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Physical Review A

Parallels between chaotic scattering and heating in cold ion-atom collisions

Saajid Chowdhury, Jesús Pérez‐Ríos

Published Dec 5, 2025• 3 citations
Publisher

Abstract

The authors study the nonhyperbolic chaotic dynamics of a Paul-trapped ion in a low-density bath of atoms above 1 $\ensuremath{\mu}$K. They find a power-law distribution for the complex lifetimes, an increase in complex formation for heavier, colder atoms, and a threshold collision energy for complex formation at approximately the trapped ion heating energy scale, establishing a connection between ion heating and chaos.

DOI
10.1103/zh5z-hhck

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The authors study the nonhyperbolic chaotic dynamics of a Paul-trapped ion in a low-density bath of atoms above 1 \ensuremathμ\ensuremath{\mu}\ensuremathμK. They find a power-law distribution for the complex lifetimes, an increase in complex formation for heavier, colder atoms, and a threshold collision energy for complex formation at approximately the trapped ion heating energy scale, establishing a connection between ion heating and chaos.
We study the classical dynamics of a Paul-trapped ion in a low-density bath of atoms above 1 μKμ\textrm{K}μK. We find that lower energy collisions with more massive atoms, especially at energies less than the initial micromotion heating, are more likely to form atom-ion complexes. These complexes evolve in a fractal structure for every scattering observable, showing non-hyperbolic chaotic dynamics. To explore the chaotic dynamics, we use a GPU-accelerated methodology allowing us to run over 3×1083\times 10^{8}3×108 trajectories of a 174^{174}174Yb+^++ and different atoms. As a result, after analyzing the dynamics as a function of the atom species, collision energy, trap parameters, and ion-atom potential depth, we find a link between heating and the onset of chaos in the first atom-ion interaction that occurs when a low-density atomic bath is merged with a trapped ion.
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.
Abstract we report on signatures of classical chaos in ultracold collisions between a trapped ion and a free atom. Using numerical simulations, we show that the scattering dynamics can be highly sensitive to initial conditions for various mass ratios and trapping frequencies, indicating the onset of chaos. We quantify this chaotic dynamics by calculating its fractal dimension. We show that for a trapped 88 Sr + ion and a free 87 Rb atom chaotic dynamic appears under experimentally relevant conditions, and find its characteristic energy scale. The observation of classical chaos in atom-trapped-ion collisions suggests that signatures of quantum chaos might appear, for example, through a Wigner–Dyson distribution of collisional resonances.
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.
We theoretically investigate the trap-assisted formation of complexes in atom-ion collisions and their impact on the stability of the trapped ion. The time-dependent potential of the Paul trap facilitates the formation of temporary complexes by reducing the energy of the atom, which gets temporarily stuck in the atom-ion potential. As a result, those complexes significantly impact termolecular reactions leading to molecular ion formation via three-body recombination. We find that complex formation is more pronounced in systems with heavy atoms, but the mass has no influence on the lifetime of the transient state. Instead, the complex formation rate strongly depends on the amplitude of the ion's micromotion. We also show that complex formation persists even in the case of a time-independent harmonic trap. In this case, we find higher formation rates and longer lifetimes than in Paul traps, indicating that the atom-ion complex plays an essential role in atom-ion mixtures in optical traps.
Ultracold atom-ion mixtures are gaining increasing interest due to their potential applications in ultracold and state-controlled chemistry, quantum computing, and many-body physics. Here, we studied the dynamics of a single ground-state cooled ion during few, to many, Langevin (spiraling) collisions with ultracold atoms. We measured the ion's energy distribution and observed a clear deviation from the Maxwell-Boltzmann distribution, characterized by an exponential tail, to a power-law distribution best described by a Tsallis function. Unlike previous experiments, the energy scale of atom-ion interactions is not determined by either the atomic cloud temperature or the ion's trap residual excess-micromotion energy. Instead, it is determined by the force the atom exerts on the ion during a collision which is then amplified by the trap dynamics. This effect is intrinsic to ion Paul traps and sets the lower bound of atom-ion steady-state interaction energy in these systems. Despite the fact that our system is eventually driven out of the ultracold regime, we are capable of studying quantum effects by limiting the interaction to the first collision when the ion is initialized in the ground state of the trap.