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

Physical Review A

Harmonic linear Paul trap: Stability diagram and effective potentials

Michael Drewsen, A. Brøner

Published Sep 11, 2000• 87 citations
Publisher

Abstract

We present the single-particle stability diagram for the radial motion in a linear Paul trap in a situation where the applied axial dc potential gives rise to a harmonic defocusing radial potential. Although most linear Paul trap experiments have been conducted in a regime where this approximation is reasonably valid, the effect of the axial confinement on the stability of the radial motion has not previously been analyzed. The defocusing effect in both radial directions leads to a stability diagram different from that of the two-dimensional quadrupole mass filter, and hence points toward new studies of few ion dynamics. Expressions for the effective or pseudopotentials for one and two charged particles are presented and discussed.

DOI
10.1103/physreva.62.045401

Related papers

Radial Two-Dimensional Ion Crystals in a Linear Paul Trap

Marissa D’Onofrio, Yuanheng Xie, A. J. Rasmusson +3 more

We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.

arXiv:2012.12766•Physical Review Letters•Jul 9, 2021•40 citations

Planar ion microtraps

Richard G. Brewer, Ralph G. DeVoe, R. Kallenbach

Planar quadrupole ion traps have been analyzed through numerical and analytic solutions of Laplace's equation. These involve either one or more conducting rings or their analogs, a hole in one or more conducting sheets. The leading terms in the potential are harmonic, corresponding to the Paul trap, but with coefficients that reduce their efficiency and for some traps, the anharmonic terms can be suppressed to eighth-order. Stable ion trapping is predicted for all electrode configurations possessing radial and axial symmetry. A three-hole microtrap with an inner hole radius of 80 \ensuremath{\mu}m trapped from one to many (dense clouds) laser-cooled ${\mathrm{Ba}}^{+}$ ions where the two-ion distance is compressed to 1 \ensuremath{\mu}m, allowing new experiments in quantum optics. Also, arrays of traps for optical clocks are contemplated using photolithographic fabrication.

Physical Review A•Dec 1, 1992•64 citations

Ion Oscillation Frequencies in a Combined Trap

David John Bate, Kishan Dholakia, Richard Claude Thompson +1 more

A combined trap is a quadrupole trap to which the fields of both the Paul and the Penning traps are applied. In this paper, equations of motion for ions confined in a combined trap are derived from first principles. The equations of motion are shown to give well-understood solutions for the Paul and Penning traps in the appropriate cases before they are solved to yield the axial and radial oscillation frequencies for ions in a combined trap. The dependence of these oscillation frequencies on the applied fields is investigated.

Journal of Modern Optics•Feb 1, 1992•55 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

One-dimensional radial Coulomb crystals in a quadrupole Paul trap

Anna V. Romanova, Semyon S. Rudyi, Yu. Rozhdestvensky

In this work, we have studied the dynamics of 7-ions Ca+ Coulomb crystal in a linear quadrupole trap with flat end-cap electrodes. We have introduced geometrical parameters to determine points of phase transitions in the crystal. Then we have numerically calculated a phase diagram for this case and simulated the corresponding Coulomb crystals. It was shown that new one-dimensional radial Coulomb crystals are observed with the application of both high end-cap voltage (more than 1200 V) and a bias voltage on linear electrodes.

Optical Manipulation and Structured Materials Conference (OMC)•Sep 20, 2023•0 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
We present the single-particle stability diagram for the radial motion in a linear Paul trap in a situation where the applied axial dc potential gives rise to a harmonic defocusing radial potential. Although most linear Paul trap experiments have been conducted in a regime where this approximation is reasonably valid, the effect of the axial confinement on the stability of the radial motion has not previously been analyzed. The defocusing effect in both radial directions leads to a stability diagram different from that of the two-dimensional quadrupole mass filter, and hence points toward new studies of few ion dynamics. Expressions for the effective or pseudopotentials for one and two charged particles are presented and discussed.
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.
Planar quadrupole ion traps have been analyzed through numerical and analytic solutions of Laplace's equation. These involve either one or more conducting rings or their analogs, a hole in one or more conducting sheets. The leading terms in the potential are harmonic, corresponding to the Paul trap, but with coefficients that reduce their efficiency and for some traps, the anharmonic terms can be suppressed to eighth-order. Stable ion trapping is predicted for all electrode configurations possessing radial and axial symmetry. A three-hole microtrap with an inner hole radius of 80 \ensuremath{\mu}m trapped from one to many (dense clouds) laser-cooled Ba+{\mathrm{Ba}}^{+}Ba+ ions where the two-ion distance is compressed to 1 \ensuremath{\mu}m, allowing new experiments in quantum optics. Also, arrays of traps for optical clocks are contemplated using photolithographic fabrication.
A combined trap is a quadrupole trap to which the fields of both the Paul and the Penning traps are applied. In this paper, equations of motion for ions confined in a combined trap are derived from first principles. The equations of motion are shown to give well-understood solutions for the Paul and Penning traps in the appropriate cases before they are solved to yield the axial and radial oscillation frequencies for ions in a combined trap. The dependence of these oscillation frequencies on the applied fields is investigated.
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.
In this work, we have studied the dynamics of 7-ions Ca+ Coulomb crystal in a linear quadrupole trap with flat end-cap electrodes. We have introduced geometrical parameters to determine points of phase transitions in the crystal. Then we have numerically calculated a phase diagram for this case and simulated the corresponding Coulomb crystals. It was shown that new one-dimensional radial Coulomb crystals are observed with the application of both high end-cap voltage (more than 1200 V) and a bias voltage on linear electrodes.
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.