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arXiv:2305.04136 · Physical Review A

Long-range interactions between rubidium and potassium Rydberg atoms

Nolan Samboy

Published Mar 15, 2017• 8 citations
arXivHTMLPDF

Abstract

We investigate the long-range, two-body interactions between rubidium and potassium atoms in highly excited $(n=70)$ 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 $70s$ state or the $70p$ 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 $n$-scaling relations for the equilibrium separation ${R}_{e}$ and the dissociation energy ${D}_{e}$ 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.

DOI
10.1103/physreva.95.032702

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Physical Review A•Oct 15, 2002•117 citations
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 \ensuremathΩ=0+\mathrm{\ensuremath{\Omega}}={0}^{+}\ensuremathΩ=0+ symmetry interactions and the \ensuremathΩ=0\ensuremath−\mathrm{\ensuremath{\Omega}}={0}^{\ensuremath{-}}\ensuremathΩ=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 \ensuremathμm\ensuremath{\mu}\mathrm{m}\ensuremathμm. 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 \ensuremathℓ\ensuremath{\ell}\ensuremathℓ 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.
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 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 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.
Abstract We present an overview over theoretical models to describe adiabatic potential-energy curves, experimental excitation spectra, and electronic and nuclear dynamics in interacting Rydberg-atom pairs at large internuclear separations. The potential-energy curves and molecular wavefunctions are determined from the multipole expansion of the static Coulomb interaction which is evaluated numerically in a product basis of atomic orbitals. The convergence of this approach both in the truncation of the multipole expansion as well as in the size of the product basis is discussed, and the comparison of simulated excitation spectra is established as a useful criterium to test the convergence of the calculation. We finally discuss the dynamics of electronic and nuclear motions of pairs of Rydberg atoms, focusing on the stability of ultralong range Rydberg molecules with respect to autoionization.
We have calculated the long-range interaction potential curves of highly excited Rydberg atom pairs for the combinations Li–Li, Na–Na, K–K, Rb–Rb and Cs–Cs in a perturbative approach. The dispersion C -coefficients are determined for all symmetries of molecular states that correlate to the n s– n s, n p– n p and n d– n d asymptotes. Fitted parameters are given for the scaling of the C -coefficients as a function of the principal quantum number n for all homonuclear pairs of alkali metal atoms.
We calculate potential energy curves for heavy alkali-metal dimers, Rb2{\mathrm{Rb}}_{2}Rb2​ and Cs2{\mathrm{Cs}}_{2}Cs2​ in which one of the atoms is in a highly excited Rydberg states. The method combines numerical integration of coupled equations, describing interaction of electron with the ground-state atom in the field of the Coulomb core of the Rydberg atom, with subsequent matching of the obtained wave function with the Coulomb Green's function in the form of the Kirchhoff integral. The spin-orbit interaction for the Rydberg electron is also included. The results show the existence of several groups of states. Most interesting of them are dominated either by the 3S{}^{3}S3S symmetry near the ground-state atom or by the 3PJ{}^{3}{P}_{J}3PJ​ symmetry, J=0,1,2.J=0,1,2.J=0,1,2. All states, except the 3P1{}^{3}{P}_{1}3P1​ state, exhibit oscillatory dependence of energy on the internuclear distance that can support long-range molecular Rydberg states [e.g., ``trilobite states'' for the 3S{}^{3}S3S symmetry, Greene et al., Phys. Rev. Lett. 85, 2458 (2000)]. These states possess large diagonal and transition dipole moments which are expressed analytically in terms of the Coulomb wave functions and calculated in a broad range of internuclear separations.