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arXiv:1104.5118 · Journal of Physics B Atomic Molecular and Optical Physics

Rubidium Rydberg macrodimers

Nolan Samboy, Robin Côté

Published Sep 14, 2011• 23 citations
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Abstract

We explore long-range interactions between two atoms excited into high principal quantum number n Rydberg states, and present calculated potential energy curves for various symmetries of doubly excited n s and n p rubidium atoms. We show that the potential curves for these symmetries exhibit deep (∼ GHz) potential wells, which can support very extended (∼ µm) bound vibrational states ( macrodimers ). We present n -scaling relations for both the depth D e of the wells and the equilibrium separations R e of these macrodimers, and explore their response to small electric fields and stability with respect to predissociation. Finally, we present a scheme to form and study these macrodimers via photoassociation, and show how one can probe the various ℓ-character of the potential wells.

DOI
10.1088/0953-4075/44/18/184006

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We explore long-range interactions between two atoms excited into high principal quantum number n Rydberg states, and present calculated potential energy curves for various symmetries of doubly excited n s and n p rubidium atoms. We show that the potential curves for these symmetries exhibit deep (∼ GHz) potential wells, which can support very extended (∼ µm) bound vibrational states ( macrodimers ). We present n -scaling relations for both the depth D e of the wells and the equilibrium separations R e of these macrodimers, and explore their response to small electric fields and stability with respect to predissociation. Finally, we present a scheme to form and study these macrodimers via photoassociation, and show how one can probe the various ℓ-character of the potential wells.
We investigate the interaction between two rubidium atoms in highly excited Rydberg states, and find that very long-range potential wells exist. These wells are shown to support many bound states. We calculate the properties of the wells and bound levels, and show that their lifetimes are limited by that of the constituent Rydberg atoms. We also show how these micrometer-sized bound states can be populated via photoassociation (PA), and how the signature of the admixing of various $\ensuremath{\ell}$ characters producing the potential wells could be probed. We discuss sharp variations of the PA rate, which could act as a switching mechanism with potential application to quantum information processing.
We investigate the interaction between two rubidium atoms in highly excited Rydberg states, and find that very long-range potential wells exist. These wells are shown to support many bound states. We calculate the properties of the wells and bound levels, and show that their lifetimes are limited by that of the constituent Rydberg atoms. We also show how these μμμm-size bound states can be populated {\it via} photoassociation (PA), and how the signature of the ad-mixing of various ℓ\ellℓ-character producing the potential wells could be probed. We discuss how sharp variations of the PA rate %to macrodimer bound levels could act as a switching mechanism with potential application to quantum information processing.
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. ^
We study long range interactions between two Rydberg atoms and predict the existence of ultralong range Rydberg dimers with equilibrium distances of many thousands of Bohr radii. We calculate the dispersion coefficients C5, C6, and C8 for two rubidium atoms in the same excited level np and find that they scale like n(8), n(11), and n(15), respectively. We show that for certain molecular symmetries these coefficients lead to long range potential wells that can support molecular bound levels. Such macrodimers would be very sensitive to their environment and could probe weak interactions. We suggest experiments to detect these macrodimers.
We investigate the long-range, two-body interactions between rubidium and potassium atoms in highly excited (n=70)(n=70)(n=70) Rydberg states. After establishing properly symmetrized asymptotic basis states, we diagonalize an interaction Hamiltonian consisting of the standard Coulombic potential expansion and atomic fine structure to calculate electronic potential energy curves. We find that when both atoms are excited to either the 70s70s70s state or the 70p70p70p state, both the $\mathrm{\ensuremath{\Omega}}={0}^{+}$ symmetry interactions and the $\mathrm{\ensuremath{\Omega}}={0}^{\ensuremath{-}}$ symmetry interactions demonstrate a deep potential well capable of supporting many bound levels; the sizes of the corresponding dimer states are of the order of 2.25 $\ensuremath{\mu}\mathrm{m}$. We establish nnn-scaling relations for the equilibrium separation Re{R}_{e}Re​ and the dissociation energy De{D}_{e}De​ and find these relations to be consistent with similar calculations involving the homonuclear interactions between rubidium and cesium. We discuss the specific effects of $\ensuremath{\ell}$ mixing and the exact composition of the calculated potential well via the expansion coefficients of the asymptotic basis states. Finally, we apply a Landau-Zener treatment to show that the dimer states are stable with respect to predissociation.
We propose a novel type of Rydberg dimer, consisting of a Rydberg-state atom bound to a distant positive ion.The molecule is formed through long-range electric-multipole interaction between the Rydberg atom and the pointlike ion.We present potential energy curves (PECs) that are asymptotically connected with Rydberg nP or nD states of rubidium or cesium.The PECs exhibit deep, long-range wells which support many vibrational states of Rydberg-atom-ion molecules (RAIMs).We consider photoassociation of RAIMs in both the weak and the strong optical-coupling regimes between initial and Rydberg states of the neutral atom.Experimental considerations for the realization of RAIMs are discussed.