We discuss the rotational structure of ultra-long range Rydberg molecules and their angular nuclear wave function. Expressing the complete molecular wave function in a laboratory fixed frame, we derive the transition matrix elements for the photoassociation of free ground state atoms. The coupling strength depends on the angular momentum coupling in the Rydberg molecule, which differs for the various types of Rydberg molecules. This work explains the different steps to calculate the wave functions and the transition matrix elements in a way, that they can be transferred to other Rydberg molecules involving different atomic species or molecular coupling cases.We discuss the rotational structure of ultra-long range Rydberg molecules and their angular nuclear wave function. Expressing the complete molecular wave function in a laboratory fixed frame, we derive the transition matrix elements for the photoassociation of free ground state atoms. The coupling strength depends on the angular momentum coupling in the Rydberg molecule, which differs for the various types of Rydberg molecules. This work explains the different steps to calculate the wave functions and the transition matrix elements in a way, that they can be transferred to other Rydberg molecules involving different atomic species or molecular coupling cases.

arXiv:1802.04683Journal of Physics B Atomic Molecular and Optical PhysicsJun 13, 201811 citations

Long-range Rydberg-Rydberg interactions and molecular resonances

Jovica Stanojevic, Robin C ot 'e

Bulletin of the American Physical SocietyMay 18, 20060 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 anisotropic interactions in Rydberg atoms and molecules

William R. Clark

Sep 1, 19982 citations

Approximate symmetries of long-range Rydberg molecules including spin effects

Homar Rivera-Rodríguez, Rocío Jáuregui

An operator that generates an approximate symmetry of long-range Rydberg molecules (LRRMs) formed by two alkali atoms, one in a Rydberg state and the other in the ground state, is identified. This is first done by evaluating the natural orbitals associated with a variational calculation of the binding wave function within the Born-Oppenheimer description of the molecule including s and p Fermi pseudopotential and the hyperfine structure energy terms. The resulting orbitals with the highest occupation number are shown to be identical to those obtained by a perturbative model for high angular momentum—trilobite and butterfly—LRRMs. Whenever the slight dependence of the quantum defects of the Rydberg electron on its total momentum j⃗=ℓ⃗+s⃗1 can be neglected, the symmetry operator of the high angular momentum LRRMs orbitals is identified as the sum of the spin of the Rydberg electron s⃗1 , spin of the valence electron s⃗2 , and the spin of nucleus i⃗ of the ground-state atom, N⃗=s1⃗+s2⃗+i⃗ . The spin orbitals that diagonalize N⃗ define compact basis sets for the description of LRRMs beyond the aforementioned approximations. The matrix elements of the Hamiltonian in these basis sets have simple expressions, so that the relevance of triplet and singlet contributions can be directly estimated. The expected consequences of this approximate spin-symmetry on the spectra of LRRMs are briefly described. Published by the American Physical Society 2024An operator that generates an approximate symmetry of long-range Rydberg molecules (LRRMs) formed by two alkali atoms, one in a Rydberg state and the other in the ground state, is identified. This is first done by evaluating the natural orbitals associated with a variational calculation of the binding wave function within the Born-Oppenheimer description of the molecule including s and p Fermi pseudopotential and the hyperfine structure energy terms. The resulting orbitals with the highest occupation number are shown to be identical to those obtained by a perturbative model for high angular momentum—trilobite and butterfly—LRRMs. Whenever the slight dependence of the quantum defects of the Rydberg electron on its total momentum j⃗=ℓ⃗+s⃗1 can be neglected, the symmetry operator of the high angular momentum LRRMs orbitals is identified as the sum of the spin of the Rydberg electron s⃗1 , spin of the valence electron s⃗2 , and the spin of nucleus i⃗ of the ground-state atom, N⃗=s1⃗+s2⃗+i⃗ . The spin orbitals that diagonalize N⃗ define compact basis sets for the description of LRRMs beyond the aforementioned approximations. The matrix elements of the Hamiltonian in these basis sets have simple expressions, so that the relevance of triplet and singlet contributions can be directly estimated. The expected consequences of this approximate spin-symmetry on the spectra of LRRMs are briefly described. Published by the American Physical Society 2024

arXiv:2310.15095Physical Review ResearchFeb 16, 20241 citation

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.