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Journal de Physique II

Rydberg molecule in a magnetic field

Niloufar Shafizadeh, Maurice Raoult, Marcel Horani, S. Guizard, D. Gauyacq

Published Apr 1, 1992• 5 citations
Publisher

Abstract

Rydberg states of the NO molecule have been probed by two-color resonantly enhanced multiphoton ionization in a magnetic field of 0.93 T. Penetrating s and d states show strong interactions with the intramolecular field while nonpenetrating f states show stronger interactions with the external magnetic field. Competition between the molecular core anisotropy and the external field anisotropy leads to a greater variety of situations than in a Rydberg atom, ranging from a “weak field” regime to a “strong field” regime. These different situations are illustrated by a multichannel quantum defect calculation on the np states of NO including the Zeeman effect. An extreme situation can be achieved in which the Rydberg molecule looses its molecular character and shows an almost pure atomic structure within each rotational channel.

DOI
10.1051/jp2:1992159

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Rydberg states of the NO molecule have been probed by two-color resonantly enhanced multiphoton ionization in a magnetic field of 0.93 T. Penetrating s and d states show strong interactions with the intramolecular field while nonpenetrating f states show stronger interactions with the external magnetic field. Competition between the molecular core anisotropy and the external field anisotropy leads to a greater variety of situations than in a Rydberg atom, ranging from a “weak field” regime to a “strong field” regime. These different situations are illustrated by a multichannel quantum defect calculation on the np states of NO including the Zeeman effect. An extreme situation can be achieved in which the Rydberg molecule looses its molecular character and shows an almost pure atomic structure within each rotational channel.
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.
A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.
Abstract A spectroscopic study of Rydberg states of helium ( n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ( n = 30, B ≤ 120 mT and F = 0–78 V cm −1 ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ( n = 45, B = 277 mT and F = 0–8 V cm −1 ). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin–orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m l values and pronounced m l -mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg–Stark deceleration.
We study the magnetic-field dependence of the interactions between two alkaline-earth(-like) Rydberg atoms, 88{}^{88}88Sr and 174{}^{174}174Yb. Considering the pair of Rydberg states ∣ns,3S1,mJ⟩|ns,{}^3S_1,m_J\rangle∣ns,3S1​,mJ​⟩ and ∣(n+1)s,3S1,mJ⟩|(n+1)s,{}^3S_1,m_J\rangle∣(n+1)s,3S1​,mJ​⟩, we show that the effective Hamiltonian takes the form of an {\it XXZ}-type quantum spin model, as in the alkali-atom case [M. Kunimi and T. Tomita, Phys. Rev. A {\bf 112}, L051301 (2025)]. We find that the behavior of the anisotropy parameter for 174{}^{174}174Yb at zero magnetic field is significantly different from that for other atomic species. This behavior arises from the interplay of strong spin-orbit coupling and the resulting multichannel redistribution of Förster defects in 174{}^{174}174Yb. We systematically calculate the interaction parameters of the {\it XXZ} model in the presence of a magnetic field and show that they can be tuned by the field. As applications to quantum many-body problems, we investigate one-dimensional systems in the large-anisotropy regime and show that the folded {\it XXZ} model can be realized in 174{}^{174}174Yb systems without fine-tuning of the field. We also investigate two-dimensional square-lattice systems and show that a supersolid phase can emerge in the ground state at the mean-field level.
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.