Photoassociation of Trilobite Rydberg Molecules via Resonant Spin-Orbit Coupling

K. S. Kleinbach, F. Meinert, F. Engel, W. J. Kwon, R. Löw, T. Pfau, and G. Raithel

Phys. Rev. Lett. 118, 223001 – Published 1 June 2017

Abstract

We report on a novel method for the photoassociation of strongly polar trilobite Rydberg molecules. This exotic ultralong-range dimer, consisting of a ground-state atom bound to the Rydberg electron via electron-neutral scattering, inherits its polar character from the admixture of high-angular-momentum electronic orbitals. The absence of low- $L$ character hinders standard photoassociation techniques. Here, we show that for suitable principal quantum numbers the resonant coupling of the orbital motion with the nuclear spin of the perturber, mediated by electron-neutral scattering, hybridizes the trilobite molecular potential with the more conventional $S$ -type molecular state. This provides a general path to associate trilobite molecules with large electric dipole moments, as demonstrated via high-resolution spectroscopy. We find a dipole moment of 135(45) D for the trilobite state. Our results are compared to theoretical predictions based on a Fermi model.

Received 20 February 2017

DOI:https://doi.org/10.1103/PhysRevLett.118.223001

Physics Subject Headings (PhySH)

Cold atoms & matter waves Exotic atoms & molecules Long-range interactions Molecular spectra Spin-orbit coupling

Atomic, Molecular & Optical

Authors & Affiliations

K. S. Kleinbach¹, F. Meinert¹, F. Engel¹, W. J. Kwon¹, R. Löw¹, T. Pfau¹, and G. Raithel²

¹5. Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
²Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

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Vol. 118, Iss. 22 — 2 June 2017

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Images

Figure 1
(a) Long-range molecular potential energy $U$ for ${}^{87}{Rb}$ as a function of the internuclear distance $R$ between the Rydberg core and the perturber atom in the vicinity of the $50 S$ Rydberg state. Zero energy corresponds to the asymptotic pair state $50 S$ , $F = 2$ . The energy gap to the next hydrogenic manifold 47 Hyd, $F = 2$ is comparable to the hyperfine splitting between $F = 2$ and $F = 1$ of $\sim 6.8 GHz$ . (b) Schematic of the two-photon laser excitation employed in the experiment for coupling to $n S$ Rydberg states. (c) Illustration of angular momentum couplings for Rydberg molecule potentials. Electron-neutral scattering couples the electron spins of the Rydberg and perturber atom. In combination with fine and hyperfine structure, the pure singlet and triplet scattering channels and the hyperfine states of the perturber get mixed. (d) Close-up showing the resulting hybridization of the 47 Hyd, $F = 1$ singlet trilobite potential with the $50 S$ , $F = 2$ molecular potential. The green shading indicates the $S$ character of the PECs. The insets depict the Rydberg electron density for three selected values of $R$ marked with blue circles.
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Figure 2
(a)–(c) Rydberg molecule spectra showing the mean ion count rate as a function of laser detuning $δ$ in the vicinity of the atomic Rydberg states $49 S$ (a), $50 S$ (b), and $51 S$ (c) at a magnetic offset field of 1.64 G. The zero of the frequency axis ( $δ = 0$ ) is referenced to the $| n S_{1 / 2}, ↑ ⟩$ atomic Rydberg level. Representative error bars in (a) indicate the standard deviation. Solid lines are fits to the data based on a sum of multiple Lorentzians. Blue solid (red open) symbols indicate the calculated binding energies of molecular states associated with PECs for which $m_{K} = 5 / 2$ ( $m_{K} = 3 / 2$ ). (d)–(f) Long-range molecular potentials in the vicinity of the Rydberg states $49 S$ (d), $50 S$ (e), and $51 S$ (f) for the experimental magnetic field of 1.64 G. Blue dotted (red solid) curves show PECs with $m_{K} = 5 / 2$ ( $m_{K} = 3 / 2$ ). Zero energy corresponds to the asymptotes of the states $n S$ , $F = 2$ with $m_{K} = 5 / 2$ .
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Figure 3
(a) Long-range molecular potentials with $m_{K} = {3 / 2, 5 / 2}$ in the vicinity of the $50 S$ state and calculated vibrational bound states $| Φ_{v} (R) |^{2}$ , offset by their respective binding energies $U_{b}$ . The red (blue) shaded states are bound in the PEC with $m_{K} = 3 / 2$ $(m_{K} = 5 / 2)$ , respectively. Bound states with a significant trilobite admixture are numbered (1)–(8). Zero energy corresponds to the asymptotes of the states $50 S$ , $F = 2$ with $m_{K} = 5 / 2$ . (b) Calculated binding energies $U_{b}$ and dipole moments $d$ for the vibrational bound states (1)–(8) in (a). (c) Rydberg Stark map showing the ion count rate as a function of the laser detuning $δ$ in the vicinity of the $50 S$ state for four values of the electric field $E$ . The zero of the frequency axis ( $δ = 0$ ) is referenced to the atomic Rydberg level $| n S_{1 / 2}, ↑ ⟩$ in the field-free case. Orange points depict the peak position of the blue-detuned trilobite molecular state extracted from Lorentzian fits to the data. The red line is a linear fit to the peak positions, which yields an electric dipole moment of 135(45) D.
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