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Physical Review A

Resolving rotationally excited states of ultralong-range Rydberg molecules

Y. Lu, J. D. Whalen, S. K. Kanungo, T. C. Killian, F. B. Dunning, S. Yoshida, Joachim Burgdörfer

Published Aug 16, 2022• 8 citations
Publisher

Abstract

We report experimental observations of the rotational structure in photoassociative spectroscopy of ultralong-range Rydberg molecules (ULRRMs) in an ultracold gas of $^{86}\mathrm{Sr}$. ULRRM spectroscopy probes scattering wave functions at much larger internuclear separations than photoassociative spectroscopy of low-lying electronic states. At such separations photon recoil momentum can lead to the transfer of significant angular momentum to the Rydberg molecule, evidence of which is provided through the distribution of excited rotational states. The visibility of the rotational structure is enhanced because, for collisions between ground-state $^{86}\mathrm{Sr}$ atoms, the large, near-resonant s-wave scattering length approaches the size of the ULRRM. Similar enhancement is not seen for $^{84}\mathrm{Sr}$, which has a much smaller scattering length. Results are interpreted with the aid of a theory that accounts for the recoil momentum associated with photoexcitation and the large $s$-wave scattering length in the entrance channel. While the observed rotational splittings and the qualitative trends in the relative intensities of the spectral features are well described by theory, the effects of recoil momentum are more prominent in the measured data than in the theory.

