Physical Review A

Highly excited Rydberg states of a rubidium atom: Theory versus experiments

Mariusz Pawlak, Nimrod Moiseyev, H. R. Sadeghpour

Published Apr 16, 2014• 11 citations

Abstract

There has been increasing interest in the energy spectrum of highly excited Rydberg states. The energy spectra of the $s$, $p$, and $d$ highly excited Rydberg states of a rubidium atom have been measured by different groups. However, there is a discrepancy between the reported data concerning the energy levels of highly excited $s$ and $d$ states of Rb. We address this issue by performing accurate calculations of Rb($ns,np,nd$) energy levels using the parametric one-electron valence potential [Marinescu, Sadeghpour, and Dalgarno, Phys. Rev. A 49, 982 (1994)] with spin-orbit coupling. We compare results with reference data from the National Institute of Standards and Technology and from available experiments. This enables us to recommend energy levels of highly excited Rydberg states of Rb that can be used as reference values.

DOI: 10.1103/physreva.89.042506

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Experimental and theoretical study of Stark patterns in Rb Rydberg levels

Eliane Luc-Koenig, Sylvain Liberman, Jacques Pinard

Physical Review AAug 1, 197920 citations

Level shifts of rubidium Rydberg states due to binary interactions

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Physical Review AMar 14, 2007156 citations

Adiabatic energy levels and electric dipole moments of Rydberg states of Rb2 and Cs2 dimers

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Physical Review AOct 15, 2002117 citations

Long-range potentials and ( n − 1 ) d + n s molecular resonances in an ultracold Rydberg gas

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Collisional depopulation of rubidium Rydberg levels by rare gases

M Hugon, B. Sayer, P. R. Fournier +1 more

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Ionization spectra of highly Stark-shifted rubidium Rydberg states

Jens Grimmel, Markus Stecker, Manuel Kaiser +4 more

arXiv:1703.01258Physical Review AJul 26, 201710 citations

Physical Review A

Highly excited Rydberg states of a rubidium atom: Theory versus experiments

Mariusz Pawlak, Nimrod Moiseyev, H. R. Sadeghpour

Published Apr 16, 2014• 11 citations

Publisher

Abstract

There has been increasing interest in the energy spectrum of highly excited Rydberg states. The energy spectra of the

s

p

, and

d

highly excited Rydberg states of a rubidium atom have been measured by different groups. However, there is a discrepancy between the reported data concerning the energy levels of highly excited

s

and

d

states of Rb. We address this issue by performing accurate calculations of Rb(

ns,np,nd

) energy levels using the parametric one-electron valence potential [Marinescu, Sadeghpour, and Dalgarno, Phys. Rev. A 49, 982 (1994)] with spin-orbit coupling. We compare results with reference data from the National Institute of Standards and Technology and from available experiments. This enables us to recommend energy levels of highly excited Rydberg states of Rb that can be used as reference values.

DOI: 10.1103/physreva.89.042506

Related papers

Experimental and theoretical study of Stark patterns in Rb Rydberg levels

Eliane Luc-Koenig, Sylvain Liberman, Jacques Pinard

Stark patterns of high-lying excited states of rubidium (Rydberg states $n\ensuremath{\sim}48$) in electric fields from 0 to 20 V/cm have been studied both experimentally and theoretically. Recordings have been obtained with high-resolution laser techniques. Theoretical interpretation takes into account a great number of close-lying levels in the diagonalization process. In order to reproduce the positions as well as the intensities of the one-photon transitions from the ground state, it is necessary to use for $s$ , $p$ , and $d$ levels the wave functions calculated from a central potential specific to the Rb spectrum.Stark patterns of high-lying excited states of rubidium (Rydberg states $n\ensuremath{\sim}48$) in electric fields from 0 to 20 V/cm have been studied both experimentally and theoretically. Recordings have been obtained with high-resolution laser techniques. Theoretical interpretation takes into account a great number of close-lying levels in the diagonalization process. In order to reproduce the positions as well as the intensities of the one-photon transitions from the ground state, it is necessary to use for $s$, $p$, and $d$ levels the wave functions calculated from a central potential specific to the Rb spectrum.

Physical Review AAug 1, 197920 citations

Level shifts of rubidium Rydberg states due to binary interactions

Aaron Reinhard, Tara Cubel Liebisch, Brenton Knuffman +1 more

We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers $n$ , $\ensuremath{\ell}$, $j$ , and ${m}_{j}$ , taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the ``Rydberg-excitation blockade.'' We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers $n$, $\ensuremath{\ell}$, $j$, and ${m}_{j}$, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the ``Rydberg-excitation blockade.'' We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.

Physical Review AMar 14, 2007156 citations

Adiabatic energy levels and electric dipole moments of Rydberg states of Rb2 and Cs2 dimers

A.A. Khuskivadze, M. I. Chibisov, I. I. Fabrikant

We calculate potential energy curves for heavy alkali-metal dimers, ${\mathrm{Rb}}_{2}$ and ${\mathrm{Cs}}_{2}$ 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 ${}^{3}S$ symmetry near the ground-state atom or by the ${}^{3}{P}_{J}$ symmetry, $J=0,1,2.$ All states, except the ${}^{3}{P}_{1}$ state, exhibit oscillatory dependence of energy on the internuclear distance that can support long-range molecular Rydberg states [e.g., ``trilobite states'' for the ${}^{3}S$ 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.We calculate potential energy curves for heavy alkali-metal dimers, ${\mathrm{Rb}}_{2}$ and ${\mathrm{Cs}}_{2}$ 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 ${}^{3}S$ symmetry near the ground-state atom or by the ${}^{3}{P}_{J}$ symmetry, $J=0,1,2.$ All states, except the ${}^{3}{P}_{1}$ state, exhibit oscillatory dependence of energy on the internuclear distance that can support long-range molecular Rydberg states [e.g., ``trilobite states'' for the ${}^{3}S$ 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.

