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arXiv:2003.13495 · Physical Review A

Long-range Rydberg molecule Rb2 : Two-electron R -matrix calculations at intermediate internuclear distances

Michal Tarana

Published Dec 1, 2020• 3 citations
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Abstract

The adiabatic potential energy curves of ${\mathrm{Rb}}_{2}$ in the long-range Rydberg electronic states are calculated using the two-electron $R$-matrix method [M. Tarana and R. \ifmmode \check{C}\else \v{C}\fi{}ur\'{\i}k, Phys. Rev. A 95, 042515 (2017)] for the intermediate internuclear separations between 37 and 200 a.u. The results are compared with the zero-range models to find a region of the internuclear distances where Fermi's pseudopotential approach provides accurate energies. A finite-range potential model of the atomic perturber is used to calculate the wave functions of the Rydberg electron and their features specific for the studied range of internuclear distances are identified.

DOI
10.1103/physreva.102.062802

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The adiabatic potential energy curves of Rb2{\mathrm{Rb}}_{2}Rb2​ in the long-range Rydberg electronic states are calculated using the two-electron RRR-matrix method [M. Tarana and R. \ifmmode \check{C}\else \v{C}\fi{}ur'{\i}k, Phys. Rev. A 95, 042515 (2017)] for the intermediate internuclear separations between 37 and 200 a.u. The results are compared with the zero-range models to find a region of the internuclear distances where Fermi's pseudopotential approach provides accurate energies. A finite-range potential model of the atomic perturber is used to calculate the wave functions of the Rydberg electron and their features specific for the studied range of internuclear distances are identified.
We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. Only diatomic molecules are considered. The method is based on a two-electron RRR-matrix approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via a multichannel version of the Coulomb Green's function. This approach is put into a test by its application to a study of Rydberg states of the hydrogen molecule for internuclear distances RRR from 20 to 400 bohrs and energies corresponding to nnn from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers nnn) and computations based on contact-potential models (higher quantum numbers nnn).
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 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.
Rydberg atom, with a large principal quantum number n, has big size, long lifetime, strong long-range interactions, and so on. These properties make Rydberg atoms potential candidate of quantum gate and single-photon source. Rydberg electron can interact with nearby ground-state atom, which is polarized by the Rydberg electron and is bound to the orbit of Rydberg electrons forming Rydberg molecule. As the kinetic energy of the Rydberg electron is very low, only the lowest partial waves will contribute to the molecular potential.#br#In this paper, the low electron-atom scattering with the semi-classical approximation is introduced, and the pseudopotential of interaction between Rydberg electron and ground-state atom is used to describe the long-range Rydberg molecular potential. Molecular potential curves for cesium (nS, n=30-60) are plotted according to the results of numerical computation, from which the outermost potential depth De and the equilibrium distance r0 of long-range cesium Rydberg molecule are deduced. Potential curves of cesium Rydberg molecules are consistent with the distribution curves in radial probability densities of cesium Rydberg electrons. Dependences of De and r0 on the principal quantum number n are investigated, this has an important role for the experimental measurements. The size of a Rydberg molecule depends on the equilibrium distance r0 and is proportional to the square of effective principal quantum number (n-δ )2. The calculated outermost potential depth De of Rydberg molecule becomes smaller with the increase of principal quantum number n. Rydberg molecule is very sensitive to the external field and can be used to measure and monitor weak signals.
The interaction between a Rydberg electron and a neutral atom situated inside its extended orbit is described via contact interactions for each atom-electron scattering channel. In ultracold environments, these interactions lead to long-range molecules with binding energies typically ranging from 10 to $1\ifmmode\times\else\texttimes\fi{}{10}^{4}$ MHz. These energies are comparable to the relativistic and hyperfine structure of the separate atomic components. Studies of molecular formation aiming to reproduce observations with spectroscopic accuracy must therefore include the hyperfine splitting of the neutral atom and the spin-orbit splittings of both the Rydberg atom and the electron-atom interaction. Adiabatic potential energy curves and permanent electric dipole moments are presented for Rb2{\mathrm{Rb}}_{2}Rb2​ and Cs2{\mathrm{Cs}}_{2}Cs2​. The influence of spin degrees of freedom on the potential energy curves and multipole moments probed in recent experimental work is elucidated, and the observed dipole moments of butterfly molecules are explained by the generalized 3PJ^{3}P_{J}3PJ​ pseudopotential derived here.
We calculated the electronic interaction associated with the exchange of an electron between an atom of calcium excited to a Rydberg state (n∼10−15) and another, neighbouring calcium atom in its ground state. In this range, the Rydberg states have an energy that is comparable to the electron affinity of Ca, enabling resonant or near resonant charge transfer at large internuclear separations (200–700 a0). We calculated the interaction strength while systematically and critically assessing the approximations made, and found it to be large, ranging from 10−5 Eh (70 GHz) to 10−8 Eh. Charge transfer is thus expected to be efficient and to significantly affect the molecular dynamics at a range of internuclear distances where ultra-long-range Rydberg molecules also exist.