DOI
10.1103/physreva.106.022809

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We report experimental observations of the rotational structure in photoassociative spectroscopy of ultralong-range Rydberg molecules (ULRRMs) in an ultracold gas of 86Sr^{86}\mathrm{Sr}86Sr. ULRRM spectroscopy probes scattering wave functions at much larger internuclear separations than photoassociative spectroscopy of low-lying electronic states. At such separations photon recoil momentum can lead to the transfer of significant angular momentum to the Rydberg molecule, evidence of which is provided through the distribution of excited rotational states. The visibility of the rotational structure is enhanced because, for collisions between ground-state 86Sr^{86}\mathrm{Sr}86Sr atoms, the large, near-resonant s-wave scattering length approaches the size of the ULRRM. Similar enhancement is not seen for 84Sr^{84}\mathrm{Sr}84Sr, which has a much smaller scattering length. Results are interpreted with the aid of a theory that accounts for the recoil momentum associated with photoexcitation and the large sss-wave scattering length in the entrance channel. While the observed rotational splittings and the qualitative trends in the relative intensities of the spectral features are well described by theory, the effects of recoil momentum are more prominent in the measured data than in the theory.
Spectroscopic measurements of the rotational distribution of 84Sr^{84}\mathrm{Sr}84Sr and 86Sr5sns1S0^{86}\mathrm{Sr}\phantom{\rule{4pt}{0ex}}\phantom{\rule{0.16em}{0ex}}5sns{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}86Sr5sns1S0​ ultralong-range Rydberg molecular dimers created via photoassociation in a cold gas are reported. The dimers are produced by two-photon excitation via the 5s5p5s5p5s5p 1P1^{1}P_{1}1P1​ intermediate state. The use of singlet states permits detailed study of the roles that the initial atom-atom interaction, photon momentum transfer during Rydberg excitation, and sample temperature play in determining the spectral line shape and final dimer rotational distribution. The results are in good agreement with the predictions of a model that includes these effects. The present work further highlights the sensitivity of ultralong-range Rydberg molecule formation to the state of the initial cold gas.
Anomalies in the rotational spectra of 86^{86}86Sr ULRRM dimers
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Anomalies in the rotational structure of 86Sr^{86}\mathrm{Sr}86Sr 3S1^{3}S_{1}3S1​ dimer ultralong-range Rydberg molecules created in a cold strontium gas by two-photon excitation via the intermediate 5s5p5s5p5s5p 3P1^{3}P_{1}3P1​ state are reported. Measurements reveal that the distribution of product rotational states is sensitive to intermediate state detuning. Comparative studies using 84Sr^{84}\mathrm{Sr}84Sr 1S0^{1}S_{0}1S0​ and 3S1^{3}S_{1}3S1​, and 86Sr^{86}\mathrm{Sr}86Sr 1S0^{1}S_{0}1S0​ dimers display no similar behavior, indicating that the observed behavior is peculiar to 86Sr^{86}\mathrm{Sr}86Sr triplet dimers. While we have no definitive hypothesis as to the physical mechanism responsible for this behavior, possible explanations might involve the very different scattering lengths for 84Sr^{84}\mathrm{Sr}84Sr and 86Sr^{86}\mathrm{Sr}86Sr, or the interchange of spin and rotational angular momentum.
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.
Measurements of the production of 5 s n d 1 D 2 – 5 s 2 1 S 0 ultralong-range Rydberg dimers through photoassocation in an ultracold Sr 84 atomic gas are reported. The molecular potential associated with the Rydberg D state is anisotropic and the molecular states are characterized by the vibrational quantum number ν and the total angular momentum K ⃗ = L ⃗ + N ⃗ , where L ⃗ and N ⃗ are the electronic orbital angular momentum and rotational angular momentum, respectively. The measured molecular binding energies agree reasonably well with theoretical predictions. Additionally, the electron-atom scattering leads to broader line shapes in the photoassociation spectrum than might be expected simply from the angular momentum of the initial colliding cold-atom pairs.
Combining ultracold atomic gases with the peculiar properties of Rydberg excited atoms gained a lot of theoretical and experimental attention in recent years. Embedded in the ultracold gas, an interaction between the Rydberg atom and the surrounding ground state atoms arises through the scattering of the Rydberg electron from an intruding perturber atom. This peculiar interaction gives rise to a plenitude of previously unobserved effects. Within the framework of the present thesis, this interaction is studied in detail for Rydberg PPP-states in rubidium. Due to their long lifetime, atoms in Rydberg states are subject to scattering with the surrounding ground state atoms in the ultracold cloud. By measuring their lifetime as a function of the ground state atom flux, we are able to obtain the total inelastic scattering cross section as well as the partial cross section for associative ionisation. The fact that the latter is three orders of magnitude larger than the size of the formed molecular ion indicates the presence of an efficient mass transport mechanism that is mediated by the Rydberg–ground state interaction. The immense acceleration of the collisional process shows a close analogy to a catalytic process. The increase of the scattering cross section renders associative ionisation an important process that has to be considered for experiments in dense ultracold systems. The interaction of the Rydberg atom with a ground state perturber gives rise to a highly oscillatory potential that supports molecular bound states. These so-called ultralong-range Rydberg molecules are studied with high resolution time-of-flight spectroscopy, where we are able to determine the binding energies and lifetimes of the molecular states between the two fine structure split 25P25P25P-states. Inside an electric field, we observe a broadening of the molecular lines that indicates the presence of a permanent electric dipole moment, induced by the mixing with high angular momentum states. Due to the mixing of the ground state atom’s hyperfine states by the molecular interaction, we are able to observe a spin-flip of the perturber upon creation of a Rydberg molecule. Furthermore, an incidental near-degeneracy in the underlying level scheme of the 25P25P25P-state gives rise to highly entangled states between the Rydberg fine structure state and the perturber’s hyperfine structure. These mechanisms can be used to manipulate the quantum state of a remote particle over distances that exceed by far the typical contact interaction range. Apart from the ultralong-range Rydberg molecules that predominantly consist of only one low angular momentum state, a class of Rydberg molecules is predicted to exist that strongly mixes the high angular momentum states of the degenerate hydrogenic manifolds. These states, the so-called trilobite- and butterfly Rydberg molecules, show very peculiar properties that cannot be observed for conventional molecules. Here we present the first experimental observation of butterfly Rydberg molecules. In addition to an extensive spectroscopy that reveals the binding energy, we are also able to observe the rotational structure of these exotic molecules. The arising pendular states inside an electric field allow us, in comparison to the model of a dipolar rotor, to extract the precise bond length and dipole moment of the molecule. With the information obtained in the present study, it is possible to photoassociate butterfly molecules with a selectable bond length, vibrational state, rotational state, and orientation inside an electric field. By shedding light on various previously unrevealed aspects, the experiments presented in this thesis significantly deepen our knowledge on the Rydberg–ground state interaction and the peculiar effects arising from it. The obtained spectroscopic information on Rydberg molecules and the changed reaction dynamics for molecular ion creation will surely provide valuable data for quantum chemical simulations and provide necessary data to plan future experiments. Beyond that, our study reveals that the hyperfine interaction in Rydberg molecules and the peculiar properties of butterfly states provide very promising new ways to alter the short- and long-range interactions in ultracold many-body systems. In this sense the investigated Rydberg–ground state interaction not only lies right at the interface between quantum chemistry, quantum many-body systems, and Rydberg physics, but also creates many new and fascinating possibilities by combining these fields.