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arXiv:2310.14686 · Physical Review A

Kato's theorem and ultralong-range Rydberg molecules

Matthew T. Eiles, Frederic Hummel

Published Feb 21, 2024• 8 citations
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Abstract

We consider nonadiabatic coupling in the “trilobite”-like long-range Rydberg molecules created by perturbing degenerate high- ℓ Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density, the avoided crossings between relevant potential energy curves can become extremely narrow, leading to highly singular nonadiabatic coupling. We find that the gap between the trilobite potential curve and neighboring “butterfly” or “dragonfly” potential curves can even vanish, as in a conical intersection, if the gap closes at an internuclear distance which matches a node of the s -wave radial wave function. This is an unanticipated outcome of Kato's theorem. Published by the American Physical Society 2024

DOI
10.1103/physreva.109.022811

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We consider nonadiabatic coupling in the “trilobite”-like long-range Rydberg molecules created by perturbing degenerate high- ℓ Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density, the avoided crossings between relevant potential energy curves can become extremely narrow, leading to highly singular nonadiabatic coupling. We find that the gap between the trilobite potential curve and neighboring “butterfly” or “dragonfly” potential curves can even vanish, as in a conical intersection, if the gap closes at an internuclear distance which matches a node of the s -wave radial wave function. This is an unanticipated outcome of Kato's theorem. Published by the American Physical Society 2024
Ultralong-range Rydberg molecules provide an exciting testbed for molecular physics at exaggerated scales. In the so-called trilobite and butterfly Rydberg molecules, the Born-Oppenheimer approximation can fail due to strong nonadiabatic couplings arising from the combination of radial oscillations and rapid energy variations in the adiabatic potential energy curves. We utilize an accurate coupled-channel treatment of the vibronic system to observe the breakdown of Born-Oppenheimer physics, such as nonadiabatic trapping and decay of molecular states found near pronounced avoided crossings in the adiabatic potential curves. Even for vibrational states localized far away from avoided crossings, a single-channel model is quantitatively sufficient only after including the diagonal nonadiabatic corrections to the Born-Oppenheimer potentials. Our results indicate the importance of including nonadiabatic physics in the description of ultralong-range Rydberg molecules and in the interpretation of measured vibronic spectra.
Ultralong-range Rydberg molecules (ULRMs) are highly imbalanced bound systems formed via the low-energy scattering of a Rydberg electron with a ground-state atom. We investigate for 23Na^{23}\mathrm{Na}23Na the ddd state and the energetically close-by trilobite state, exhibiting avoided crossings that lead to the breakdown of the adiabatic Born-Oppenheimer (BO) approximation. We develop a coupled-channel approach to explore the nonadiabatic interaction effects between these electronic states. The resulting spectrum exhibits stark differences in comparison to the BO spectra, such as the existence of above-threshold resonant states without any adiabatic counterparts, and a significant rearrangement of the spectral structure as well as the localization of the eigenstates. Our study motivates the use of 23Na^{23}\mathrm{Na}23Na ULRMs, as a probe to explore vibronic interaction effects on exaggerated timescales and length scales.
Long-range Rydberg molecules are typically bound in wells formed in their oscillatory potential energy curves. In alkaline Rydberg molecules, bound vibrational states exist even when these potential wells are disrupted by level repulsion from the steep butterfly potential energy curve induced by a scattering shape resonance. The binding in this case is attributed to quantum reflection. However, the rapidly varying regions of the potential energy landscape where quantum reflection occurs often coincide with regions where nonadiabatic coupling becomes significant. By comparing the molecular states calculated within the Born-Oppenheimer approximation, where quantum reflection is the only binding mechanism, with those obtained from the full set of coupled channel equations, we assess the effects of nonadiabatic coupling on vibrational energies and lifetimes. Our findings show that these couplings can stabilize the molecule by providing an additional barrier which protects the vibrational states from predissociation and nonradiative transitions. There can also be extreme cases where nonadiabatic coupling completely dominates the binding and the molecular lifetimes saturate at the atomic Rydberg lifetime.
We consider ultralong-range polyatomic Rydberg molecules formed by combining a Rydberg cesium atom and a ground-state RbCs molecule. We explore the regime where the charge-dipole interaction due to the Rydberg electron with the diatomic polar molecule couples the quantum defect Rydberg states Cs(ns)\mathrm{Cs}(ns)Cs(ns) to the nearest degenerate hydrogenic manifold. We consider polyatomic Rydberg molecules in states which are amenable to production in optical tweezers and study the influence of nonadiabatic coupling on the likelihood of their formation. The decay rates of the vibrational states reflect the interference signature of wave function spread in different coupled potential wells.
We investigate the non-adiabatic quantum dynamics of ultralong-range Rydberg molecules using a vibronically coupled two-channel treatment. The two-channels are composed of coupled trilobite and butterfly electronic states, formed as a result of SSS-wave and PPP-wave scattering of high angular momentum Rydberg electrons with perturbing ground state atoms. Within the Born-Oppenheimer treatment, the PPP-wave scattering channel introduces an adiabatic decay pathway that affects the stability and lifetimes of trilobite states. Our numerical results show that the vibronic coupling is dependent on the principal quantum number nnn, and for certain nnn there is non-adiabatic stabilization against internal molecular decay, facilitating previously studied dynamical effects in pure trilobite molecules. Apart from the internal diffraction effect caused by the backscattering of vibrational wavepackets from the trilobite potential, we also observe interesting multi-well tunneling effects during low-energy oscillations for a range of nnn-values. Our work serves to highlight that the unique vibrational coordinate dependent electronic structure of these polar molecules, along with high level densities, promise many exciting dynamical effects.
We report on the observation of highly excited ( ν ∼ 100 ) vibrational states of a trilobite ultralong-range Rydberg molecule in Rb 87 . These states manifest spectroscopically in a regularly spaced series of peaks red-detuned from the 25 f 7 / 2 dissociation threshold. The existence and observed stability of these states require the almost complete suppression of the adiabatic decay pathway induced by the P -wave shape resonance of Rb. This stabilization is predicted to occur only for certain Rydberg levels where the avoided crossing between trilobite and P -wave-dominated butterfly potential energy curves nearly vanishes, allowing the vibrational states to diabatically traverse the crossing with almost unit probability. This is the first direct measurement of beyond-Born-Oppenheimer physics in long-range Rydberg molecules, and paves the way for future experiments to access and manipulate wave packets formed from high-lying vibrational states.