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arXiv:1901.08792 · Physical Review Research

Observation of spin-orbit-dependent electron scattering using long-range Rydberg molecules

Markus Deiß, Shinsuke Haze, Joschka Wolf, Limei Wang, Florian Meinert, Christian Fey, Frederic Hummel, Peter Schmelcher, Johannes Hecker Denschlag

Published Jan 14, 2020• 21 citations
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Abstract

The authors observe spin-orbit interaction in electron-neutral scattering, which has been elusive so far. This result is obtained by using ultralong-range Rydberg molecules as a micro laboratory for low-energy scattering experiments. The spin-orbit interaction gives rise to a fine structure multiplet in the molecular term spectrum which is resolved via photoassociation spectroscopy.

DOI
10.1103/physrevresearch.2.013047

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We present an experimental and theoretical study of the spin- and vibrational states of 16P−5S16P-5S16P−5S ultralong-range Rb2_22​ Rydberg molecules that are bound in the second outermost potential well. Due to resonant ppp-wave interaction, the admixture of a butterfly state, and the combination of spin-spin and spin-orbit couplings these molecules feature non-trivial spin state energy level manifolds. By carrying out Rydberg spectroscopy we observe several vibrational ladders. Each ladder exhibits a characteristic multiplet substructure which facilitates assigning a spin state to each level. Our calculations show that a specific type of spin-orbit interaction can significantly contribute to the multiplet line splittings. This spin-orbit interaction is given by the coupling between the total electron spin and the orbital angular momentum of the Rydberg electron in the reference frame of the ground state atom. Furthermore, we find that the diabaticity of the molecular motion across an avoided crossing in the potential energy curve has a strong impact on the vibrational level structure. Our investigation paves the way for further in-depth studies of subtle interaction mechanisms in Rydberg molecules.
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The level structure of negative-ions near the electron detachment limit dictates the low-energy scattering of an electron with the parent neutral atom. We demonstrate that a single ultracold atom bound inside a Rydberg orbit forming an ultralong-range Rydberg molecule provides an atomic-scale system which is highly sensitive to electron-neutral scattering and thus allows for detailed insights into the underlying near-threshold anion states. Our measurements reveal the so far unobserved fine structure of the 3PJ^3P_J3PJ​ triplet of Rb−^-− and allow us to extract parameters of the associated ppp-wave scattering resonances which deviate from previous theoretical estimates. Moreover, we observe a novel alignment mechanism for Rydberg molecules mediated by spin-orbit coupling in the negative ion.
The interaction between a Rydberg electron and a neutral atom situated inside its extended orbit is described via contact interactions for each atom-electron scattering channel. In ultracold environments, these interactions lead to long-range molecules with binding energies typically ranging from 10 to $1\ifmmode\times\else\texttimes\fi{}{10}^{4}$ MHz. These energies are comparable to the relativistic and hyperfine structure of the separate atomic components. Studies of molecular formation aiming to reproduce observations with spectroscopic accuracy must therefore include the hyperfine splitting of the neutral atom and the spin-orbit splittings of both the Rydberg atom and the electron-atom interaction. Adiabatic potential energy curves and permanent electric dipole moments are presented for Rb2{\mathrm{Rb}}_{2}Rb2​ and Cs2{\mathrm{Cs}}_{2}Cs2​. The influence of spin degrees of freedom on the potential energy curves and multipole moments probed in recent experimental work is elucidated, and the observed dipole moments of butterfly molecules are explained by the generalized 3PJ^{3}P_{J}3PJ​ pseudopotential derived here.
We report on the observation of long-range Cs 2 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.