Journal of Physics B Atomic Molecular and Optical Physics

Energies and dipole moments of long-range molecular Rydberg states

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

Published May 9, 2002• 72 citations

Abstract

Adiabatic wavefunctions and dipole moments of Rydberg states perturbed by a neutral atom have been investigated. Wavefunctions are equal to sums of products of Coulomb wavefunctions and differ very substantially from any single Coulomb wavefunction. Using the Kirchhoff-integral method (Fabrikant I I 1993 J. Phys. B: At. Mol. Opt. Phys. 26 2533) we calculate the potential curves of two adiabatic Rydberg states for the Rb*( n ≃30) + Rb(5s) system: one dominated by the 3 S symmetry near the ground-state Rb atom, and the other dominated by the 3 P symmetry.

DOI: 10.1088/0953-4075/35/10/101

Related papers

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

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

Physical Review AOct 15, 2002117 citations

Hamiltonian for the inclusion of spin effects in long-range Rydberg molecules

Matthew T. Eiles, Chris H. Greene

arXiv:1611.04508Physical Review AApr 25, 201762 citations

Adiabatic potential-energy curves of long-range Rydberg molecules: Two-electron R -matrix approach

Michal Tarana, Roman Čurı́k

arXiv:1510.08773Physical Review AJan 22, 201615 citations

Angular-momentum couplings in long-range Rb 2 Rydberg molecules

David Alexander Anderson, Stephanie Miller, Georg A. Raithel

arXiv:1409.2543Physical Review ADec 31, 201464 citations

Long-range interactions between Rydberg atoms

Johannes Deiglmayr

Physica ScriptaSep 22, 201620 citations

Long-range Interactions Between Ultracold Rydberg Atoms and the Formation Properties of Long-range Rydberg Molecules

Nolan Samboy

Jan 1, 20111 citation

Journal of Physics B Atomic Molecular and Optical Physics

Energies and dipole moments of long-range molecular Rydberg states

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

Published May 9, 2002• 72 citations

Publisher

Abstract

DOI: 10.1088/0953-4075/35/10/101

Related papers

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

Hamiltonian for the inclusion of spin effects in long-range Rydberg molecules

Matthew T. Eiles, Chris H. Greene

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 ${\mathrm{Rb}}_{2}$ and ${\mathrm{Cs}}_{2}$ . 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 $^{3}P_{J}$ pseudopotential derived here.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 ${\mathrm{Rb}}_{2}$ and ${\mathrm{Cs}}_{2}$. 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 $^{3}P_{J}$ pseudopotential derived here.

arXiv:1611.04508Physical Review AApr 25, 201762 citations

Adiabatic potential-energy curves of long-range Rydberg molecules: Two-electron R -matrix approach

Michal Tarana, Roman Čurı́k

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 $R$ -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 $R$ from 20 to 400 bohrs and energies corresponding to $n$ from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers $n$ ) and computations based on contact-potential models (higher quantum numbers $n$ ).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 $R$-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 $R$ from 20 to 400 bohrs and energies corresponding to $n$ from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers $n$) and computations based on contact-potential models (higher quantum numbers $n$).

arXiv:1510.08773Physical Review AJan 22, 201615 citations

Angular-momentum couplings in long-range Rb 2 Rydberg molecules

David Alexander Anderson, Stephanie Miller, Georg A. Raithel

We study angular-momentum couplings in $^{87}\mathrm{Rb}{}_{2}$ Rydberg molecules formed between a Rydberg and $5{S}_{1/2}$ ground-state atom. We use a Fermi model that includes $S$ -wave and $P$ -wave singlet and triplet scattering of the Rydberg electron with the $5{S}_{1/2}$ atom, along with the fine-structure coupling of the Rydberg atom and hyperfine-structure coupling of the $5{S}_{1/2}$ atom. We discuss the effects of these couplings on the adiabatic molecular potentials. We obtain bound-state energies, lifetimes, and electric and magnetic dipole moments for the vibrational ground states of the $^{87}\mathrm{Rb}(nD+5{S}_{1/2})$ molecules in all adiabatic potentials, with fine and hyperfine structure included. The hyperfine structure gives rise to mixed singlet-triplet potentials. We also study the effect of the hyperfine structure on the deep ${}^{3}S$ -wave- and ${}^{3}P$ -wave-dominated adiabatic molecular potentials, which support high-$\ensuremath{\ell}$ $^{87}\mathrm{Rb}{}_{2}$ Rydberg molecules.We study angular-momentum couplings in $^{87}\mathrm{Rb}{}_{2}$ Rydberg molecules formed between a Rydberg and $5{S}_{1/2}$ ground-state atom. We use a Fermi model that includes $S$-wave and $P$-wave singlet and triplet scattering of the Rydberg electron with the $5{S}_{1/2}$ atom, along with the fine-structure coupling of the Rydberg atom and hyperfine-structure coupling of the $5{S}_{1/2}$ atom. We discuss the effects of these couplings on the adiabatic molecular potentials. We obtain bound-state energies, lifetimes, and electric and magnetic dipole moments for the vibrational ground states of the $^{87}\mathrm{Rb}(nD+5{S}_{1/2})$ molecules in all adiabatic potentials, with fine and hyperfine structure included. The hyperfine structure gives rise to mixed singlet-triplet potentials. We also study the effect of the hyperfine structure on the deep ${}^{3}S$-wave- and ${}^{3}P$-wave-dominated adiabatic molecular potentials, which support high-$\ensuremath{\ell}$ $^{87}\mathrm{Rb}{}_{2}$ Rydberg molecules.

arXiv:1409.2543Physical Review ADec 31, 201464 citations

Long-range interactions between Rydberg atoms

Johannes Deiglmayr

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.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.

Physica ScriptaSep 22, 201620 citations

Long-range Interactions Between Ultracold Rydberg Atoms and the Formation Properties of Long-range Rydberg Molecules

Nolan Samboy

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. ^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. ^

Jan 1, 20111 citation

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.

{\mathrm{Rb}}_{2}

and

{\mathrm{Cs}}_{2}

. 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

^{3}P_{J}

pseudopotential derived here.

R

-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

R

from 20 to 400 bohrs and energies corresponding to

n

from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers

n

) and computations based on contact-potential models (higher quantum numbers

n

We study angular-momentum couplings in

^{87}\mathrm{Rb}{}_{2}

Rydberg molecules formed between a Rydberg and

5{S}_{1/2}

ground-state atom. We use a Fermi model that includes

S

-wave and

P

-wave singlet and triplet scattering of the Rydberg electron with the

5{S}_{1/2}

atom, along with the fine-structure coupling of the Rydberg atom and hyperfine-structure coupling of the

5{S}_{1/2}

atom. We discuss the effects of these couplings on the adiabatic molecular potentials. We obtain bound-state energies, lifetimes, and electric and magnetic dipole moments for the vibrational ground states of the

^{87}\mathrm{Rb}(nD+5{S}_{1/2})

molecules in all adiabatic potentials, with fine and hyperfine structure included. The hyperfine structure gives rise to mixed singlet-triplet potentials. We also study the effect of the hyperfine structure on the deep

{}^{3}S

-wave- and

{}^{3}P

-wave-dominated adiabatic molecular potentials, which support high-$\ensuremath{\ell}$

^{87}\mathrm{Rb}{}_{2}

Rydberg molecules.