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Journal of Physics B Atomic Molecular and Optical Physics

Shape-resonance-induced long-range molecular Rydberg states

Edward L Hamilton, Chris H. Greene, H. R. Sadeghpour

Published May 9, 2002• 158 citations
Publisher

Abstract

When an excited atomic electron interacts with a neutral perturbing atom or molecule that possesses a shape resonance, it generates a characteristic class of Born-Oppenheimer potential curves that rise with internuclear distance. We document this effect, and predict the existence of a diverse class of stable, strongly bound atom-atom and atom-molecule states that result from this phenomenon. For the specific case in which Rb is the perturbing atom, we show that such states should be observable in the spectroscopy of an ultracold gas or condensate.

DOI
10.1088/0953-4075/35/10/102

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When an excited atomic electron interacts with a neutral perturbing atom or molecule that possesses a shape resonance, it generates a characteristic class of Born-Oppenheimer potential curves that rise with internuclear distance. We document this effect, and predict the existence of a diverse class of stable, strongly bound atom-atom and atom-molecule states that result from this phenomenon. For the specific case in which Rb is the perturbing atom, we show that such states should be observable in the spectroscopy of an ultracold gas or condensate.
We predict the existence of a ubiquitous class of long-range molecular Rydberg states, whose Born-Oppenheimer potential curves are oscillatory in nature. These oscillations reflect the nodal structure of the atomic Rydberg state wave functions. The temperature and density of atoms in a Bose-Einstein condensate are particularly favorable for the laser excitation of ultra-long-range vibrational bound states localized at internuclear distances in the range 10(3)- 10(5) a.u. A surprising trilobitelike class of polar homonuclear diatomics should exhibit electric dipole moments in the kilodebye range.
Summary form only given. The discovery of ultracold and dilute ensembles of atoms and molecules in magneto-optical traps (MOT) and in atomic Bose-Einstein condensates (BECs) has ushered in a new era of precision atomic and molecular spectroscopy. Since the atoms in such cold environments predominantly interact via long-range forces, the creation of BECs and dilute atomic samples has made the study of very long-range molecular states possible. In this work (Greene et al, Phys. Rev. Lett. vol. 85, p. 2458, 2000), we discuss a particular interatomic arrangement that should be favored in modern-day MOT and BEC setups and should result in the production of molecular Rydberg states whose vibrational wave functions are localized at internuclear distances of order n/sup 2/ Bohr radii, where n is the principal quantum number. The vibrational binding energies of these molecules for n=20-50 fall in the MHz and GHz range, for molecules excited from /sup 87/Rb ultracold atomic gas. We predict two distinct classes of molecular Rydberg states. The nonpolar class of Rydberg molecules form from the interaction between a Rb(nl/sub j/) Rydberg atom with low orbital angular momentum l/sub j//spl les/2 and a distant Rb ground state atom. Rydberg molecules of the second class form from the interaction between an excited Rb atom in high (l/sub j/>2) orbital angular momentum states with a ground state Rb atom.
We have calculated long-range molecular potentials of the 0g+{0}_{g}^{+}0g+​, ${0}_{u}^{\ensuremath{-}}$, and 1u{1}_{u}1u​ symmetries between highly excited rubidium atoms. Strong np+npnp+npnp+np potentials characterized by these symmetries are important in describing interaction-induced phenomena in the excitation spectra of high npnpnp Rydberg states. Long-range molecular resonances are one such phenomenon and they were first reported in S. M. Farooqi et al., Phys. Rev. Lett. 91, 183002 (2003). One class of these resonances occurs at energies corresponding to excited atom pairs $(n\ensuremath{-}1)d+ns$. Such resonances are attributed to l\mathcal{l}l-mixing due to Rydberg-Rydberg interactions so that otherwise forbidden molecular transitions become allowed. We calculate molecular potentials in Hund's case (c), use them to find the resonance line shape, and compare to experimental results.
We present a novel binding mechanism where a neutral Rydberg atom and an atomic ion form a molecular bound state at a large internuclear distance. The binding mechanism is based on Stark shifts and level crossings that are induced in the Rydberg atom due to the electric field of the ion. At particular internuclear distances between the Rydberg atom and the ion, potential wells occur that can hold atom–ion molecular bound states. Apart from the binding mechanism, we describe important properties of the long-range atom–ion Rydberg molecule, such as its lifetime and decay paths, its vibrational and rotational structure, and its large dipole moment. Furthermore, we discuss methods of how to produce and detect it. The unusual properties of the long-range atom–ion Rydberg molecule give rise to interesting prospects for studies of wave packet dynamics in engineered potential energy landscapes.
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.
A recent study suggests the existence of highly polar and nonpolar long-range Rydberg molecules under temperature and density conditions representative of those found in atomic Bose-Einstein condensates. The electronic wave functions of these Rydberg molecules are characterized by an elliptically shaped nodal structure. We use a combination of quantum and semiclassical methods to explore this unique nodal structure and its correlations with the Born-Oppenheimer potential curves of the molecules. We demonstrate a special ``quasiseparability'' that arises in elliptic coordinates at certain internuclear separations and give a semiclassical interpretation of this in terms of quantized Einstein-Brillouin-Keller orbits.