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Physical Review A

Giant cross sections for L changing in Rydberg-Rydberg collisions

S. Yoshida, Joachim Burgdörfer, G. Fields, R. Brienza, F. B. Dunning

Published Aug 4, 2020• 2 citations
Publisher

Abstract

State changing in thermal-energy collisions between strontium atoms in very-high-$n$, $n\ensuremath{\approx}300$, $n{\phantom{\rule{0.16em}{0ex}}}^{1}{F}_{3}$ Rydberg states is studied. In collisions between Rydberg atoms, the dipole-dipole interaction generates an effective electric field at each atom, which triggers Stark precession and the evolution of their angular momenta, $L$. Such $L$-changing collisions are examined using both quantum and classical theory. The theoretical predictions are experimentally verified by monitoring the damping of quantum beats induced by the sudden application of a DC ``pump'' field. The present work shows that, due to the long-range nature of the interactions, the cross sections, $\ensuremath{\sigma}$, for $L$ changing are considerably larger than the geometric collision cross section. For thermal collisions the cross section $\ensuremath{\sigma}$ for $n{\phantom{\rule{0.28em}{0ex}}}^{1}{F}_{3}$ Rydberg states with $n\ensuremath{\simeq}300$ is $\ensuremath{\approx}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}$. Scaling rules derived in this paper predict that for cold collisions $\ensuremath{\sigma}$ may increase by a further factor of 4.

DOI
10.1103/physreva.102.022805

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State changing in thermal-energy collisions between strontium atoms in very-high-nnn, n\ensuremath≈300n\ensuremath{\approx}300n\ensuremath≈300, n1F3n{\phantom{\rule{0.16em}{0ex}}}^{1}{F}_{3}n1F3​ Rydberg states is studied. In collisions between Rydberg atoms, the dipole-dipole interaction generates an effective electric field at each atom, which triggers Stark precession and the evolution of their angular momenta, LLL. Such LLL-changing collisions are examined using both quantum and classical theory. The theoretical predictions are experimentally verified by monitoring the damping of quantum beats induced by the sudden application of a DC ``pump'' field. The present work shows that, due to the long-range nature of the interactions, the cross sections, \ensuremathσ\ensuremath{\sigma}\ensuremathσ, for LLL changing are considerably larger than the geometric collision cross section. For thermal collisions the cross section \ensuremathσ\ensuremath{\sigma}\ensuremathσ for n1F3n{\phantom{\rule{0.28em}{0ex}}}^{1}{F}_{3}n1F3​ Rydberg states with n\ensuremath≃300n\ensuremath{\simeq}300n\ensuremath≃300 is \ensuremath≈8\ifmmode×\else\texttimes\fi10\ensuremath−5cm2\ensuremath{\approx}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{2}\ensuremath≈8\ifmmode×\else\texttimes\fi10\ensuremath−5cm2. Scaling rules derived in this paper predict that for cold collisions \ensuremathσ\ensuremath{\sigma}\ensuremathσ may increase by a further factor of 4.
Rydberg atoms are increasingly being used as a means of introducing long-range, tunable interactions into atomic systems through their strong dipole-dipole interactions. When creating such interactions, however, there are a variety of potential effects that can occur, such as state (n and/or L) changing or Penning ionization, which can complicate the dynamics of the system. In the following work, such interactions are investigated for Rydberg-Rydberg collisions using very high-n, n ~300, strontium Rydberg atoms in an atomic beam configuration. By exploiting Rydberg blockade and the inherent distribution of atomic velocities present in an atomic beam, it is possible to create a 1D array of moving Rydberg atoms which will naturally overtake each other over time. Measurements of both Penning ionization and state changing for such collisions are made and compared with classical trajectory Monte-Carlo (CTMC) simulations, with both indicating large collisional cross sections on the order of 1 x 10-6 cm2 for Penning ionization and nearly 8 x 10-5 cm2 for state changing interactions. In a second series of experiments, previous work involving doubly-excited Rydberg states is expanded upon by investigating autoionization with high-n, L > 3, Rydberg states. Past research involving autoionization has shown that the effect is strongly L-dependent, with high-L states having significantly smaller autoionizing rates. To create well-defined, L > 3 states, the use of microwave fields to drive various high-n, n ~ 150, n1F3 → (n+1)1G4, (n+2)1H5 transitions is investigated, with spectroscopic measurements of these transitions providing quantum defect values for n1G4 and n1H5 states. These measurements provide a basis for future studies into the L-dependence of high-n, n ~ 300, autoionizing Rydberg atoms, with the eventual goal of creating a long-lived, doubly-excited “planetary” Rydberg state.
We have observed the sharply resonant enhancement of the cross section of the collision process $ns+ns\ensuremath{\rightarrow}np+(n\ensuremath{-}1)p$ between two Nans\mathrm{Na}nsNans (16< n< 2716<~n<~2716< n< 27) atoms which occurs when the levels are shifted by an electric field so that the nsnsns level lies midway between the two ppp states. The widths of the collisional resonances scale as ${n}^{\ensuremath{-}2}$ and the magnitudes of the cross sections as n4{n}^{4}n4, with values of 0.5 GHz and 8\ifmmode\times\else\texttimes\fi{}108{10}^{8}108 A˚2{\mathrm{\AA{}}}^{2}A˚2 for the 20s20s20s state. These results are in good agreement with calculations based on the long-range dipole-dipole interaction between the two atoms.
Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the sss-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the lll-mixing cross section at a particular nnn is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on nnn. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of Na(nd)+He\mathrm{Na}(\mathrm{nd})+\mathrm{He}Na(nd)+He, Ne, and Ar are treated as specific examples.
The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms (n=10,15,and20n=10, 15, \mathrm{and} 20n=10,15,and20) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number mmm. The origin of this tendency is discussed.
The title processes are theoretically investigated based on the model in which an excited Rydberg electron behaves as if it were 'free' and slow, with its interaction with the rare-gas atom playing a decisive role. The cross sections of l-changing collisions of the Rydberg atoms with the rare-gas atoms are evaluated for small angular momentum changes. They are compared with experimental data available at present, under the assumption that there is no selection rule for the distribution over the final angular momentum states of the Rydberg atom, and are found to be consistent with experimental findings. The relation between this approach and some others is examined. The possibility of learning about low-energy electron-rare-gas collisions from refined experimental data on the title processes is briefly discussed.