Physical Review AOct 15, 2002117 citations

Long-range potentials and ( n − 1 ) d + n s molecular resonances in an ultracold Rydberg gas

Jovica Stanojevic, Robin Côté, D. Tong +2 more

We have calculated long-range molecular potentials of the ${0}_{g}^{+}$ , ${0}_{u}^{\ensuremath{-}}$, and ${1}_{u}$ symmetries between highly excited rubidium atoms. Strong $np+np$ potentials characterized by these symmetries are important in describing interaction-induced phenomena in the excitation spectra of high $np$ 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 $\mathcal{l}$ -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 have calculated long-range molecular potentials of the ${0}_{g}^{+}$, ${0}_{u}^{\ensuremath{-}}$, and ${1}_{u}$ symmetries between highly excited rubidium atoms. Strong $np+np$ potentials characterized by these symmetries are important in describing interaction-induced phenomena in the excitation spectra of high $np$ 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 $\mathcal{l}$-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.

arXiv:0801.2386Physical Review ANov 14, 200839 citations

Collisional depopulation of rubidium Rydberg levels by rare gases

M Hugon, B. Sayer, P. R. Fournier +1 more

The cross sections for the quenching of highly excited Rb(nS) (32<or=n<or=45) and Rb(nD) (30<or=n<or=41) states have been measured for the different rare gases. In most cases studied, the quenching cross sections seem rather constant or slightly decreasing with n for a given series and a given rare gas. The experimental data are compared with the results of calculations using various theoretical approaches. It is shown that in this range of large n values the main process responsible for the quenching is the Rydberg-electron-rare-gas interaction, as previously stated for lower n values (10<or=n<or=20).The cross sections for the quenching of highly excited Rb(nS) (32<or=n<or=45) and Rb(nD) (30<or=n<or=41) states have been measured for the different rare gases. In most cases studied, the quenching cross sections seem rather constant or slightly decreasing with n for a given series and a given rare gas. The experimental data are compared with the results of calculations using various theoretical approaches. It is shown that in this range of large n values the main process responsible for the quenching is the Rydberg-electron-rare-gas interaction, as previously stated for lower n values (10<or=n<or=20).

Journal of Physics B Atomic and Molecular PhysicsAug 14, 198234 citations

Ionization spectra of highly Stark-shifted rubidium Rydberg states

Jens Grimmel, Markus Stecker, Manuel Kaiser +4 more

We report on the observation and numerical calculation of ionization spectra of highly Stark-shifted Rydberg states of rubidium beyond the classical ionization threshold. In the numerical calculations, a complex absorbing potential (CAP) allows us to predict the energy levels and ionization rates of Rydberg states in this regime. Our approach of adjusting the CAP to the external electric field reduces the number of free parameters from one per resonance to a single one. Furthermore, we have measured the ionization spectra of magneto-optically trapped rubidium atoms which are excited to principal quantum numbers of 43 and 70 at various electric fields. The emerging ions are detected using an ion optics. We find good agreement between the numerically and experimentally obtained spectra.We report on the observation and numerical calculation of ionization spectra of highly Stark-shifted Rydberg states of rubidium beyond the classical ionization threshold. In the numerical calculations, a complex absorbing potential (CAP) allows us to predict the energy levels and ionization rates of Rydberg states in this regime. Our approach of adjusting the CAP to the external electric field reduces the number of free parameters from one per resonance to a single one. Furthermore, we have measured the ionization spectra of magneto-optically trapped rubidium atoms which are excited to principal quantum numbers of 43 and 70 at various electric fields. The emerging ions are detected using an ion optics. We find good agreement between the numerically and experimentally obtained spectra.

arXiv:1703.01258Physical Review AJul 26, 201710 citations

There has been increasing interest in the energy spectrum of highly excited Rydberg states. The energy spectra of the

s

p

, and

d

highly excited Rydberg states of a rubidium atom have been measured by different groups. However, there is a discrepancy between the reported data concerning the energy levels of highly excited

s

and

d

states of Rb. We address this issue by performing accurate calculations of Rb(

ns,np,nd

s

p

, and

d

levels the wave functions calculated from a central potential specific to the Rb spectrum.

We use perturbation theory to directly calculate the van der Waals and dipole-dipole energy shifts of pairs of interacting Rb Rydberg atoms for different quantum numbers

n

, $\ensuremath{\ell}$,

j

, and

{m}_{j}

, taking into account a large number of perturbing states. Our results can be used to identify good experimental parameters and illuminate important considerations for applications of the ``Rydberg-excitation blockade.'' We also use the results of the calculation to explain features of previous experimental data on the Rydberg-excitation blockade. To explore control methods for the blockade, we discuss energy shifts due to atom-atom interaction in an external electric field.

We calculate potential energy curves for heavy alkali-metal dimers,

{\mathrm{Rb}}_{2}

and

{\mathrm{Cs}}_{2}

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

{}^{3}S

symmetry near the ground-state atom or by the

{}^{3}{P}_{J}

symmetry,

J=0,1,2.

All states, except the

{}^{3}{P}_{1}

state, exhibit oscillatory dependence of energy on the internuclear distance that can support long-range molecular Rydberg states [e.g., ``trilobite states'' for the

{}^{3}S

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.

We have calculated long-range molecular potentials of the

{0}_{g}^{+}

, ${0}_{u}^{\ensuremath{-}}$, and

{1}_{u}

symmetries between highly excited rubidium atoms. Strong

np+np

potentials characterized by these symmetries are important in describing interaction-induced phenomena in the excitation spectra of high

np

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

\mathcal{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.