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

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

M. A. N. Razvi, X. Z. Chu, R. Alheit, Günther Werth, R. Blümel

Published Jul 1, 1998• 35 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.58.r34

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

Nonlinear collective oscillations of an ion cloud in a Paul trap

R. Alheit, X. Z. Chu, M. Hoefer +3 more

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.

Physical Review A•Nov 1, 1997•43 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

Measurement of Secular Motion Frequency in Miniature Paul Trap to Ascertain the Stability Parameters

Bin Guo, Guan Hua, Liu Qu +3 more

40 Ca + ions are trapped and laser cooled in a miniature Paul trap. The secular motion was observed by the radio-frequency resonance of the ion cloud and Zeeman profile sidebands of a single ion experimentally. The trap stability parameters a and q are determined with an uncertainty under 1 % by the secular motion frequency measurement. The trap efficiency is 0.75. A practicable suggestion is given for the benefits of a new trap design.

Chinese Physics Letters•Jan 1, 2010•4 citations

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

Paul trap for optical frequency standards

Steven R. Jefferts, Christopher R. Monroe, A. S. Barton +1 more

We describe a variant of the quadrupole rf (Paul) ion trap capable of localization of a trapped ion within much less than an optical wavelength (Lamb-Dicke regime). Attainment of the Lamb-Dicke regime reduces the sensitivity of the central absorption feature to atomic motion, thereby reducing an important source of noise in an optical frequency standard. The trapping potentials are generated by a high-Q, vacuum-compatible, quarter-wave resonator driven at about 240 MHz. Secular frequencies of tens of megahertz have been achieved for trapped magnesium and beryllium ions.>

IEEE Transactions on Instrumentation and Measurement•Apr 1, 1995•7 citations
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.
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.
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 ${10}^{\ensuremath{-}9}$-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.
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.
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.
We describe a variant of the quadrupole rf (Paul) ion trap capable of localization of a trapped ion within much less than an optical wavelength (Lamb-Dicke regime). Attainment of the Lamb-Dicke regime reduces the sensitivity of the central absorption feature to atomic motion, thereby reducing an important source of noise in an optical frequency standard. The trapping potentials are generated by a high-Q, vacuum-compatible, quarter-wave resonator driven at about 240 MHz. Secular frequencies of tens of megahertz have been achieved for trapped magnesium and beryllium ions.>