Spin-orbit-dependent lifetimes of long-range Rydberg molecules

TL;DR

The study addresses long-range Rydberg molecules formed when a Rydberg electron scatters off a ground-state perturber, focusing on decay via autoionisation and how spin–orbit coupling shapes lifetimes. It combines a relativistic scattering theory with hyperfine structure and a continuum decay channel to predict vibronic states, then validates by photoassociation in ultracold Cs and late-PFI lifetime measurements. The work reveals two families of vibrational wells (outer and inner) with lifetimes set by tunnelling and short-range decay, and shows that inner-well lifetimes are strongly reduced by spin–orbit interactions, correlating with binding energy; Cs2+ detection confirms associative ionisation as a key channel. These results illuminate spin-orbit–controlled autoionisation pathways in LRMs and point to pathways for creating ultracold ion-pair states in molecular systems.

Abstract

Long-range Rydberg molecules (LRMs) form when a highly excited Rydberg electron scatters from ground-state atoms inside its orbit, creating oscillatory, long-range potentials. We present a combined theoretical and experimental study of caesium dimers correlated to 402P3/2 Rydberg states, with an emphasis on decay via autoionisation (associative ionisation). Our model includes a relativistic treatment of electron-atom scattering with spin-orbit coupling, the perturber's hyperfine structure, and coupling of vibrational levels to a continuum of short-range decay channels. Calculated potential-energy curves predict two families of wells: outer wells near the classical outer turning point supporting long-lived states, and inner wells at shorter range whose lifetimes are limited by tunneling and subsequent vibronic decay. Using photoassociation in an ultracold Cs gas and an analysis of pulsed-field-ionisation signals which are highly selective for the detection of molecules, we assign resonances by binding energy and measure lifetimes. The measured lifetimes of inner-well states increase systematically with increasing detuning and agree with calculated lifetimes; detection of Cs2+ product ions supports autoionisation as a dominant channel. We show that the lifetimes are strongly reduced by spin-orbit interactions in the transient Cs-collision complex, which lift the near-degeneracy in Omega observed for states in the outer well and control the inner-well binding. The identified states also provide promising pathways to create ultracold molecules in ion-pair states.

Figures (6)

• Figure 1: Calculated potential-energy curves of LRMs correlated to the atomic asymptote $40\,^2P_{3/2}-6\,^2S_{1/2}(F=4)$. The projection of the total angular momentum on the internuclear axis, $\Omega$, is indicated by the line color, see the legend. Features marked by letters are discussed in the text.
• Figure 2: a) Potential energy curves of selected states from Fig. \ref{['fig:theo:pecs40P32F4overview']} are shown on an enlarged scale. The vibrational levels of these states are illustrated by their probability densities, which overlay the curves. The baseline of each overlay indicates the binding energy of the vibrational level, and its area is proportional to the level’s lifetime. Levels with binding energies within the gray-shaded area are omitted from the figure for clarity. b) Late-PFI signal (see Sect. \ref{['sec:experiment']} for details) for different detunings of the photoassociating UV laser from the transition $40\,^2P_{3/2}\leftarrow6\,^2S_{1/2}(F=4)$ and a photoassociation-pulse length of 10µs. Before excitation, all atoms are optically pumped into the $6~^2S_{1/2}(F=4)$ state. Calculated binding energies are shown as solid or dotted lines depending on whether their lifetimes are longer or shorter than 1.2µs. Because the lines are drawn semi-transparently, overlapping resonances accumulate opacity and appear darker, as apparent for the $\Omega$-degenerate resonances at -26.4MHz.
• Figure 3: Comparison of electron time-of-flight traces recorded after exciting the ensemble of ground-state atoms at the atomic resonance $40\,^2P_{3/2}\leftarrow6\,^2S_{1/2}(F=4)$ ($V(t)_{0MHz}$) and at a photoassociation resonance with a detuning of -26.4MHz ($V(t)_{-26.4MHz}$). The traces have been normalised to the same maximal amplitude and are drawn on a logarithmic scale. Shaded regions mark the time intervals in which the time-of-flight traces were integrated to obtain the late-PFI signal (red-shaded region) and the background-correction signal (gray-shaded region).
• Figure 4: Comparison of decay constants and binding energies determined experimentally (red dots with error bars) and theoretically (gray bands) for the four photoassociation resonances with binding energies larger than 30MHz (compare Fig. \ref{['fig:theo:pecs40P32F4vibs']} b)). The gray bands indicate the range of decay constants compatible with our calculations, see Sec. \ref{['sec:theory']} for details.
• Figure A1: Schematic illustration of the couplings of angular momenta in a long-range Rydberg molecule composed of a ground-state atom GS (red circle) and a Rydberg atom with Rydberg ion core A$^+$ (gray circle) and electron $e^-$ (blue circle). The molecular axis is along the vector $\vec{R}$ from $A^+$ to GS, the electron's coordinate $\vec{r}$ is defined relative to $A^+$. The electron's orbital angular momentum $\vec{l}$ and its spin $\vec{s}_\mathrm{Ryd}$ couple to the Rydberg electron's total angular momentum $\vec{j}$. The spin $\vec{s}_\mathrm{Ryd}$ couples to the electronic spin of GS, $\vec{s}$, to form the total electronic spin $\vec{S}$. The orbital angular momentum of $e^-$ with respect to GS, $\vec{L}$, and $\vec{S}$ couple to form the total angular momentum $\vec{J}$ of the $e^-$-GS scattering state. The nuclear spin of GS, $\vec{i}$, couples with $\vec{s}$ to form $\vec{F}$, the total angular momentum including nuclear spin of GS. Figure and caption adapted from Figure 5.1 of Ref. peperPrecisionSpectroscopyUltracold2020.