Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2307.01811 · Physical Review A

Cold atom-ion systems in radio-frequency multipole traps: Event-driven molecular dynamics and stochastic simulations

Mateo Londoño, Javier Madroñero, Jesús Pérez‐Ríos

Published Nov 27, 2023• 3 citations
arXivHTMLPDF

Abstract

We study the general aspects of the dynamics of an ion trapped in an ideal multipolar radio-frequency trap while interacting with a dense cold atomic gas. In particular, we explore the dynamical stability, the energy relaxation, and the characteristic harmonic motion exhibited by a trapped ${\mathrm{Yb}}^{+}$ ion in different multipolar potentials and immersed in various cold atomic samples (Li, Na, Rb, Yb). For this purpose, we use 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 that relate the ion's dynamical properties with the trap parameters.

DOI
10.1103/physreva.108.053324

Related papers

Buffer-Gas Cooling of a Single Ion in a Multipole Radio Frequency Trap Beyond the Critical Mass Ratio

Bastian Höltkemeier, Pascal Weckesser, Henry López-Carrera +1 more

We theoretically investigate the dynamics of a trapped ion immersed in a spatially localized buffer gas. For a homogeneous buffer gas, the ion's energy distribution reaches a stable equilibrium only if the mass of the buffer gas atoms is below a critical value. This limitation can be overcome by using multipole traps in combination with a spatially confined buffer gas. Using a generalized model for elastic collisions of the ion with the buffer-gas atoms, the ion's energy distribution is numerically determined for arbitrary buffer-gas distributions and trap parameters. Three regimes characterized by the respective analytic form of the ion's equilibrium energy distribution are found. Final ion temperatures down to the millikelvin regime can be achieved by adiabatically decreasing the spatial extension of the buffer gas and the effective ion trap depth (forced sympathetic cooling).

arXiv:1505.06909•Physical Review Letters•Jun 9, 2016•55 citations

Dynamics of a single trapped ion immersed in a buffer gas

Bastian Höltkemeier, Pascal Weckesser, Henry López-Carrera +1 more

We provide a comprehensive theoretical framework for describing the dynamics of a single trapped ion interacting with a neutral buffer gas, thus extending our previous studies on buffer-gas cooling of ions beyond the critical mass ratio [B. H\"oltkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ion's micromotion is assigned to the buffer-gas atoms, our model allows us to investigate the influence of nonhomogeneous buffer-gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depending on the neutral-to-ion mass ratio, three regimes of sympathetic cooling are identified which are characterized by the form of the ion's energy distribution in equilibrium. We provide analytic expressions and numerical simulations of the ion's energy distribution, spatial profile, and cooling rates for these different regimes. Based on these findings, a method for actively decreasing the ion's energy by reducing the spatial expansion of the buffer gas arises (forced sympathetic cooling).

arXiv:1608.07120•Physical Review A•Dec 7, 2016•18 citations

Analysis of Multipolar Linear Paul Traps for Ion–Atom Ultracold Collision Experiments

M. Niranjan, Anand Prakash, S. A. Rangwala

We evaluate the performance of multipole, linear Paul traps for the purpose of studying cold ion–atom collisions. A combination of numerical simulations and analysis based on the virial theorem is used to draw conclusions on the differences that result, by considering the trapping details of several multipole trap types. Starting with an analysis of how a low energy collision takes place between a fully compensated, ultracold trapped ion and an stationary atom, we show that a higher order multipole trap is, in principle, advantageous in terms of collisional heating. The virial analysis of multipole traps then follows, along with the computation of trapped ion trajectories in the quadrupole, hexapole, octopole and do-decapole radio frequency traps. A detailed analysis of the motion of trapped ions as a function of the amplitude, phase and stability of the ion’s motion is used to evaluate the experimental prospects for such traps. The present analysis has the virtue of providing definitive answers for the merits of the various configurations, using first principles.

