[Paper Review] Long-Range Atom–Ion Rydberg Molecule: A Novel Molecular Binding Mechanism

Markus Deiß, Shinsuke Haze+1 more|arXiv (Cornell University)|Jun 21, 2021

Cold Atom Physics and Bose-Einstein CondensatesPhysics and Astronomy57 references35 citations

TL;DR

This paper proposes a novel long-range molecular binding mechanism where a neutral Rydberg atom forms a bound state with a nearby ion at micrometer-scale distances, driven by Stark shifts and avoided crossings induced by the ion's electric field. The key result is the prediction of stable, long-lived molecules with kilo-Debye dipole moments, vibrational frequencies in the MHz–GHz range, and tunable coupling via radio/microwave fields, enabling engineered wave packet dynamics in tailored potential landscapes.

ABSTRACT

We present a novel binding mechanism where a neutral Rydberg atom and an atomic ion form a molecular bound state at a large internuclear distance. The binding mechanism is based on Stark shifts and level crossings that are induced in the Rydberg atom due to the electric field of the ion. At particular internuclear distances between the Rydberg atom and the ion, potential wells occur that can hold atom–ion molecular bound states. Apart from the binding mechanism, we describe important properties of the long-range atom–ion Rydberg molecule, such as its lifetime and decay paths, its vibrational and rotational structure, and its large dipole moment. Furthermore, we discuss methods of how to produce and detect it. The unusual properties of the long-range atom–ion Rydberg molecule give rise to interesting prospects for studies of wave packet dynamics in engineered potential energy landscapes.

Motivation & Objective

• To identify a new molecular binding mechanism between a Rydberg atom and an ion at large internuclear distances.
• To characterize the formation of potential wells due to avoided crossings in Stark-shifted Rydberg levels.
• To analyze the vibrational, rotational, and dipole properties of the resulting long-range molecules.
• To propose experimental production and detection methods in hybrid atom-ion systems.
• To explore prospects for wave packet dynamics and potential landscape engineering in these molecules.

Proposed method

• Using the Alkali.Rydberg Calculator (ARC) to compute unperturbed Rydberg states and their energies for rubidium atoms.
• Applying a multipole expansion of the ion-Rydberg interaction potential, including electrostatic terms up to l=1, to model the Stark shifts.
• Calculating avoided crossings between high-field-seeking (e.g., 17P3/2) and low-field-seeking (e.g., n=14 P states) levels as a function of internuclear distance r.
• Identifying potential wells at avoided crossing points where molecular bound states can form, with vibrational levels determined quantum-mechanically.
• Evaluating the dipole moment, rotational constants, and vibrational frequencies to assess alignment and spectroscopic accessibility.
• Proposing experimental schemes using laser-cooled atoms and trapped ions, with detection via ion energy spectroscopy or time-of-flight methods.

Experimental results

Research questions

• RQ1 Can a stable bound state form between a Rydberg atom and an ion at micrometer-scale distances due to Stark shifts?
• RQ2 What are the conditions under which avoided crossings generate potential wells capable of binding the system?
• RQ3 How do the vibrational and rotational structures of these molecules depend on the principal quantum number n?
• RQ4 What is the magnitude of the dipole moment, and can it be aligned with weak external fields?
• RQ5 How can these molecules be produced and detected in current hybrid atom-ion experimental setups?

Key findings

• The long-range atom-ion Rydberg molecule forms at internuclear distances up to ~1 µm, with binding lengths around 80 nm for n=17 states.
• The binding mechanism arises from avoided crossings between high- and low-field-seeking Rydberg states due to the ion's electric field, creating potential wells that support bound states.
• The calculated dipole moment reaches approximately 1900 Debye for a binding length of 80 nm, enabling strong alignment with V/m-scale electric fields.
• Vibrational oscillation frequencies are in the 10 MHz to 1 GHz range, with timescales of 1–100 ns, suitable for studying wave packet dynamics.
• Microwave and radio-frequency fields can coherently couple vibrational and rotational states within and between potential wells, enabling potential landscape engineering.
• The predicted lifetime and stability are sufficient for experimental detection, especially in current hybrid atom-ion setups with sub-mK collision energies.