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Communications Physics

Effects of the delocalized charge distribution in trapped ion-atom collisions

R. S. Shi, Michael Drewsen, Jesús Pérez‐Ríos

Published Nov 26, 2025• 1 citation
Publisher

Abstract

The study of ion-atom interactions often requires the ion to be trapped, however the effects of the trapping potential have been elusive. The authors find that if the trapped ion is described as a delocalized charged distribution according to its motional ground state in the trap, the trap frequency modifies the scattering and transport properties of the ion in a neutral bath.

DOI
10.1038/s42005-025-02381-x

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The study of ion-atom interactions often requires the ion to be trapped, however the effects of the trapping potential have been elusive. The authors find that if the trapped ion is described as a delocalized charged distribution according to its motional ground state in the trap, the trap frequency modifies the scattering and transport properties of the ion in a neutral bath.
In the study of ion-atom interactions, the ion often remain trapped during the experiments. However, the effects of the trapping potential of the ion on ion-neutral interactions remain largely unexplored. Although trap-assisted ion-neutral complex formation has been experimentally studied and described by applying semiclassical theories where the ion is treated as a point charge particle, the potential effect of a delocalized charge distribution of a confined ion due to its quantum mechanical wavefunction has not been considered. To remedy this, in the present theoretical work we substitute the point charge of the ion with a delocalized charged distribution according to its motional ground state in the trap. Our results show that the trapping frequency and hence the spatial extension of the ion's ground-state wavefunction drastically affects the elastic and transport cross sections in interactions with neutral atoms. Stimulated by these results, we propose experimental procedures to verify the effects of the delocalize charge distribution in ion-atom interactions via measuring the heating rate of the ion due to the energy transfer in atomic collisions. Our novel approach brings new possibilities for investigating ion-neutral systems and, through them, new perspectives on ionic polarons and potentially a better understanding of trap-induced losses in ion-neutral experiments.
A trapped ion immersed in a neutral bath shows long-lived atom-ion complexes that significantly alter its chemical properties and thus the ion stability. In this work, we present a general study of trapped-ion--atom scattering with the ion modeled as a charge distribution defined by the spatial extent of its ground-state wave function. After mapping the time-dependent problem onto a time-independent framework, we investigate the conditions under which chaotic scattering arises and develops using classical trajectory simulations. In particular, we characterize the role of the trap, the atomic species, the atom-ion interaction, and the collision energy in shaping the chaotic dynamics of the system.
Abstract Experiments in which ultra-cold neutral atoms and charged ions are overlapped, constitute a new field in atomic and molecular physics, with applications ranging from studying out-of-equilibrium dynamics to simulating quantum many-body systems. The holy grail of ion-neutral systems is reaching the quantum low-energy scattering regime, known as the s-wave scattering. However, in most atom–ion systems, there is a fundamental limit that prohibits reaching this regime. This limit arises from the time-dependent trapping potential of the ion, the Paul trap, which sets a lower collision energy limit which is higher than the s-wave energy. In this work, we studied both theoretically and experimentally, the way the Paul trap parameters affect the energy distribution of an ion that is immersed in a bath of ultra-cold atoms. Heating rates and energy distributions of the ion are calculated for various trap parameters by a molecular dynamics (MD) simulation that takes into account the attractive atom–ion potential. The deviation of the energy distribution from a thermal one is discussed. Using the MD simulation, the heating dynamics for different atom–ion combinations is also investigated. In addition, we performed measurements of the heating rates of a ground-state cooled 88Sr+ ion that is immersed in an ultra-cold cloud of 87Rb atoms, over a wide range of trap parameters, and compare our results to the MD simulation. Both the simulation and the experiment reveal no significant change in the heating for different parameters of the trap. However, in the experiment a slightly higher global heating is observed, relative to the simulation.
We consider a system composed of a trapped atom and a trapped ion. The ion charge induces in the atom an electric dipole moment, which attracts it with an ${r}^{\ensuremath{-}4}$ dependence at large distances. In the regime considered here, the characteristic range of the atom-ion interaction is comparable or larger than the characteristic size of the trapping potential, which excludes the application of the contact pseudopotential. The short-range part of the interaction is described in the framework of quantum-defect theory, by introducing some short-range parameters, which can be related to the sss-wave scattering length. When the separation between traps is changed we observe trap-induced shape resonances between molecular bound states and vibrational states of the external trapping potential. Our analysis is extended to quasi-one-dimensional geometries, when the scattering exhibit confinement-induced resonances, similar to the ones studied before for short-range interactions. For quasi-one-dimensional systems we investigate the effects of coupling between the center of mass and relative motion, which occurs for different trapping frequencies of atom and ion traps. Finally, we show how the two types of resonances can be employed for quantum state control and spectroscopy of atom-ion molecules.
A kinetic theory based on the Boltzmann equation is developed for the trapping of atomic ions in a radio-frequency quadrupole ion trap containing enough neutral atoms that ion-neutral collisions cannot be ignored. The collisions are treated at the same level of sophistication and detail as is used to deal with the time- and space-dependent electric fields in the trap. As a result, microscopic definitions are obtained for the damping and stochastic forces that originate from such collisions. These definitions contrast with corresponding phenomenological terms added ad hoc in previous treatments to create damped Mathieu and Langevin equations, respectively. Furthermore, the theory indicates that either collisional cooling or heating of the ions is possible, depending upon details of the ion-neutral mass ratios and interaction potential. The kinetic theory is not dependent on any special assumptions about the electric field strengths, the ion-neutral interaction potentials, or the ion-neutral mass ratio. It also provides an ab initio way to describe the ion kinetic energies, temperatures, and other properties by a series of successive approximations.
We study the quantum dynamics of an ion confined in a radio-frequency trap in interaction with either a Bose or spin-polarized Fermi gas. To this end, we derive quantum optical master equations in the limit of weak coupling and the Lamb-Dicke approximations. For the bosonic bath, we also include the so-called ``Lamb-shift'' correction to the ion trap due to the coupling to the quantum gas as well as the extended Fr\"ohlich interaction within the Bogolyubov approximation that have been not considered in previous studies. We calculate the ion kinetic energy for various atom-ion scattering lengths as well as gas temperatures by considering the intrinsic micromotion and we analyze the damping of the ion motion in the gas as a function of the gas temperature. We find that the ion's dynamics depends on the quantum statistics of the gas and that a fermionic bath enables to attain lower ionic energies.