Atoms•Jun 29, 2021•11 citations

Effect of ion-trap parameters on energy distributions of ultra-cold atom–ion mixtures

Meirav Pinkas, Ziv Meir, Tomáš Šikorský +3 more

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.

arXiv:1907.12815•New Journal of Physics•Jan 1, 2020•20 citations

Efficient computational scheme for ion dynamics in RF-field of Paul trap

Vladimir S. Melezhik

We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom ∼ 10 × 2/ defined by the atomic trap frequency ∼ 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.

Вестник Российского университета дружбы народов. Серия: Математика, информатика, физика•Dec 15, 2019•4 citations

Description of ion motion in a Paul trap immersed in a cold atomic gas

Michał Krych, Zbigniew Idziaszek

We investigate the problem of a single ion in a radio-frequency trap immersed in an ultracold Bose gas in either a condensed or a noncondensed phase. We develop a master-equation formalism describing the sympathetic cooling, and we determine the cooling rates of ions. We show that the cold atomic reservoir modifies the stability diagram of the ion in the Paul trap, creating regions where the ion is either cooled or heated due to the energy quanta exchanged with the time-dependent potential.

arXiv:1312.0279•Physical Review A•Feb 25, 2015•49 citations
We study the general aspects of the dynamics of an ion trapped in an ideal multipolar radio-frequency trap while interacting with a dense cold atomic gas. In particular, we explore the dynamical stability, the energy relaxation, and the characteristic harmonic motion exhibited by a trapped Yb+{\mathrm{Yb}}^{+}Yb+ ion in different multipolar potentials and immersed in various cold atomic samples (Li, Na, Rb, Yb). For this purpose, we use 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 that relate the ion's dynamical properties with the trap parameters.
We theoretically investigate the dynamics of a trapped ion immersed in a spatially localized buffer gas. For a homogeneous buffer gas, the ion's energy distribution reaches a stable equilibrium only if the mass of the buffer gas atoms is below a critical value. This limitation can be overcome by using multipole traps in combination with a spatially confined buffer gas. Using a generalized model for elastic collisions of the ion with the buffer-gas atoms, the ion's energy distribution is numerically determined for arbitrary buffer-gas distributions and trap parameters. Three regimes characterized by the respective analytic form of the ion's equilibrium energy distribution are found. Final ion temperatures down to the millikelvin regime can be achieved by adiabatically decreasing the spatial extension of the buffer gas and the effective ion trap depth (forced sympathetic cooling).
We provide a comprehensive theoretical framework for describing the dynamics of a single trapped ion interacting with a neutral buffer gas, thus extending our previous studies on buffer-gas cooling of ions beyond the critical mass ratio [B. H\"oltkemeier et al., Phys. Rev. Lett. 116, 233003 (2016)]. By transforming the collisional processes into a frame, where the ion's micromotion is assigned to the buffer-gas atoms, our model allows us to investigate the influence of nonhomogeneous buffer-gas configurations as well as higher multipole orders of the radio-frequency trap in great detail. Depending on the neutral-to-ion mass ratio, three regimes of sympathetic cooling are identified which are characterized by the form of the ion's energy distribution in equilibrium. We provide analytic expressions and numerical simulations of the ion's energy distribution, spatial profile, and cooling rates for these different regimes. Based on these findings, a method for actively decreasing the ion's energy by reducing the spatial expansion of the buffer gas arises (forced sympathetic cooling).
We evaluate the performance of multipole, linear Paul traps for the purpose of studying cold ion–atom collisions. A combination of numerical simulations and analysis based on the virial theorem is used to draw conclusions on the differences that result, by considering the trapping details of several multipole trap types. Starting with an analysis of how a low energy collision takes place between a fully compensated, ultracold trapped ion and an stationary atom, we show that a higher order multipole trap is, in principle, advantageous in terms of collisional heating. The virial analysis of multipole traps then follows, along with the computation of trapped ion trajectories in the quadrupole, hexapole, octopole and do-decapole radio frequency traps. A detailed analysis of the motion of trapped ions as a function of the amplitude, phase and stability of the ion’s motion is used to evaluate the experimental prospects for such traps. The present analysis has the virtue of providing definitive answers for the merits of the various configurations, using first principles.
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 have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom ∼ 10 × 2/ defined by the atomic trap frequency ∼ 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.