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arXiv:2209.05163 · Physical Review Letters

Trap-Assisted Complexes in Cold Atom-Ion Collisions

Henrik Hirzler, Eleanor Trimby, R. Gerritsma, Arghavan Safavi-Naini, Jesús Pérez‐Ríos

Published Apr 5, 2023• 18 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.130.143003

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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.
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Advances in research in fields such as quantum information and quantum chemistry require subtle methods for trapping particles, including ions, neutral atoms, and molecules. Here, we propose a hybrid ion-trapping method that combines a Paul trap with optical tweezers. This trap incorporates both the deep-potential characteristic of the Paul trap and the micromotion-free nature of the optical dipole trap. By modulating the optical dipole trap synchronously with the radio-frequency voltage of the Paul trap, the alternating electrical force in the trap center is fully counteracted, and the micromotion temperature of a cold trapped ion can reach the nanokelvin scale, while the trap depth exceeds 300 K. These features will allow cold collisions between an ion and an atom in the sss-wave regime and stably trap the produced molecular ion in the cold hybrid system. This provides a unique platform for probing the interactions between the ions and the surrounding neutral particles and enables the investigation of new reaction pathways and reaction products in the cold regime.
During the last few decades, the two fields of ultracold neutral atoms and of single trapped ions have undergone an amazing development. The incorporation of these systems into a single experiment exploits the complementary physical properties of the subsystems and opens up novel lines of research. I present experimental results obtained in one of the first hybrid atom-ion setups accessing the cold regime. Single ions interact with ultracold samples of 87Rb atoms. The collision energies are set by heating mechanisms in the Paul trap and are on the order of mK·kB. Interactions are generally strong and long-ranged. We observe elastic atom-ion scattering in the semi-classical energy regime in which the cross section depends on the collision energy and favors scattering at small angles. We were able to obtain a general good understanding of atom-ion two-body collisions. We observed sympathetic cooling of the ion over four orders of magnitude in energy through collisions with the ultracold atoms. Further, we utilized atom-ion scattering events to develop a novel method to compensate excess ion micromotion, the primary source of ion heating. Three-body collisions between two atoms and the ion play an important role. We identified these processes through the large amounts of energy that they release. This makes them detectable despite their suppression with respect to two-body collisions. We also showed that atom-ion three-body collisions become more prominent as the collision energy decreases. Finally, we employed our atom-ion apparatus to gain novel insights into three-body recombination between ultracold atoms. In these experiments the ion trap acts as an extremely sensitive ion detector. Through three-body recombination a Rb2 molecule is formed and can undergo ionization by absorbing photons from a strong laser. By scanning the frequency of the ionization laser we obtained a molecular spectrum and identified a relatively broad distribution over final molecular states.
Over the recent years a new research field emerged that combines technologies for cooling and trapping of neutral atoms and charged ions in one experimental apparatus. These atom-ion hybrid traps enable the investigation of atom-ion interactions at unprecedentedly low collision energies targeting the ultracold s-wave regime. In this thesis I report on experiments performed in an hybrid atom-ion apparatus combining single Ba^+ or Rb^+ ions with ultracold neutral Rb atoms. The main focus of this work is studying the emerging three-body reaction dynamics in a cold charged gas. First, I will present measurements investigating cold reactions in the hetero-nuclear Ba^+ - Rb system. So far, most theoretical and experimental studies have been dealing with reactions between two particles. However, we find that three-body reactions already dominate over two-body ones at atomic densities down to 10^{−11} cm^{−3} once collision energies are in the low mK regime. We then investigate the energy scaling of inelastic ternary collisions between an ion and two atoms. A power-law scaling of the three-body rate coefficient is predicted by theory. We find agreement with the experiment if we include the ion’s kinetic energy distribution that we access numerically. The next study elaborates on the very first observation of ternary reactions in a hybrid cold atom-ion setup. For this we immerse a single Rb^+ ion into ultracold Rb atoms with sufficiently reduced excess micromotion. Occurring reactions are signaled by the creation of highly energetic Rb^+ ions. I will also showcase novel techniques to investigate the atom and the ion system by using the respective other one which were developed by us over the course of the last years. In order to reduce the total ion kinetic energy in a Paul trap one has to compensate the ion’s excess micromotion. This is routinely being done by analyzing the ion’s fluorescence. By observing collision energy dependent elastic atom-ion collisions in an ultracold atom cloud we directly infer the ion’s micromotion energy. This way we can perform atom-ion experiments with optically dark Rb^+ ions and good excess micromotion. Without the need of visible laser light for micromotion compensation we are able to investigate the evolution of quasi-static stray electric fields in a Paul trap over a period of several months. The last study I will present is targeted at neutral Rb only. There, we spectroscopically access the molecular state distribution of Rb_2 molecules formed in neutral three-body recombination by state-selective ionization of these molecules. Trapping and subsequent detection of these ions is being done with our Paul trap, which has the role of a very sensitive single ion detector in these measurements.
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.
In the development of atomic, molecular, and optical (AMO) physics, atom-ion hybrid systems are characterized by the presence of a new tool in the experimental AMO toolbox: atom-ion interactions. One of the main limitations in state-of-the-art atom-ion experiments is represented by the micromotion component of the ions’ dynamics in a Paul trap, as the presence of micromotion in atom-ion collisions results in a heating mechanism that prevents atom-ion mixtures from undergoing a coherent evolution. Here, we report the design and the simulation of a novel ion trapping setup especially conceived of for integration with an ultracold atoms experiment. The ion confinement is realized by using an electro-optical trap based on the combination of an optical and an electrostatic field, so that no micromotion component will be present in the ions’ dynamics. The confining optical field is generated by a deep optical lattice created at the crossing of a bow-tie cavity, while a static electric quadrupole ensures the ions’ confinement in the plane orthogonal to the optical lattice. The setup is also equipped with a Paul trap for cooling the ions produced by photoionization of a hot atomic beam, and the design of the two ion traps facilitates the swapping of the ions from the Paul trap to the electro-optical trap.