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

Communications in Theoretical Physics

Ordered Structures of a Few Ions in the Paul Trap

Shi Lei, Zhu XiWen, Feng Mang, Fang XiMing

Published Jun 15, 1999• 4 citations
Publisher

Abstract

We have carried out a molecular dynamics stimulation for a few Paul-trapped ions exerted by a trapping force, inter-ion Coulomb forces and a damping force from a cooling source. The geometric structure in the ordered phase is studied in detail. It is found that the structure varies regularly with the ion number and forms concentric shells when the ion number grows. Furthermore, the similarity between the ions' structure and the potential of the trap is also presented. Finally, the case in the second stability region is investigated, which gives a comparison with that in the first stability region.

DOI
10.1088/0253-6102/31/4/491

Related papers

Dynamics of charged particles in a Paul radio-frequency quadrupole trap

John D. Prestage, Ann Katherine Williams, Lute Maleki +2 more

We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for ${\mathit{q}}_{\mathit{z}}$\ensuremath{\lesssim}0.6, whereas rapid heating is seen for ${\mathit{q}}_{\mathit{z}}$=0.8.

Physical Review Letters•Jun 10, 1991•65 citations

Simulation of motion of many ions in a linear Paul trap

Martin Oral, Ondřej Čı́p, L. Slodička

The quadrupole linear Paul trap is one of the key instruments in building highly stable atomic clocks. However, a frequency reference based on a single trapped ion is limited in stability due to the time needed for the interrogation cycle which cannot be further shortened. A promising strategy is the utilization of multiple trapped ions. The ions of the same kind then repulse each other with the Coulomb force, which is countered by the ponderomotive force of the time depended field in the trap. A few ions form a chain along the axis of a linear Paul trap. Adding more ions (a few tens or hundreds) gives rise to Coulomb crystals. We created an efficient simulation code which calculates the motion of such collections of ions in quasi-static radiofrequency fields of real linear quadrupole traps (including the micromotion). We include a model for laser cooling of the ions. The simulation tool can be used to study the formation and the dynamics of Coulomb crystals under conditions corresponding to various experimental setups.

arXiv:2112.02203•International Journal of Modern Physics A•Dec 30, 2019•2 citations

Characteristics of Trapped Ions in the Second Stability Region of a Paul Trap

Xiwen Zhu, Dongxiang Qi

Characteristics of single ion motion and mechanisms of trapping ions in the second stability region of a Paul trap are discussed. The mean kinetic energy and mean width of the spatial distribution of an ion cloud in that region are calculated. Similarities and differences of the results between the first and second stability regions are emphasized.

Journal of Modern Optics•Feb 1, 1992•12 citations

Sympathetic Crystallization of Trapped Ions

Paul David Bowe, Liv Hornekær, Christina Brodersen +3 more

We have created multispecies Coulomb crystals in a linear Paul trap containing up to a few hundred ions of which more than $50%$ were cooled only sympathetically through the Coulomb interaction with laser-cooled ${\mathrm{Mg}}^{+}$ ions. In an extreme case, one laser-cooled ion maintained order in a 15 ion string. Ion species segregation was obtained by radiation pressure. Previous experiments and molecular dynamics simulations suggest the temperature is 10 mK or lower. These results indicate that a wide range of atomic and molecular ions can be cooled and localized in linear Paul traps which is important for improvements in spectroscopic studies of such ions.

Physical Review Letters•Mar 8, 1999•83 citations

Crystalline ion structures in a Paul trap

M. Block, A. Drakoudis, H Leuthner +6 more

We have observed crystalline structures formed by laser cooled Ca + ions in a three-dimensional confining potential. The potential has been realized using a linear Paul trap with different ratios of potential strength in the axial and radial directions. For radial confining potentials stronger than the axial potential, we find linear structures with a continuous transition from strings to helices with decreasing potential asymmetry. When a quasi-two-dimensional potential is formed we observe ring structures with a given maximum ion number per ring which we followed up to 19. The observations are essentially in agreement with molecular dynamics calculations in static two-dimensional potentials.

Journal of Physics B Atomic Molecular and Optical Physics•May 16, 2000•52 citations

Ion Coulomb Crystals With Long Range Order in RF-traps

A. Mortensen, Esben Nielsen, Thierry Matthey +2 more

In this contribution, we present results on the structural properties of single‐component as well as two‐component ion Coulomb crystals confined in a linear Paul trap. Metastable long range ordered structures as the face‐centered cubic (fcc) and body‐centered cubic (bcc) lattices are observed in single‐component ion crystals of sizes down to ∼ 1000 ions. In the case of two‐component ion crystals we observe a stable long range ordered structure in one of the trapped components, which is compared with a Molecular Dynamics (MD) simulation of a two‐component crystal.

AIP conference proceedings•Jan 1, 2006•0 citations
We have carried out a molecular dynamics stimulation for a few Paul-trapped ions exerted by a trapping force, inter-ion Coulomb forces and a damping force from a cooling source. The geometric structure in the ordered phase is studied in detail. It is found that the structure varies regularly with the ion number and forms concentric shells when the ion number grows. Furthermore, the similarity between the ions' structure and the potential of the trap is also presented. Finally, the case in the second stability region is investigated, which gives a comparison with that in the first stability region.
We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.
The quadrupole linear Paul trap is one of the key instruments in building highly stable atomic clocks. However, a frequency reference based on a single trapped ion is limited in stability due to the time needed for the interrogation cycle which cannot be further shortened. A promising strategy is the utilization of multiple trapped ions. The ions of the same kind then repulse each other with the Coulomb force, which is countered by the ponderomotive force of the time depended field in the trap. A few ions form a chain along the axis of a linear Paul trap. Adding more ions (a few tens or hundreds) gives rise to Coulomb crystals. We created an efficient simulation code which calculates the motion of such collections of ions in quasi-static radiofrequency fields of real linear quadrupole traps (including the micromotion). We include a model for laser cooling of the ions. The simulation tool can be used to study the formation and the dynamics of Coulomb crystals under conditions corresponding to various experimental setups.
We have created multispecies Coulomb crystals in a linear Paul trap containing up to a few hundred ions of which more than 5050%50 were cooled only sympathetically through the Coulomb interaction with laser-cooled Mg+{\mathrm{Mg}}^{+}Mg+ ions. In an extreme case, one laser-cooled ion maintained order in a 15 ion string. Ion species segregation was obtained by radiation pressure. Previous experiments and molecular dynamics simulations suggest the temperature is 10 mK or lower. These results indicate that a wide range of atomic and molecular ions can be cooled and localized in linear Paul traps which is important for improvements in spectroscopic studies of such ions.
We have observed crystalline structures formed by laser cooled Ca + ions in a three-dimensional confining potential. The potential has been realized using a linear Paul trap with different ratios of potential strength in the axial and radial directions. For radial confining potentials stronger than the axial potential, we find linear structures with a continuous transition from strings to helices with decreasing potential asymmetry. When a quasi-two-dimensional potential is formed we observe ring structures with a given maximum ion number per ring which we followed up to 19. The observations are essentially in agreement with molecular dynamics calculations in static two-dimensional potentials.
In this contribution, we present results on the structural properties of single‐component as well as two‐component ion Coulomb crystals confined in a linear Paul trap. Metastable long range ordered structures as the face‐centered cubic (fcc) and body‐centered cubic (bcc) lattices are observed in single‐component ion crystals of sizes down to ∼ 1000 ions. In the case of two‐component ion crystals we observe a stable long range ordered structure in one of the trapped components, which is compared with a Molecular Dynamics (MD) simulation of a two‐component crystal.