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

Physica Scripta

An improved pseudo potential for the two-ion Paul trap

M. G. Moore, R. Blümel

Published Jan 1, 1995• 2 citations
Publisher

Abstract

Keeping terms up to second order in the micro motion of two ions stored in a Paul trap we derive an improved two-ion pseudo potential which predicts crystal alignment effects that go beyond a standard pseudo-potential analysis and are supported by numerical evidence. The dynamical predictions can be checked experimentally with existing set-ups.

DOI
10.1088/0031-8949/1995/t59/062

Related papers

Prediction of an alignment transition region of two-ion crystals in a Paul trap

M. G. Moore, R. Blümel

Contrary to the results of standard pseudopotential analysis we predict the existence of an alignment transition region in the parameter space of the Paul trap in which the orientation of two-ion crystals with average angular momentum zero is different from x-y or z alignment. This prediction is based on an improved pseudopotential derived by keeping terms up to second order in the micromotion amplitudes. Our analytical predictions are supported by numerical evidence and can be checked experimentally with existing setups.

Physical Review A•Dec 1, 1994•12 citations

Stability of two-ion crystals in the Paul trap: A comparison of exact and pseudopotential calculations

John A. Hoffnagle, Richard G. Brewer

Applied Physics B•Jan 1, 1995•15 citations

The Pseudopotential As a Tool for Describing Ion Crystal Morphology

Varun Ursekar

Describing the structure of ion Coulomb crystals in periodically-driven systems, such as cylindrical and linear Paul traps, is important for applications in quantum information processing, quantum simulation, spectroscopy, and frequency standard determination. The pseudopotential, a time-independent effective potential obtained by averaging the explicitly time-dependent trapping potential, is often used for this specific purpose, among other uses in the general study of trapped ion dynamics. This thesis examines the strengths and weaknesses of the pseudopotential approximation as a tool for describing few-ion crystal configurations in a Paul trap. Numerical evidence for the failure of the standard pseudopotential commonly found in the literature in predicting crystal alignment effects in such systems is provided. A method for deriving an improved pseudopotential for a general set of coupled differential equations is presented and applied to the cylindrical and linear traps, providing analytical evidence for these "exotic'' crystal alignment effects. The limitations of the improved pseudopotential in explaining crystal instability in certain regions of trap parameter space and in terms of scalability to many-ion systems are discussed.

•Jan 1, 2017•0 citations

174Yb+–113Cd+ sympathetic-cooling bi-species Coulomb crystal applied to microwave frequency standard

Y.Z. Zheng, H. R. Qin, S. N. Miao +5 more

We reported the realization of a 174Yb+–113Cd+ bi-species Coulomb crystal comprising 174Yb+, a heavier ion, as coolant and verified the potential of applying a coolant ion with a greater mass than the clock ion to sympathetically cooled microwave frequency standard. The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The 113Cd+ ions are trapped in the center, which reduces considerably RF heating and excess micro-motion to which the 113Cd+ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to 5×10−16, which represents an order of magnitude improvement over sympathetic cooled 40Ca+–113Cd+ crystal. The second-order Zeeman frequency shift, which contributes the largest term of the systematic frequency shifts to the microwave ion frequency standard, is estimated to be as low as 7.133×10−13 corresponding to the low value of the operating magnetic field. The relevant AC Stark shift uncertainty is estimated to be 4×10−19. These results demonstrate that using a heavier coolant ion is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a 174Yb+–113Cd+ bicrystal.

Applied Physics Letters•Aug 21, 2023•8 citations

Prediction of exotic ion-crystal structures in a Paul trap

Varun Ursekar, J. M. Silvester, Yun Seong Nam +1 more

The European Physical Journal D•Sep 1, 2018•1 citation

Effects of micromotion on the squeezing and on the dynamical behaviour of ion in a Paul trap

Dolan Krishna Bayen, Swapan Mandal

The European Physical Journal Plus•Mar 24, 2023•2 citations
Keeping terms up to second order in the micro motion of two ions stored in a Paul trap we derive an improved two-ion pseudo potential which predicts crystal alignment effects that go beyond a standard pseudo-potential analysis and are supported by numerical evidence. The dynamical predictions can be checked experimentally with existing set-ups.
Contrary to the results of standard pseudopotential analysis we predict the existence of an alignment transition region in the parameter space of the Paul trap in which the orientation of two-ion crystals with average angular momentum zero is different from x-y or z alignment. This prediction is based on an improved pseudopotential derived by keeping terms up to second order in the micromotion amplitudes. Our analytical predictions are supported by numerical evidence and can be checked experimentally with existing setups.
Describing the structure of ion Coulomb crystals in periodically-driven systems, such as cylindrical and linear Paul traps, is important for applications in quantum information processing, quantum simulation, spectroscopy, and frequency standard determination. The pseudopotential, a time-independent effective potential obtained by averaging the explicitly time-dependent trapping potential, is often used for this specific purpose, among other uses in the general study of trapped ion dynamics. This thesis examines the strengths and weaknesses of the pseudopotential approximation as a tool for describing few-ion crystal configurations in a Paul trap. Numerical evidence for the failure of the standard pseudopotential commonly found in the literature in predicting crystal alignment effects in such systems is provided. A method for deriving an improved pseudopotential for a general set of coupled differential equations is presented and applied to the cylindrical and linear traps, providing analytical evidence for these "exotic'' crystal alignment effects. The limitations of the improved pseudopotential in explaining crystal instability in certain regions of trap parameter space and in terms of scalability to many-ion systems are discussed.
We reported the realization of a 174Yb+–113Cd+ bi-species Coulomb crystal comprising 174Yb+, a heavier ion, as coolant and verified the potential of applying a coolant ion with a greater mass than the clock ion to sympathetically cooled microwave frequency standard. The two species of massive ions stably trapped in a Paul trap make up this large two-component crystal. The 113Cd+ ions are trapped in the center, which reduces considerably RF heating and excess micro-motion to which the 113Cd+ ions are subjected. Under this scheme, the uncertainty due to the second-order Doppler effect is reduced to 5×10−16, which represents an order of magnitude improvement over sympathetic cooled 40Ca+–113Cd+ crystal. The second-order Zeeman frequency shift, which contributes the largest term of the systematic frequency shifts to the microwave ion frequency standard, is estimated to be as low as 7.133×10−13 corresponding to the low value of the operating magnetic field. The relevant AC Stark shift uncertainty is estimated to be 4×10−19. These results demonstrate that using a heavier coolant ion is far superior and confirm the feasibility of a sympathetic-cooled cadmium-ion microwave clock system employing a 174Yb+–113Cd+ bicrystal.