Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1711.08748 · Physical Review A

Spin-interaction effects for ultralong-range Rydberg molecules in a magnetic field

Frederic Hummel, Christian Fey, Peter Schmelcher

Published Apr 23, 2018• 21 citations
arXivHTMLPDF

Abstract

We investigate the fine and spin structure of ultralong-range Rydberg molecules exposed to a homogeneous magnetic field. Each molecule consists of a $^{87}\mathrm{Rb}$ Rydberg atom the outer electron of which interacts via spin-dependent $s$- and $p$-wave scattering with a polarizable $^{87}\mathrm{Rb}$ ground-state atom. Our model includes also the hyperfine structure of the ground-state atom as well as spin-orbit couplings of the Rydberg and ground-state atom. We focus on $d$-Rydberg states and principal quantum numbers $n$ in the vicinity of 40. The electronic structure and vibrational states are determined in the framework of the Born-Oppenheimer approximation for varying field strengths ranging from a few up to hundred Gauss. The results show that the interplay between the scattering interactions and the spin couplings gives rise to a large variety of molecular states in different spin configurations as well as in different spatial arrangements that can be tuned by the magnetic field. This includes relatively regularly shaped energy surfaces in a regime where the Zeeman splitting is large compared to the scattering interaction but small compared to the Rydberg fine structure, as well as more complex structures for both weaker and stronger fields. We quantify the impact of spin couplings by comparing the extended theory to a spin-independent model.

DOI
10.1103/physreva.97.043422

Related papers

Alignment of s -state Rydberg molecules in magnetic fields

Frederic Hummel, Christian Fey, Peter Schmelcher

We unravel some peculiar properties of ultra-long-range Rydberg molecules formed by an $s$-state $^{87}\mathrm{Rb}$ Rydberg atom and a corresponding ground-state atom whose electronic orbitals are spherically symmetric and therefore should not be influenced by the presence of weak magnetic fields. However, the electron-atom interaction, which establishes the molecular bond, is under certain conditions subject to a sizable spin-orbit coupling and, hence, sensitive to the magnetic field. This mechanism can be harnessed to counterintuitively align the $s$-state molecules with respect to the field axis. We demonstrate this by analyzing the angular-dependent Born-Oppenheimer potential energy surfaces and the supported vibrational molecular states. Our predictions open interesting possibilities for accessing the physics of relativistic electron-atom scattering experimentally.

arXiv:1809.02021•Physical Review A•Feb 1, 2019•21 citations

Ultralong-range Rydberg molecules in combined electric and magnetic fields

Markus Kurz, Peter Schmelcher

We investigate the impact of combined electric and magnetic fields on the structure of ultralong-range polar Rydberg molecules. Our focus is hereby on the parallel as well as the crossed field configuration, taking into account both the s -wave and p -wave interactions of the Rydberg electron and the neutral ground state atom. We show the strong impact of the p -wave interaction on the ultralong-range molecular states for a pure B -field configuration. In the presence of external fields, the angular degrees of freedom acquire vibrational character, and we encounter two- and three-dimensional oscillatory adiabatic potential energy surfaces for the parallel and crossed field configuration, respectively. The equilibrium configurations of local potential wells can be controlled via the external field parameters for both field configurations depending on the specific degree of electronic excitation. This allows us to tune the molecular alignment and orientation. The resulting electric dipole moment is in the order of several kDebye, and the rovibrational level spacings are in the range of 2– . Both properties are analyzed with varying field strengths.

arXiv:1405.0429•Journal of Physics B Atomic Molecular and Optical Physics•Aug 6, 2014•21 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.

arXiv:1409.2543•Physical Review A•Dec 31, 2014•64 citations

Observation of spin-structure of ultralong-range Rydberg molecules

Markus Deiß, Shinsuke Haze, Joschka Wolf +6 more

We present an experimental and theoretical study of the spin- and vibrational states of $16P-5S$ ultralong-range Rb$_2$ Rydberg molecules that are bound in the second outermost potential well. Due to resonant $p$-wave interaction, the admixture of a butterfly state, and the combination of spin-spin and spin-orbit couplings these molecules feature non-trivial spin state energy level manifolds. By carrying out Rydberg spectroscopy we observe several vibrational ladders. Each ladder exhibits a characteristic multiplet substructure which facilitates assigning a spin state to each level. Our calculations show that a specific type of spin-orbit interaction can significantly contribute to the multiplet line splittings. This spin-orbit interaction is given by the coupling between the total electron spin and the orbital angular momentum of the Rydberg electron in the reference frame of the ground state atom. Furthermore, we find that the diabaticity of the molecular motion across an avoided crossing in the potential energy curve has a strong impact on the vibrational level structure. Our investigation paves the way for further in-depth studies of subtle interaction mechanisms in Rydberg molecules.

