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:1809.02021 · Physical Review A

Alignment of s -state Rydberg molecules in magnetic fields

Frederic Hummel, Christian Fey, Peter Schmelcher

Published Feb 1, 2019• 21 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.99.023401

Related papers

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

Frederic Hummel, Christian Fey, Peter Schmelcher

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.

arXiv:1711.08748•Physical Review A•Apr 23, 2018•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

Rotational hybridization, and control of alignment and orientation in triatomic ultralong-range Rydberg molecules

Rosario González‐Férez, H. R. Sadeghpour, Peter Schmelcher

We explore the electronic structure and rovibrational properties of an ultralong-range triatomic Rydberg molecule formed by a Rydberg atom and a ground state heteronuclear diatomic molecule. We focus here on the interaction of a Rb( ) Rydberg atom with a KRb( N = 0) diatomic polar molecule. There is significant electronic hybridization with the Rb( n = 24, ) degenerate manifold. The polar diatomic molecule is allowed to rotate in the electric fields generated by the Rydberg electron and core as well as an external field. We investigate the metamorphosis of the Born–Oppenheimer potential curves, essential for the binding of the molecule, with varying electric field and analyze the resulting properties such as the vibrational structure and the alignment and orientation of the polar diatomic molecule.

arXiv:1406.6549•New Journal of Physics•Jan 15, 2015•23 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

Ultralong-range Rydberg molecules

Fey, C., Hummel, F., Schmelcher, P.

We review ultralong-range Rydberg molecules (ULRMs), which are bound states between a Rydberg atom and one or more ground-state atoms with bond lengths on the order of thousands of Bohr radii. The binding originates from multiple electron-atom scattering and leads to exotic oscillatory potential energy surfaces that reflect the probability density of the Rydberg electron. This unconventional binding mechanism opens fascinating possibilities to tune molecular properties via weak external fields, to study spin-resolved low-energy electron-atom scattering as well as to control and to probe interatomic forces in few- and many-body systems. Here, we provide an overview on recent theoretical and experimental progress in the field with an emphasis on polyatomic ULRMs, field control and spin interactions.

•Oct 23, 2019•9 citations

Ultralong-range Rydberg molecules

Christian Fey, Frederic Hummel, Peter Schmelcher

We review ultralong-range Rydberg molecules (ULRMs), which are bound states between a Rydberg atom and one or more ground-state atoms with bond lengths on the order of thousands of Bohr radii. The binding originates from multiple electron-atom scattering and leads to exotic oscillatory potential energy surfaces that reflect the probability density of the Rydberg electron. This unconventional binding mechanism opens fascinating possibilities to tune molecular properties via weak external fields, to study spin-resolved low-energy electron-atom scattering as well as to control and to probe interatomic forces in few- and many-body systems. Here, we provide an overview on recent theoretical and experimental progress in the field with an emphasis on polyatomic ULRMs, field control and spin interactions.

arXiv:1907.13416•Molecular Physics•Oct 23, 2019•55 citations
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 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 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 explore the electronic structure and rovibrational properties of an ultralong-range triatomic Rydberg molecule formed by a Rydberg atom and a ground state heteronuclear diatomic molecule. We focus here on the interaction of a Rb( ) Rydberg atom with a KRb( N = 0) diatomic polar molecule. There is significant electronic hybridization with the Rb( n = 24, ) degenerate manifold. The polar diatomic molecule is allowed to rotate in the electric fields generated by the Rydberg electron and core as well as an external field. We investigate the metamorphosis of the Born–Oppenheimer potential curves, essential for the binding of the molecule, with varying electric field and analyze the resulting properties such as the vibrational structure and the alignment and orientation of the polar diatomic molecule.
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 review ultralong-range Rydberg molecules (ULRMs), which are bound states between a Rydberg atom and one or more ground-state atoms with bond lengths on the order of thousands of Bohr radii. The binding originates from multiple electron-atom scattering and leads to exotic oscillatory potential energy surfaces that reflect the probability density of the Rydberg electron. This unconventional binding mechanism opens fascinating possibilities to tune molecular properties via weak external fields, to study spin-resolved low-energy electron-atom scattering as well as to control and to probe interatomic forces in few- and many-body systems. Here, we provide an overview on recent theoretical and experimental progress in the field with an emphasis on polyatomic ULRMs, field control and spin interactions.
We review ultralong-range Rydberg molecules (ULRMs), which are bound states between a Rydberg atom and one or more ground-state atoms with bond lengths on the order of thousands of Bohr radii. The binding originates from multiple electron-atom scattering and leads to exotic oscillatory potential energy surfaces that reflect the probability density of the Rydberg electron. This unconventional binding mechanism opens fascinating possibilities to tune molecular properties via weak external fields, to study spin-resolved low-energy electron-atom scattering as well as to control and to probe interatomic forces in few- and many-body systems. Here, we provide an overview on recent theoretical and experimental progress in the field with an emphasis on polyatomic ULRMs, field control and spin interactions.