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Physical Review A

Colliding atomic pair distribution in an ultralong-range Rydberg potential

Luís Gustavo Marcassa, A. L. de Oliveira, Matthias Weidemüller, Vanderlei Salvador Bagnato

Published May 11, 2005• 7 citations
Publisher

Abstract

In a previous Letter by Oliveira et al. [Phys. Rev. Lett. 90, 143002 (2003)], the time evolution of the $34{S}_{1∕2}$ population, resulting from energy-transfer collisions between $33{P}_{3∕2}+33{P}_{3∕2}$ Rb atoms in a magneto-optical trap, was explained based on an ultralong-range potential. However, some experimental oscillations observed in the signal could not be reproduced by that model. In this work we reanalyze such a experimental results considering an internuclear separation-dependent colliding atomic pair distribution. This analysis suggests that such a distribution in the ultralong-range Rydberg molecular potential is responsible for the observed oscillations.

DOI
10.1103/physreva.71.054701

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•Jan 1, 2010•1 citation
In a previous Letter by Oliveira et al. [Phys. Rev. Lett. 90, 143002 (2003)], the time evolution of the 34S1∕234{S}_{1∕2}34S1∕2​ population, resulting from energy-transfer collisions between 33P3∕2+33P3∕233{P}_{3∕2}+33{P}_{3∕2}33P3∕2​+33P3∕2​ Rb atoms in a magneto-optical trap, was explained based on an ultralong-range potential. However, some experimental oscillations observed in the signal could not be reproduced by that model. In this work we reanalyze such a experimental results considering an internuclear separation-dependent colliding atomic pair distribution. This analysis suggests that such a distribution in the ultralong-range Rydberg molecular potential is responsible for the observed oscillations.
In this work we measure the time evolution of the population resulting from energy-transfer collisions as a function of the energy difference between the entrance and exit collisional channels using a sample of cold Rydberg atoms produced in a rubidium magneto-optical trap. The 34S(1/2) population, produced by collisions between atoms in the 33P(3/2) state, is monitored as a function of time through the pulsed-field ionization technique. The experimental results are compared with a recent published model based on a two-body interaction considering an attractive potential [Phys. Rev. A 65, 023405 (2002)]]; which is calculated according to a recent Letter by Boisseau et al. [Phys. Rev. Lett. 88, 133004 (2002)]]. The agreement is remarkable, which suggests the existence of such ultralong range potential proposed by Boisseau et al.
In a recent letter Li et al. [Phys. Rev. Lett. 94, 173001 (2005)] have studied experimentally the role of dipole-dipole interactions in the ionization of Rydberg atoms and the formation of a cold plasma. The authors associated their observations with atomic motion due to such interaction. In this work, we adapt the dynamical model proposed by De Oliveira et al. [Phys. Rev. Lett. 90, 143002 (2003)] based on a two atom interaction, which reproduce qualitatively well some experimental results observed by Li and co-workers. This comparison presents clear evidences of motion in such ultralong range potential between cold-Rydberg atoms, which may be important for some applications, as quantum computation.
Abstract We present an overview over theoretical models to describe adiabatic potential-energy curves, experimental excitation spectra, and electronic and nuclear dynamics in interacting Rydberg-atom pairs at large internuclear separations. The potential-energy curves and molecular wavefunctions are determined from the multipole expansion of the static Coulomb interaction which is evaluated numerically in a product basis of atomic orbitals. The convergence of this approach both in the truncation of the multipole expansion as well as in the size of the product basis is discussed, and the comparison of simulated excitation spectra is established as a useful criterium to test the convergence of the calculation. We finally discuss the dynamics of electronic and nuclear motions of pairs of Rydberg atoms, focusing on the stability of ultralong range Rydberg molecules with respect to autoionization.
Using state-selective field ionization, the state distributions of Rydberg atoms in cold Rydberg gases are measured for various initially excited Rydberg levels, populations, and evolution times. We provide direct experimental evidence for lll-changing collisions that we previously observed indirectly [S. K. Dutta, D. Feldbaum, A. Walz-Flannigan, J. R. Guest, and G. Raithel, Phys. Rev. Lett. 86, 3993 (2001)]. We also observe nnn-mixing and find that its effects are largely in agreement with recent theoretical work on nnn-changing collisions between electrons and Rydberg atoms, thus enabling an estimation of the electron temperature. Unexpectedly large populations of atoms are found in states with principal quantum numbers much lower than that of the initially excited atoms. We explain this observation by collisions between high-lll Rydberg atoms, which are highly polar and can collide due to static electric-dipole forces between them.
