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit. The electronic character of this hybrid class of "trilobite" molecules is dominated by degenerate Rydberg manifolds, making them difficult to produce by conventional photoassociation. We used detailed coupled-channel calculations to reproduce their properties quantitatively. Our findings may lead to progress in ultracold chemistry and strongly correlated many-body physics.

Experimental characterization of singlet scattering channels in long-range Rydberg molecules.

We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 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 enables 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.

Potentials of long-range cesium Rydberg molecule

Rydberg atom, with a large principal quantum number n, has big size, long lifetime, strong long-range interactions, and so on. These properties make Rydberg atoms potential candidate of quantum gate and single-photon source. Rydberg electron can interact with nearby ground-state atom, which is polarized by the Rydberg electron and is bound to the orbit of Rydberg electrons forming Rydberg molecule. As the kinetic energy of the Rydberg electron is very low, only the lowest partial waves will contribute to the molecular potential.#br#In this paper, the low electron-atom scattering with the semi-classical approximation is introduced, and the pseudopotential of interaction between Rydberg electron and ground-state atom is used to describe the long-range Rydberg molecular potential. Molecular potential curves for cesium (nS, n=30-60) are plotted according to the results of numerical computation, from which the outermost potential depth De and the equilibrium distance r0 of long-range cesium Rydberg molecule are deduced. Potential curves of cesium Rydberg molecules are consistent with the distribution curves in radial probability densities of cesium Rydberg electrons. Dependences of De and r0 on the principal quantum number n are investigated, this has an important role for the experimental measurements. The size of a Rydberg molecule depends on the equilibrium distance r0 and is proportional to the square of effective principal quantum number (n-δ )2. The calculated outermost potential depth De of Rydberg molecule becomes smaller with the increase of principal quantum number n. Rydberg molecule is very sensitive to the external field and can be used to measure and monitor weak signals.

Rotational hybridization, and control of alignment and orientation in triatomic ultralong-range Rydberg molecules

We explore the electronic structure and rovibrational properties of an ultralong-range triatomic Rydberg molecule formed by a Rydberg atom and a ground state heteronuclear diatomic molecule. We focus here on the interaction of a Rb() Rydberg atom with a KRb(N = 0) diatomic polar molecule. There is significant electronic hybridization with the Rb(n = 24, ) degenerate manifold. The polar diatomic molecule is allowed to rotate in the electric fields generated by the Rydberg electron and core as well as an external field. We investigate the metamorphosis of the Born–Oppenheimer potential curves, essential for the binding of the molecule, with varying electric field and analyze the resulting properties such as the vibrational structure and the alignment and orientation of the polar diatomic molecule.

Angular-momentum couplings in long-rangeRb2Rydberg molecules

We study angular-momentum couplings in $^{87}$Rb$_2$ Rydberg molecules formed between Rydberg and 5S$_{1/2}$ ground-state atoms. We use a Fermi model that includes S-wave and P-wave singlet and triplet scattering of the Rydberg electron with the 5S$_{1/2}$ atom, along with the fine structure coupling of the Rydberg atom and hyperfine structure coupling of the 5S$_{1/2}$ 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 $^{87}$Rb$(n$D$+5$S$_{1/2})$ molecules in all adiabatic potentials, with fine and hyperfine structure included. 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-$\ell$ $^{87}$Rb$_2$ Rydberg molecules.