Jesús Pérez Ríos

We study the classical dynamics of a Paul-trapped ion in a low-density bath of atoms above 1 $μ\textrm{K}$. 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 $3\times 10^{8}$ trajectories of a $^{174}$Yb$^+$ 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.

We present a MATLAB script which can use GPU acceleration to simulate a trapped ion interacting with a low-density cloud of atoms. This script, called atomiongpu.m, can massively parallelize MD simulations of trajectories of a trapped ion and an atom starting far away. The script uses ode45gpu, which is our optimized and specialized implementation of the Runge-Kutta algorithm used in MATLAB's ODE solver ode45. We first discuss the physical system and show how ode45gpu can solve it up to 22x faster than MATLAB's ode45. Then, we show how to easily modify the inputs to atomiongpu.m to account for different kinds of atoms, ions, atom-ion interactions, trap potentials, simulation parameters, initial conditions, and computational hardware, so that atomiongpu.m automatically finds the probability of complex formation, the distribution of observables such as the scattering angle and complex lifetime, and plots of specific trajectories.

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 wavefunction. After mapping the time-dependent problem onto a time-independent framework, we investigate the role of the trap, the atomic species, atom-ion interaction, and collision energy in shaping the chaotic dynamics of the system. We find that the probability of atom-ion complex formation directly measures its chaoticity. Therefore, our results establish a clear relationship between the emergence of chaotic scattering and the presence of ion-atom complexes.

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.

Solvation, the result of the complicated interplay between solvent-solute and solvent-internal interactions, is one of the most important chemical processes. Consequently, a complete theoretical understanding of solvation seems a heroic task. However, it is possible to elucidate fundamental solvation mechanisms by looking into simpler systems, such as ion solvation in atomic baths. In this work, we study ion solvation by calculating the ground state properties of a single ion in a neutral bath from the high-density regime to the low-density regime, finding common ground for these two, in principle, disparate regimes. Our results indicate that a single $^{174}$Yb$^+$ ion in a bath of $^{7}$Li atoms forms a coordination complex at high densities with a coordination number of 8, with strong electrostriction, characteristic of the snowball effect. On the contrary, treating the atomic bath as a dilute quantum gas at low densities, we find that the ion-atom interaction's short-range plays a significant role in the physics of many-body bound states and polarons. Furthermore, in this regime, we explore the role of a putative ion trap, which drastically affects the binding mechanism of the ion and atoms from a quantum gas. Therefore, our results give a novel insight into the universality of ion-neutral systems in the ultracold regime and the possibilities of observing exotic many-body effects.

We have studied the general aspects of the dynamics of an ion trapped in an ideal multipolar radiofrequency trap while interacting with a dense cold atomic gas. In particular, we have explored the dynamical stability, the energy relaxation and the characteristic harmonic motion exhibited by a trapped Yb$^{+}$ ion in different multipolar potentials and immersed in various cold atomic samples (Li, Na, Rb, Yb). For this purpose, we used two different molecular dynamics simulations; one based on a time-event drive algorithm and the other based on the stochastic Langevin equation. Relevant values for experimental realizations, such as the associated ion's lifetimes and observable distributions, are presented along with some analytical expressions which relate the ion's dynamical properties with the trap parameters.

Based on the Langevin equation, a stochastic formulation is implemented to describe the dynamics of a trapped ion in a bath of ultracold atoms, including an excess of micromotion. The ion dynamics is described following a hybrid analytical-numerical approach in which the ion is treated as a classical impurity in a thermal bath. As a result, the ion energy's time evolution and distribution are derived from studying the sympathetic cooling process. Furthermore, the ion dynamics under different stochastic noise terms is also considered to gain information on the bath properties' role in the system's energy transfer processes. Finally, the results obtained from this formulation are contrasted with those obtained with a more traditional Monte Carlo approach.

We present a full quantal study on the dissociation of a weakly bound molecular ion in the presence of an external time-dependent electric field. We focus on the dissociation dynamics of a molecular ion in a Paul trap relevant for atom-ion hybrid traps. Our results show that a weakly bound molecular ion survives in a Paul trap giving a theoretical ground to previous experimental findings [A. Krükow et al. Phys. Rev. Lett. 116, 193201 (2016) and A. Mohammadi et al. Phys. Rev. Research 3, 013196 (2021)]. In particular, we find that weakly bound molecular ions are more likely to survive in traps with large RF frequency. Similarly, we show that applying an electric field ramp is an efficient method to state-selectively detect weakly bound molecular ions, analogous to the well-known selective field ionization technique applied in Rydberg atoms, that it may also be used to detect these species in atom-ion hybrid traps.

Impurity physics is a traditional topic in condensed matter physics that nowadays is being explored in the field of ultracold gases. Among the different classes of impurities, we focus on charged impurities in an ultracold bath. When a single ion is brought in contact with an ultracold gas it is subjected to different reactive processes that can be understood from a cold chemistry approach. In this work, we present an outlook of approaches for the dynamics of a single ion in a bath of ultracold atoms or molecules, complementing the usual many-body approaches characteristic of impurity physics within condensed matter physics. In particular, we focus on the evolution of a charged impurity in different baths, including external time-dependent trapping potentials and we explore the effect of the external laser sources present in ion-neutral hybrid traps into the lifetime of an impurity.

We theoretically study the dynamics of a trapped ion that is immersed in an ultracold gas of weakly bound atomic dimers created by a Feshbach resonance. Using quasi-classical simulations, we find a crossover from dimer dissociation to molecular ion formation depending on the binding energy of the dimers. The location of the crossover strongly depends on the collision energy and the time-dependent fields of the Paul trap. Deeply bound dimers lead to fast molecular ion formation, with rates approaching the Langevin collision rate $Γ'_\text{L}\approx4.8\times10^{-9}\,$cm$^3$s$^{-1}$. The kinetic energies of the created molecular ions have a median below $1\,$mK, such that they will stay confined in the ion trap. We conclude that interacting ions and Feshbach molecules may provide a novel approach towards the creation of ultracold molecular ions with applications in precision spectroscopy and quantum chemistry.

We study three-body recombination of Ba$^+$ + Rb + Rb in the mK regime where a single $^{138}$Ba$^{+}$ ion in a Paul trap is immersed into a cloud of ultracold $^{87}$Rb atoms. We measure the energy dependence of the three-body rate coefficient $k_3$ and compare the results to the theoretical prediction, $k_3 \propto E_{\textrm{col}}^{-3/4}$ where $E_{\textrm{col}}$ is the collision energy. We find agreement if we assume that the non-thermal ion energy distribution is determined by at least two different micro-motion induced energy scales. Furthermore, using classical trajectory calculations we predict how the median binding energy of the formed molecules scales with the collision energy. Our studies give new insights into the kinetics of an ion immersed into an ultracold atom cloud and yield important prospects for atom-ion experiments targeting the s-wave regime.