The Stark effect in molecular Rydberg states: Calculation of Rydberg-Stark manifolds of H${}_2$ and D${}_2$ including fine and hyperfine structures

Abstract

We present a general theoretical treatment and calculations of the fine and hyperfine structures in the spectra of high-$n$ molecular Rydberg states in static uniform electric fields. The treatment combines (i) multichannel quantum-defect theory and long-range polarization models to determine the field-free energies of $n\ell$ Rydberg states of the molecules ($\ell$ is the orbital-angular-momentum quantum number of the Rydberg electron), (ii) a matrix-diagonalization approach to calculate the Stark shifts including their hyperfine structure, and (iii) sequences of angular-momentum frame transformations to predict the line positions and intensities in Stark spectra as they would be observed in single or multiphoton excitation sequences. To clarify how the molecular rotation and the nuclear spins influence the fine and hyperfine structure of molecular Rydberg-Stark spectra, we compare calculated spectra of ortho-D${}_2$ with a D${}_2^{+}$ ion core in the rotational ground state ($N^{+}=0$) for total nuclear spins $I$ of 0 (i.e., without hyperfine structure) and 2 (i.e., with hyperfine structure) with the corresponding spectra of para-H${}_2$ with an H${}_2^{+}$ ion core in the first excited rotational state ($N^{+}=2$) but zero nuclear spin ($I=0$). The calculations show that the hyperfine interaction alone does not significantly modify the Stark effect, but splits each Stark state by almost exactly the hyperfine Fermi-contact splitting of the ion core. In contrast, the effect of the molecular rotation, which is coupled both to the ion-core electron spin by the magnetic spin-rotation interaction and to the Rydberg-electron orbital motion by the core-polarization and charge-quadrupole interactions, induces Stark-state specific splittings that significantly differ from the spin-rotation splitting of the ($N^{+}=2$) ion core.

30 pages, 16 figures

References in corpus (13)

• Dipole blockade in a cold Rydberg atomic sample
• Electric-field induced dipole blockade with Rydberg atoms
• The static and dynamic polarisability, and the Stark and black-body radiation frequency shifts of the molecular hydrogen ions H2+, HD+, and D2+
• Measurement and numerical calculation of Rubidium Rydberg Stark spectra
• High-angular-momentum Rydberg states in a room-temperature vapor cell for DC electric-field sensing
• Slow decay processes of electrostatically trapped Rydberg NO molecules
• Accurate Born-Oppenheimer potentials for excited ${\Sigma }^{+}$ states of the hydrogen molecule
• Excitation and characterization of long-lived hydrogenic Rydberg states of nitric oxide
• Born-Oppenheimer potentials for $\Pi$, $\Delta$, and $\Phi$ states of the hydrogen molecule
• Interacting Circular Rydberg Atoms Trapped in Optical Tweezers
• Precision millimetre-wave spectroscopy and calculation of the Stark manifolds in high Rydberg states of para-H${}_2$
• Metrology of Rydberg states of the hydrogen atom
• Hyperfine structure and electric quadrupole transitions in the deuterium molecular ion