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

Nonlinear collective oscillations of an ion cloud in a Paul trap

R. Alheit, X. Z. Chu, M. Hoefer, M. Holzki, Günther Werth, R. Blümel

Published Nov 1, 1997• 43 citations
Publisher

Abstract

In an experiment using a Paul trap, we create a ${\mathrm{H}}_{2}^{+}$ ion cloud by electron ionization of the background gas at ${10}^{\ensuremath{-}9}$-mbar residual pressure. Exciting the ions parametrically at twice the frequency of the secular motion of ions in the $r$ or $z$ direction, we observe a narrow resonance at some distance from the motional resonance center if the amplitude of the exciting field exceeds a threshold value. The threshold value decreases with increasing ion number. Since the narrow resonance does not shift with ion number, we interpret it as a collective resonance of the center of mass of the ion cloud. The resonance shape exhibits the typical form of a driven anharmonic oscillator. The conclusions drawn from the experiments are supported by detailed analytical and numerical computations.

DOI
10.1103/physreva.56.4023

Related papers

Fractional frequency parametric resonances in a Paul trap

M. A. N. Razvi, X. Z. Chu, R. Alheit +2 more

Excitation of the motional frequencies of clouds of H2+ and N2+ ions, confined in a Paul trap, by an additionally applied radiofrequency quadrupole field leads to the observation of parametric resonances that are predicted to occur at frequencies 2ωz/n, n=1,2,3…, where ωz is the axial secular frequency. In the case of clouds of N2+ ions resonances up to n=10 are detected. They can be explained by parametric instabilities of the center-of-mass motion in the axial direction. The fractional resonances are observable only if the excitation field surpasses a critical strength. We find an odd-even staggering of the thresholds.

AIP conference proceedings•Jan 1, 1999•0 citations

Fractional frequency collective parametric resonances of an ion cloud in a Paul trap

M. A. N. Razvi, X. Z. Chu, R. Alheit +2 more

We report the observation of the first ten collective parametric resonances of an uncooled ${N}_{2}^{+}$ ion cloud in a Paul trap driven at simple fractions of twice the secular frequency of the trap by an additionally applied quadrupole field. The fractional resonances are observable only if the excitation field surpasses a critical strength. Odd-even staggering of the thresholds is observed.

Physical Review A•Jul 1, 1998•35 citations

Collective Phenomena Induced by Ion Mixturesin a RF Ion Trap

Akihiro Kajita, Masahiro Kimura, Shunsuke Ohtani +2 more

Collective motions and anharmonic oscillations induced by a mixture of two ion species with different masses in a rf ion trap are reported. The absorption spectra of the probing rf power by the resonant oscillations of ion clouds have been observed for several ion species with various mixing ratios. It is shown that significant nonlinear effects manifest themselves strongly when the mass difference is in a certain range. One of such nonlinear effects, the first observation of significant hysteresis in the absorption spectrum of the probing rf field, is understood to be due to the anharmonic force term of the third order induced by the interactions of two ion clouds. The term has been estimated by fitting the observed absorption profile to the approximate solution of Duffing's equation.

Journal of the Physical Society of Japan•Sep 15, 1991•5 citations

Periodical motion of an ion-cloud in an anharmonic Paul trap

Hai Kuo

Interaction between an external detecting field and an ion-cloud in an actual Paul trap is described by the Duffing equation.In this paper,we reported an exactly periodical solution,which reveals the dependence of the trap parameters and external field on the ion-cloud's periodical motion.The result shows that under the periodicity condition the frequency of ion's motion is one third of the frequency of detecting field,the motion amplitude is positively correlated to the frequency and amplitude of the detecting field and the trap frequency respectively,and is negatively correlated with the anharmonic parameters of the Paul trap.

Journal of Atomic and Molecular Physics•Jan 1, 2007•0 citations

Mass-selective removal of ions from Paul traps using parametric excitation

Julian Schmidt, Daniel Hönig, Pascal Weckesser +3 more

Abstract We study a method for mass-selective removal of ions from a Paul trap by parametric excitation. This can be achieved by applying an oscillating electric quadrupole field at twice the secular frequency $$\omega _{\text {sec}}$$ ω sec using pairs of opposing electrodes. While excitation near the resonance with the secular frequency $$\omega _{\text {sec}}$$ ω sec only leads to a linear increase of the amplitude with excitation duration, parametric excitation near $$2\, \omega _{\text {sec}}$$ 2 ω sec results in an exponential increase of the amplitude. This enables efficient removal of ions from the trap with modest excitation voltages and narrow bandwidth, therefore, substantially reducing the disturbance of ions with other charge-to-mass ratios. We numerically study and compare the mass selectivity of the two methods. In addition, we experimentally show that the barium isotopes with 136 and 137 nucleons can be removed from small ion crystals and ejected out of the trap while keeping $$^{138}\text {Ba}^{+}$$ 138 Ba + ions Doppler cooled, corresponding to a mass selectivity of better than $$\Delta m / m = 1/138$$ Δ m / m = 1 / 138 . This method can be widely applied to ion trapping experiments without major modifications since it only requires modulating the potential of the ion trap.

arXiv:2005.02675•Applied Physics B•Oct 9, 2020•21 citations

Nonlinear Resonances of Laser Cooled Ions in a Linear Paul Trap due to the Anharmonicity of the Trap Potential

Toshihiko MORI, Kenji Toyoda, Masayoshi Watanabe +1 more

The anharmonicity of the trap potential influences the motion of trapped and laser-cooled ions. The magnitudes of higher-order components of the trap potential depend on the electrode geometry. In this paper we provide a numerical study of the anharmonicity of linear Paul trap potentials with different electorode geometies. We have also experimentally observed nonlinear resonances of laser-cooled ions, and have studied the effect of anharmonicity in three types of liner Paul trap that have different distances between electrodes.