•Jan 25, 2019•0 citations

Observation of mixed singlet-triplet Rb2 Rydberg molecules

Fabian Böttcher, Anita Gaj, K. M. Westphal +6 more

We present high-resolution spectroscopy of ${\mathrm{Rb}}_{\text{2}}$ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet $s$-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the $p$-wave contribution and all orders in the relative momentum $k$, and compare the obtained molecular binding energies to the experimental data.

arXiv:1510.01097•Physical Review A•Mar 21, 2016•59 citations

Ultralong-range Rydberg molecules of Hg atoms

Agata Wojciechowska, Michał Tomza, Matthew T. Eiles

Ultralong-range Rydberg molecules, composed of an excited Rydberg atom and a ground-state atom, are characterized by large bond lengths, dipole moments, sensitivity to external fields, and an unusual binding mechanism based on low-energy elastic electron scattering. Although Rydberg molecules formed between alkali atoms have received the most attention, the additional complexity found in atoms with more than a single valence electron poses new theoretical challenges as well as new possibilities for control and design of the molecular structure. In this paper, we extend the theory of Rydberg molecules to include the additional spin coupling of the Rydberg states of a multivalent atom. We employ this theory to describe the properties of Rydberg molecules composed of mercury atoms. We calculate the potential energy curves of both heteronuclear (${\mathrm{Hg}}^{*}\mathrm{Rb}$) and homonuclear (${\mathrm{Hg}}^{*}\mathrm{Hg}$) molecules. In the former case, we propose the realization of long-range spin entanglement and remote spin flip. In the latter, we show how long-lived metastable molecular states of ${\mathrm{Hg}}^{*}\mathrm{Hg}$ exist as resonances above the dissociation threshold.

