Spin-Interaction Effects for Ultralong-range Rydberg Molecules in a Magnetic Field

TL;DR

This paper explores how magnetic fields influence the complex spin and electronic structures of ultralong-range Rydberg molecules, revealing tunable molecular states through detailed modeling of spin interactions and external field effects.

Contribution

It introduces a comprehensive model including spin-dependent scattering, hyperfine, and spin-orbit interactions to analyze Rydberg molecules in magnetic fields, highlighting the tunability of their states.

Findings

Magnetic fields significantly alter molecular energy surfaces and spin configurations.

The interplay of scattering and spin couplings creates diverse, tunable molecular states.

Comparison shows spin interactions are crucial for accurate modeling of these molecules.

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 Gau{\ss}. 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.