The Review of Laser Engineering•Jan 1, 2003•1 citation
In an experiment using a Paul trap, we create a H2+{\mathrm{H}}_{2}^{+}H2+​ ion cloud by electron ionization of the background gas at 10\ensuremath−9{10}^{\ensuremath{-}9}10\ensuremath−9-mbar residual pressure. Exciting the ions parametrically at twice the frequency of the secular motion of ions in the rrr or zzz direction, we observe a narrow resonance at some distance from the motional resonance center if the amplitude of the exciting field exceeds a threshold value. The threshold value decreases with increasing ion number. Since the narrow resonance does not shift with ion number, we interpret it as a collective resonance of the center of mass of the ion cloud. The resonance shape exhibits the typical form of a driven anharmonic oscillator. The conclusions drawn from the experiments are supported by detailed analytical and numerical computations.
Excitation of the motional frequencies of clouds of H2+ and N2+ ions, confined in a Paul trap, by an additionally applied radiofrequency quadrupole field leads to the observation of parametric resonances that are predicted to occur at frequencies 2ωz/n, n=1,2,3…, where ωz is the axial secular frequency. In the case of clouds of N2+ ions resonances up to n=10 are detected. They can be explained by parametric instabilities of the center-of-mass motion in the axial direction. The fractional resonances are observable only if the excitation field surpasses a critical strength. We find an odd-even staggering of the thresholds.
We report the observation of the first ten collective parametric resonances of an uncooled N2+{N}_{2}^{+}N2+​ ion cloud in a Paul trap driven at simple fractions of twice the secular frequency of the trap by an additionally applied quadrupole field. The fractional resonances are observable only if the excitation field surpasses a critical strength. Odd-even staggering of the thresholds is observed.
Collective motions and anharmonic oscillations induced by a mixture of two ion species with different masses in a rf ion trap are reported. The absorption spectra of the probing rf power by the resonant oscillations of ion clouds have been observed for several ion species with various mixing ratios. It is shown that significant nonlinear effects manifest themselves strongly when the mass difference is in a certain range. One of such nonlinear effects, the first observation of significant hysteresis in the absorption spectrum of the probing rf field, is understood to be due to the anharmonic force term of the third order induced by the interactions of two ion clouds. The term has been estimated by fitting the observed absorption profile to the approximate solution of Duffing's equation.
Interaction between an external detecting field and an ion-cloud in an actual Paul trap is described by the Duffing equation.In this paper,we reported an exactly periodical solution,which reveals the dependence of the trap parameters and external field on the ion-cloud's periodical motion.The result shows that under the periodicity condition the frequency of ion's motion is one third of the frequency of detecting field,the motion amplitude is positively correlated to the frequency and amplitude of the detecting field and the trap frequency respectively,and is negatively correlated with the anharmonic parameters of the Paul trap.
Abstract We study a method for mass-selective removal of ions from a Paul trap by parametric excitation. This can be achieved by applying an oscillating electric quadrupole field at twice the secular frequency ωsec\omega _{\text {sec}}ωsec​ ω sec using pairs of opposing electrodes. While excitation near the resonance with the secular frequency ωsec\omega _{\text {sec}}ωsec​ ω sec only leads to a linear increase of the amplitude with excitation duration, parametric excitation near 2 ωsec2\, \omega _{\text {sec}}2ωsec​ 2 ω sec results in an exponential increase of the amplitude. This enables efficient removal of ions from the trap with modest excitation voltages and narrow bandwidth, therefore, substantially reducing the disturbance of ions with other charge-to-mass ratios. We numerically study and compare the mass selectivity of the two methods. In addition, we experimentally show that the barium isotopes with 136 and 137 nucleons can be removed from small ion crystals and ejected out of the trap while keeping 138Ba+^{138}\text {Ba}^{+}138Ba+ 138 Ba + ions Doppler cooled, corresponding to a mass selectivity of better than Δm/m=1/138\Delta m / m = 1/138Δm/m=1/138 Δ m / m = 1 / 138 . This method can be widely applied to ion trapping experiments without major modifications since it only requires modulating the potential of the ion trap.
The anharmonicity of the trap potential influences the motion of trapped and laser-cooled ions. The magnitudes of higher-order components of the trap potential depend on the electrode geometry. In this paper we provide a numerical study of the anharmonicity of linear Paul trap potentials with different electorode geometies. We have also experimentally observed nonlinear resonances of laser-cooled ions, and have studied the effect of anharmonicity in three types of liner Paul trap that have different distances between electrodes.