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arXiv:1802.04683 · Journal of Physics B Atomic Molecular and Optical Physics

Photoassociation of rotating ultra-long range Rydberg molecules

O Thomas, C Lippe, T Eichert, H Ott

Published Jun 13, 2018• 11 citations
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Abstract

We discuss the rotational structure of ultra-long range Rydberg molecules and their angular nuclear wave function. Expressing the complete molecular wave function in a laboratory fixed frame, we derive the transition matrix elements for the photoassociation of free ground state atoms. The coupling strength depends on the angular momentum coupling in the Rydberg molecule, which differs for the various types of Rydberg molecules. This work explains the different steps to calculate the wave functions and the transition matrix elements in a way, that they can be transferred to other Rydberg molecules involving different atomic species or molecular coupling cases.

DOI
10.1088/1361-6455/aacc30

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We discuss the rotational structure of ultra-long range Rydberg molecules and their angular nuclear wave function. Expressing the complete molecular wave function in a laboratory fixed frame, we derive the transition matrix elements for the photoassociation of free ground state atoms. The coupling strength depends on the angular momentum coupling in the Rydberg molecule, which differs for the various types of Rydberg molecules. This work explains the different steps to calculate the wave functions and the transition matrix elements in a way, that they can be transferred to other Rydberg molecules involving different atomic species or molecular coupling cases.
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We present photodissociation of ultracold long-range Rydberg molecules as a tool to characterize their electronic properties. We photoassociate 39K2372P^{39}\mathrm{K}_{2} 37\phantom{\rule{0.16em}{0ex}}^{2}P39K2​372P molecules with highly entangled electronic and nuclear spins of the two bound atoms and quantify the entanglement by projection of the molecular state onto noninteracting atoms using radio-frequency photodissociation. By comparison of experimental photodissociation rates with theoretical predictions, we further characterize the electronic and nuclear wave function of the photoassociated molecules. Based on the complete characterization of the formed long-range Rydberg molecules, we demonstrate a full hyperfine-spin flip of a free ground-state atom through the interaction with a Rydberg atom.
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The work presented in this dissertation represents a comprehensive study on long-range interactions between alkali Rydberg atoms. As a consequence of their size, Rydberg atoms possess very large dipole moments, making them highly sensitive to external fields and to other Rydberg atoms. The strong dipole-dipole interaction between two Rydberg atoms results in a mixing of their angular momentum characters, which is the cornerstone of the work presented here. We describe the ℓ-mixing between various local molecular asymptotes through a residual Coulomb potential, assuming no electron cloud overlap. We then directly diagonalize an interaction Hamiltonian consisting of these Rydberg-Rydberg interactions and spin-orbit (fine structure) coupling in the Hund's case (c). In this manner, we calculate potential energy curves for various molecular symmetries and find that some of these curves exhibit deep potential wells, capable of supporting very extended bound molecular states ( macrodimers). We analyze the specific structure of the ℓ-mixing for these potential wells and derive convenient n-scaling relations for both their equilibrium separations Re and well depths De. We also explore various properties of the macrodimers, including their response to small electric fields and stability with respect to predissociation. We note throughout the dissertation that the detection of such extended dimers could help progress studies in a variety of areas such as exotic, ultracold chemistry and quantum information and computing. To facilitate detection, we propose a scheme to form and study the macrodimers via photoassociation (PA). We present calculated PA lineshapes from two different electronic ground states based on a harmonic trapping model. We find that both PA signals vary significantly with the laser detunings, indicating that different ℓ-characters could be probed at different equilibrium lengths. Finally, we extend the two-body formalism to the case of three interacting Rydberg atoms and present preliminary results for triply excited 58p rubidium atoms along a common axis. We provide a few examples of surface plots corresponding to different local asymptotes, each with a unique three-dimensional "landscape" and discuss the relevance of the physical features. The highlight of our analysis is the appearance of a potential well, which indicates the formation of a linear trimer. ^
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