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

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.

💡 Research Summary

The paper presents a combined theoretical and experimental investigation of spin‑orbit‑dependent lifetimes of long‑range Rydberg molecules (LRMs) formed from cesium dimers correlated to the 40 P₃/₂ Rydberg asymptote. The authors develop a relativistic model of the electron–atom scattering that includes spin‑orbit coupling, the hyperfine structure of the ground‑state perturber, and coupling of vibrational levels to a continuum of short‑range decay channels. By diagonalising the full Hamiltonian H = H₀ + H_HF + V_FC for each projection Ω of the total electronic angular momentum on the internuclear axis, they obtain potential‑energy curves (PECs) that display two distinct families of wells.

The outer wells (region “A”, around R ≈ 2500 a₀) lie near the classical outer turning point of the Rydberg electron orbit. Here the Ω‑degeneracy is almost preserved, giving rise to a deep well (≈30 MHz binding) and a shallow well (≈15 MHz). These wells support long‑lived vibrational states whose lifetimes are limited only by radiative decay, not by tunnelling.

In contrast, the inner wells (region “B”, R ≈ 1700 a₀) appear at shorter internuclear distances where the spin‑orbit interaction in the electron‑Cs scattering lifts the Ω‑degeneracy completely. The vibrational levels bound in these wells are subject to tunnelling through the surrounding barrier and subsequent vibronic decay, primarily auto‑ionisation (associative ionisation). The authors calculate tunnelling widths Γ using a Milne phase‑amplitude method with open boundary conditions; the lifetime τ = 1/(2πΓ) ranges from about 1 µs for the shallowest bound state (Ω = 1/2) up to 17 µs for the deepest (Ω = 9/2). The exponential dependence of τ on barrier height and width explains the systematic increase of lifetime with binding energy.

A third region (C, R ≈ 2000 a₀) is dominated by a p‑wave shape resonance associated with the 3 P₀ scattering channel. This resonance produces a rapid drop in the PEC, creating “butterfly”‑type deep wells that strongly enhance tunnelling and thus shorten lifetimes for states located there.

Experimentally, the team prepares an ultracold cesium sample (≈2 × 10⁷ atoms, density 7 × 10¹⁰ cm⁻³, temperature 40 µK) in the 6 S₁/₂(F = 4) ground state. Photoassociation is driven with a narrow‑band UV laser tuned near the 40 P₃/₂ ← 6 S₁/₂ transition. After a controlled excitation pulse, a pulsed‑field‑ionisation (PFI) sequence selectively ionises molecules, and the resulting ion signal (including Cs₂⁺) is recorded. By scanning the laser detuning, the authors map out resonance lines corresponding to different vibrational levels. The late‑PFI signal, integrated over a time window after the main field pulse, provides a measure of the molecular population that survived the excitation interval, thus yielding lifetimes.

The measured lifetimes of inner‑well states increase with larger detuning (i.e., deeper binding), in excellent agreement with the calculated tunnelling lifetimes. Detection of Cs₂⁺ ions confirms that auto‑ionisation is the dominant decay channel for these states. Moreover, the data reveal that spin‑orbit coupling in the transient Cs‑collision complex strongly reduces lifetimes by lifting the near‑degeneracy of Ω in the outer well and by controlling the binding of inner‑well states.

The authors also point out that states with Ω < 9/2 retain contributions from the 1 P₁ scattering channel, making them promising precursors for creating ultracold ion‑pair (heavy‑Rydberg) molecules via stimulated de‑excitation.

In summary, this work demonstrates that spin‑orbit interactions play a crucial role in shaping the potential landscape and decay dynamics of long‑range Rydberg molecules. The combination of a fully relativistic scattering model with precise lifetime measurements provides a quantitative understanding of auto‑ionisation processes and offers a pathway to engineer molecular lifetimes and to access exotic ion‑pair states in ultracold gases.