We have studied the development of gases of ultra-cold Rydberg atoms in Magneto Optic Traps, and discovered that such gases exhibit a range of density-dependent phenomena. In particular, we have found that at the densities of ∼ 10 7 cm -3 the Rydberg atoms spontaneously evolve into long-lived high angular momentum states. These states slowly decay due to microwave background radiation over tens of milliseconds. We have numerically simulated the effects leading to such behavior, and investigated numerically the l- and n-mixing collisions of Rydberg atoms with electrons in the range of 10 meV. These calculations show that the l- and n-mixing cross-sections follow the n 5 scaling law, expected from simple Stark map considerations, but also depend on the velocities of the colliding electrons, reflecting the adiabaticity of the atom-electron interactions. We have developed a novel technique of measuring the electric fields inside plasmas by using Rydberg excitation spectroscopy of embedded atoms, based on the disappearance of regions of zero oscillator strength in the presence of such fields. We have applied this technique to study the evolution of ultra-cold non-neutral plasmas excited from the MOT, and have found that it expands over 1 mus. We have simulated such an expansion by considering only Coulomb repulsion between the constituent ions, and have found that such a model is consistent with the experimental observations.
In this work the existence of a novel type of molecule is shown whose binding is based solely on electron-atom scattering. These molecules are composed of a Rydberg atom and a ground state atom - here Rb(ns) and Rb(5s) - where the binding arises from scattering of the Rydberg electron from the ground state atom. The ground state atom is bound to the Rydberg wavefunction, which has radii on the order of 100nm, and thus these molecules are of long-range. Although the theoretical description of this interaction goes back to the famous work of Fermi in the year 1934 which was expanded in the following decades by Omont and Greene, the experimental proof of their existence was still missing. Up to now, experimental evidence for the ultralong-range Rydberg molecules was found only in spectral line broadenings. The present experiments have demonstrated the direct photoassociation of these ultralong-range Rydberg molecules for Rb(ns)-Rb(5s) triplet states from a cold and dense sample of rubidium 87 atoms for a range of principal quantum numbers, n, between 34 and 40. The high-resolution photoassociation spectra allowed for the observation of several vibrational states separated by only a few Megahertz. Based on the model by Greene the vibrational ground states v=0 are assigned and the dependence of their binding energy on the principal quantum number, n, is used to extract the triplet s-wave scattering length for electron-Rb(5s) collisions from the data. The remarkably good agreement between experiment and theory for the vibrational ground state v=0 over a range of principal quantum numbers attests to the accuracy of Fermi's original pseudopotential approach in describing interactions in excited multi-atom systems. Aside from this good agreement for the state v=0, the measurements also show that contributions from p-wave scattering cannot be neglected, as a number of excited vibrational states is observed in the experiment that are not predicted from the theory assuming only s-wave scattering. Calculations of Li, Pohl and coworkers have shown that a full solution of the electron-atom scattering is necessary for the assignment of all vibrational states. This work finds the molecular bound states to be very sensitive to both s-wave as well as p-wave electron-atom scattering and the Rydberg molecules turn out to be an accurate experimental platform to study electron-atom collisions in a previously inaccessible ultralow-energy regime. In general, the ultralong-range Rydberg molecules investigated here for rubidium are expected for all species with negative scattering length for electron-atom interaction, e. g. the other alkali atoms. Rydberg atom and ground state atom do not even have to be of the same chemical element, the only requirement is a negative scattering length of the ground state atom for electron scattering. Moreover, the binding force of the Rydberg electron is not restricted to a single ground state atom and molecules with more than one ground state atom can be created. The fact that these exotic molecules have huge bond lengths but nevertheless a vibrational spectrum with several states make a new type of ultracold Rydberg chemistry feasible. In the future, larger polymers or even heteronuclear molecules can be realized, where the number of atoms, the constituent atomic elements and the addressed Rydberg state allow to precisely select the properties of the long-range molecule.