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

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 Rb Rydberg atom whose outer electron interacts via spin-dependent s-and p-wave scattering with a polarizable 87 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.

Trilobites, butterflies, and other exotic specimens of long-range Rydberg molecules

“…This should be fairly straightforward to accomplish, and it will have a significant impact on the practicality of including spin into a study of polyatomic molecules. As the present moment the enlarged Hilbert space including the hyperfine structure of each perturber rapidly increases the basis size needed for diagonalization [202,196], and the massive reduction in basis size within the trilobite overlap approach would dramatically reduce the computational effort.…”

“…[193] investigated these potential energy surfaces and alignment in an electric field, while Refs. [194,195,196,197] concentrate on magnetic fields effects. These studies showed that the strong coupling to external fields can prove destructive to LRRMs, as the Zeeman splitting can eliminate the trilobite states [194].…”

Observation of spin-orbit-dependent electron scattering using long-range Rydberg molecules

“…For L p = 0 there is s-wave interaction, while p-wave interaction is given for L p = 1. We employ a generalized Fermi pseudopotential [7,40]…”

Ultralong-range Rydberg molecules

“…Comparison to experimental photoassociation spectra (blue and black dots) confirms the alignment mechanism and allows one to associate the experimental signals to different molecular geometries. Quantative corrections due to spin-spin and spin-orbit interactions have been in the focus of [8] and will be discussed in Sec. VI.…”