arXiv:2412.05025•Physical Review A•Apr 14, 2025•4 citations
We investigate the fine and spin structure of ultralong-range Rydberg molecules exposed to a homogeneous magnetic field. Each molecule consists of a 87Rb^{87}\mathrm{Rb}87Rb Rydberg atom the outer electron of which interacts via spin-dependent sss- and ppp-wave scattering with a polarizable 87Rb^{87}\mathrm{Rb}87Rb ground-state atom. Our model includes also the hyperfine structure of the ground-state atom as well as spin-orbit couplings of the Rydberg and ground-state atom. We focus on ddd-Rydberg states and principal quantum numbers nnn in the vicinity of 40. The electronic structure and vibrational states are determined in the framework of the Born-Oppenheimer approximation for varying field strengths ranging from a few up to hundred Gauss. The results show that the interplay between the scattering interactions and the spin couplings gives rise to a large variety of molecular states in different spin configurations as well as in different spatial arrangements that can be tuned by the magnetic field. This includes relatively regularly shaped energy surfaces in a regime where the Zeeman splitting is large compared to the scattering interaction but small compared to the Rydberg fine structure, as well as more complex structures for both weaker and stronger fields. We quantify the impact of spin couplings by comparing the extended theory to a spin-independent model.
We unravel some peculiar properties of ultra-long-range Rydberg molecules formed by an sss-state 87Rb^{87}\mathrm{Rb}87Rb Rydberg atom and a corresponding ground-state atom whose electronic orbitals are spherically symmetric and therefore should not be influenced by the presence of weak magnetic fields. However, the electron-atom interaction, which establishes the molecular bond, is under certain conditions subject to a sizable spin-orbit coupling and, hence, sensitive to the magnetic field. This mechanism can be harnessed to counterintuitively align the sss-state molecules with respect to the field axis. We demonstrate this by analyzing the angular-dependent Born-Oppenheimer potential energy surfaces and the supported vibrational molecular states. Our predictions open interesting possibilities for accessing the physics of relativistic electron-atom scattering experimentally.
We investigate the impact of combined electric and magnetic fields on the structure of ultralong-range polar Rydberg molecules. Our focus is hereby on the parallel as well as the crossed field configuration, taking into account both the s -wave and p -wave interactions of the Rydberg electron and the neutral ground state atom. We show the strong impact of the p -wave interaction on the ultralong-range molecular states for a pure B -field configuration. In the presence of external fields, the angular degrees of freedom acquire vibrational character, and we encounter two- and three-dimensional oscillatory adiabatic potential energy surfaces for the parallel and crossed field configuration, respectively. The equilibrium configurations of local potential wells can be controlled via the external field parameters for both field configurations depending on the specific degree of electronic excitation. This allows us to tune the molecular alignment and orientation. The resulting electric dipole moment is in the order of several kDebye, and the rovibrational level spacings are in the range of 2– . Both properties are analyzed with varying field strengths.
We study angular-momentum couplings in 87Rb2^{87}\mathrm{Rb}{}_{2}87Rb2​ Rydberg molecules formed between a Rydberg and 5S1/25{S}_{1/2}5S1/2​ ground-state atom. We use a Fermi model that includes SSS-wave and PPP-wave singlet and triplet scattering of the Rydberg electron with the 5S1/25{S}_{1/2}5S1/2​ atom, along with the fine-structure coupling of the Rydberg atom and hyperfine-structure coupling of the 5S1/25{S}_{1/2}5S1/2​ 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 87Rb(nD+5S1/2)^{87}\mathrm{Rb}(nD+5{S}_{1/2})87Rb(nD+5S1/2​) 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 3S{}^{3}S3S-wave- and 3P{}^{3}P3P-wave-dominated adiabatic molecular potentials, which support high-$\ensuremath{\ell}$ 87Rb2^{87}\mathrm{Rb}{}_{2}87Rb2​ Rydberg molecules.
We present an experimental and theoretical study of the spin- and vibrational states of 16P−5S16P-5S16P−5S ultralong-range Rb2_22​ Rydberg molecules that are bound in the second outermost potential well. Due to resonant ppp-wave interaction, the admixture of a butterfly state, and the combination of spin-spin and spin-orbit couplings these molecules feature non-trivial spin state energy level manifolds. By carrying out Rydberg spectroscopy we observe several vibrational ladders. Each ladder exhibits a characteristic multiplet substructure which facilitates assigning a spin state to each level. Our calculations show that a specific type of spin-orbit interaction can significantly contribute to the multiplet line splittings. This spin-orbit interaction is given by the coupling between the total electron spin and the orbital angular momentum of the Rydberg electron in the reference frame of the ground state atom. Furthermore, we find that the diabaticity of the molecular motion across an avoided crossing in the potential energy curve has a strong impact on the vibrational level structure. Our investigation paves the way for further in-depth studies of subtle interaction mechanisms in Rydberg molecules.
We present high-resolution spectroscopy of Rb2{\mathrm{Rb}}_{\text{2}}Rb2​ ultralong-range Rydberg molecules bound by mixed singlet-triplet electron-neutral atom scattering. The mixing of the scattering channels is a consequence of the hyperfine interaction in the ground-state atom, as predicted recently by Anderson et al. [Phys. Rev. A 90, 062518 (2014)]. Our experimental data enable the determination of the effective zero-energy singlet sss-wave scattering length for Rb. We show that an external magnetic field can tune the contributions of the singlet and the triplet scattering channels and therefore the binding energies of the observed molecules. This mixing of molecular states via the magnetic field results in observed shifts of the molecular line which differ from the Zeeman shift of the asymptotic atomic states. Finally, we calculate molecular potentials using a full diagonalization approach including the ppp-wave contribution and all orders in the relative momentum kkk, and compare the obtained molecular binding energies to the experimental data.
Ultralong-range Rydberg molecules, composed of an excited Rydberg atom and a ground-state atom, are characterized by large bond lengths, dipole moments, sensitivity to external fields, and an unusual binding mechanism based on low-energy elastic electron scattering. Although Rydberg molecules formed between alkali atoms have received the most attention, the additional complexity found in atoms with more than a single valence electron poses new theoretical challenges as well as new possibilities for control and design of the molecular structure. In this paper, we extend the theory of Rydberg molecules to include the additional spin coupling of the Rydberg states of a multivalent atom. We employ this theory to describe the properties of Rydberg molecules composed of mercury atoms. We calculate the potential energy curves of both heteronuclear (Hg∗Rb{\mathrm{Hg}}^{*}\mathrm{Rb}Hg∗Rb) and homonuclear (Hg∗Hg{\mathrm{Hg}}^{*}\mathrm{Hg}Hg∗Hg) molecules. In the former case, we propose the realization of long-range spin entanglement and remote spin flip. In the latter, we show how long-lived metastable molecular states of Hg∗Hg{\mathrm{Hg}}^{*}\mathrm{Hg}Hg∗Hg exist as resonances above the dissociation threshold.