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Journal of Modern Optics

Analysis of long-range Cs Rydberg potential wells

Arne Schwettmann, K. Richard Overstreet, Jonathan Tallant, James P. Shaffer

Published Nov 10, 2007• 34 citations
Publisher

Abstract

We analyse bound states at long-range (R∼5 μm) for pairs of Cs atoms in the 89D and neighbouring states. These wells are due solely to avoided crossings between the van der Waals pair interaction potentials. The depth of the wells is ∼40 MHz, and vibrational spectra consist of hundreds of bound states. We present detailed calculations of the properties of two of these wells at different electric fields (∼ mV cm− 1), since the electric field changes the well depth and shape. We estimate bound-state lifetimes μs, lineshapes, and two-photon excitation and detection rates ∼Hz from the 6P state at a temperature of T = 40 μK for these molecules.

DOI
10.1080/09500340701584076

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We analyse bound states at long-range (R∼5 μm) for pairs of Cs atoms in the 89D and neighbouring states. These wells are due solely to avoided crossings between the van der Waals pair interaction potentials. The depth of the wells is ∼40 MHz, and vibrational spectra consist of hundreds of bound states. We present detailed calculations of the properties of two of these wells at different electric fields (∼ mV cm− 1), since the electric field changes the well depth and shape. We estimate bound-state lifetimes μs, lineshapes, and two-photon excitation and detection rates ∼Hz from the 6P state at a temperature of T = 40 μK for these molecules.
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 report the observation of cold Cs Rydberg atom molecules bound at internuclear separations of R~3-9 um. The bound states result from avoided crossings between Rydberg atom pair interaction potentials in an applied electric field. The molecular states can be modified by changing the applied electric field. The molecules are observed by mapping the radial separation of the two Rydberg atoms as a function of time delay between excitation and detection using the Coulomb repulsion of the ions after pulsed field ionization. Measurements were performed for 63D+65D, 64D+66D, 65D+67D, and 66D+68D pairs. The experiment is in good agreement with calculations of the pair interactions for these states.
We present evidence for molecular resonances in a cold dense gas of rubidium Rydberg atoms. Single UV photon excitation from the 5s ground state to np Rydberg states (n=50-90) reveals resonances at energies corresponding to excited atom pairs (n-1)d+ns. We attribute these normally forbidden transitions to avoided crossings between the long-range molecular potentials of two Rydberg atoms. These strong van der Waals interactions result in avoided crossings at extremely long range, e.g., approximately 58 000 times the Bohr radius (a(0)) for n=70.
We present calculations of potential curves for very high-nnn (89D)(89D)(89D) Cs Rydberg-atom pairs, including a background electric field. From these potentials, we show that energy transfer occurs at rates of $\ensuremath{\sim}30--70\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$, background electric fields play an important role and dipole-dipole- and quadrupole-quadrupole-induced avoided curve crossings should lead to conversion of electronic to kinetic energy, nnn-changing collisions, and observable ultracold long-range Rydberg molecules.
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. ^
Long-range Rydberg molecules (LRMs) form when a highly excited Rydberg electron scatters from ground-state atoms inside its orbit, creating oscillatory, long-range potentials. We present a combined theoretical and experimental study of caesium dimers correlated to 402P3/2 Rydberg states, with an emphasis on decay via autoionisation (associative ionisation). Our model includes a relativistic treatment of electron-atom scattering with spin-orbit coupling, the perturber's hyperfine structure, and coupling of vibrational levels to a continuum of short-range decay channels. Calculated potential-energy curves predict two families of wells: outer wells near the classical outer turning point supporting long-lived states, and inner wells at shorter range whose lifetimes are limited by tunneling and subsequent vibronic decay. Using photoassociation in an ultracold Cs gas and an analysis of pulsed-field-ionisation signals which are highly selective for the detection of molecules, we assign resonances by binding energy and measure lifetimes. The measured lifetimes of inner-well states increase systematically with increasing detuning and agree with calculated lifetimes; detection of Cs2+ product ions supports autoionisation as a dominant channel. We show that the lifetimes are strongly reduced by spin-orbit interactions in the transient Cs-collision complex, which lift the near-degeneracy in Omega observed for states in the outer well and control the inner-well binding. The identified states also provide promising pathways to create ultracold molecules in ion-pair states.