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

Sympathetic cooling of a mass-mismatched two-ion chain in a double-well trap potential

Taro Hasegawa

Published May 6, 2011• 2 citations
Publisher

Abstract

Sympathetic cooling of two-ion system, in which one is laser-cooled and the other is sympathetically cooled and their masses are mismatched, in a linear rf trap with a double-well potential is proposed. The double-well potential consists of two wells, and there is one ion in each well. The axial frequencies of the two wells and the spatial interval between them are experimentally controllable. By theoretical analysis, the normal modes of the small oscillations around the equilibrium are derived, and a measure of the sympathetic cooling rate is obtained. As a result, it is found that the sympathetic cooling rate is fast when the frequency of the axial motion of the sympathetically cooled ion is close to that of the laser-cooled ion. In the double-well potential, the sympathetic cooling rate of the ion species whose mass is much heavier or lighter than that of the laser-cooled ion can be fast. The sympathetic cooling rate of ${\mathrm{C}}_{60}$${}^{+}$ by the laser-cooled Ba${}^{+}$ in the double-well potential is estimated to be about 80 times faster than in the conventional setup. The double-well potential may be made by the microfabricated electrode configuration or by the optical dipole force trap.

DOI
10.1103/physreva.83.053407

Related papers

Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals*

Lijun Du, Yansong Meng, Yuling He +1 more

A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however, there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional (3D) secular spectra of trapped ions using molecular dynamics simulations. The 3D resonance peaks of the 40Ca+–27Al+ pair obtained by using this method were in good agreement with the 3D in- and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%. The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the 40Ca+–27Al+ pair was primarily determined by its axial in-phase coupling. In addition, the frequencies and amplitudes of the ion pair’s resonance modes (in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the 40Ca+–27Al+ pair were slightly weaker than those of the 24Mg+–27Al+ pair, but significantly stronger than those of 9Be+–27Al+. However, the Doppler cooling limit temperature of 40Ca+ is comparable to that of 9Be+ but lower than approximately half of that of 24Mg+. Furthermore, laser cooling systems for 40Ca+ are more reliable than those for 24Mg+ and 9Be+. Therefore, 40Ca+ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of 27Al+ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable 27Al+ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.

Chinese Physics B•Apr 28, 2021•2 citations

Resonant oscillation modes of sympathetically cooled ions in a radio-frequency trap

Taro Hasegawa, Tadao Shimizu

Sympathetic cooling of ${\mathrm{Ca}}^{+},$ ${\mathrm{Zn}}^{+},$ ${\mathrm{Sr}}^{+},$ ${\mathrm{Ba}}^{+},$ and ${\mathrm{Yb}}^{+}$ as guest ions with laser-cooled ${}^{24}{\mathrm{Mg}}^{+}$ as host ions in a rf ion trap is carried out, and resonant frequencies of their motion in the trap potential are measured. Various oscillation modes of the sympathetically cooled ions are observed. The resonant frequency of the oscillation mode is different from the frequency of either the collective oscillation frequency of the trapped ions or the oscillation frequency of each ion without host ions. This difference is well explained by a theoretical model in which coupled equations of motion of the host ion cloud with a single guest ion are considered.

Physical Review A•Dec 12, 2002•10 citations

An empirical study of sympathetic cooling using a large single-species ion cloud

Nikolaos Efthymiadis, Tudor Stefan, Stephen A. Jones

Abstract Sympathetic cooling is an important technique for achieving low motional temperatures in trapped ion systems that cannot be directly laser cooled. In this paper, we report on the sympathetic cooling of large samples (5 × 10 4 ) of Ba + ions which have been optically pumped into a dark state, using laser cooled Ba + ions in a linear radiofrequency (RF) ion trap. The trap lifetime was evaluated with different dark ion fractions as a function of the RF amplitude, the DC trapping potentials, the power and frequency of the cooling lasers, the quality of the vacuum, and the total number of ions. We found that the RF amplitude was the dominant factor contributing to the loss of ions, and that under optimal conditions and with a dark ion fraction as high as 85%, no losses were observed over 100 s long measurement periods, and fewer than 10% of the ions were lost after 1000 s.

Journal of Physics B Atomic Molecular and Optical Physics•Jul 14, 2026•0 citations

Observation and temperature measurement of the sympathetically cooled ions in an rf trap

T. Hasegawa, T. Shimizu

The barium ions are trapped with the laser-cooled magnesium ions simultaneously in an rf trap and cooled sympathetically. Sympathetically cooled ions are one of the candidates of accurate optical frequency standard. The barium ions are ionized by the charge transfer with the magnesium ions for avoiding the loss due to the shallow trapping potential. The temperature of the barium ions is measured and the effect of the sympathetic cooling is observed. It is also found that the application of the ionization by the charge transfer to other ion species is possible.

Conference on Precision Electromagnetic Measurements•Nov 7, 2002•0 citations

Sympathetic cooling of molecular ion motion to the ground state

René Rugango, J E Goeders, T H Dixon +5 more

We demonstrate sympathetic sideband cooling of a 40 CaH + molecular ion co-trapped with a 40 Ca + atomic ion in a linear Paul trap. Both axial modes of the two-ion chain are simultaneously cooled to near the ground state of motion. The center of mass mode is cooled to an average quanta of harmonic motion , corresponding to a temperature of . The breathing mode is cooled to , corresponding to a temperature of .

arXiv:1412.0782•New Journal of Physics•Mar 12, 2015•42 citations

Sympathetic cooling of trapped ions with resonant laser radiation [frequency standard application]

T. Shimizu, Y. Oshima, Yoshiki Moriwaki +1 more

We propose a novel model to describe dynamic properties of ions that are cooled by collisions with other laser-cooled ions in a quadrupole rf trap. The limit temperature of the sympathetic cooling is estimated as functions of the trap and laser parameters, and the mass of the ions.>

Conference on Precision Electromagnetic Measurements•Dec 17, 2002•0 citations
Sympathetic cooling of two-ion system, in which one is laser-cooled and the other is sympathetically cooled and their masses are mismatched, in a linear rf trap with a double-well potential is proposed. The double-well potential consists of two wells, and there is one ion in each well. The axial frequencies of the two wells and the spatial interval between them are experimentally controllable. By theoretical analysis, the normal modes of the small oscillations around the equilibrium are derived, and a measure of the sympathetic cooling rate is obtained. As a result, it is found that the sympathetic cooling rate is fast when the frequency of the axial motion of the sympathetically cooled ion is close to that of the laser-cooled ion. In the double-well potential, the sympathetic cooling rate of the ion species whose mass is much heavier or lighter than that of the laser-cooled ion can be fast. The sympathetic cooling rate of {\mathrm{C}}_{60}$${}^{+} by the laser-cooled Ba+{}^{+}+ in the double-well potential is estimated to be about 80 times faster than in the conventional setup. The double-well potential may be made by the microfabricated electrode configuration or by the optical dipole force trap.
A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however, there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional (3D) secular spectra of trapped ions using molecular dynamics simulations. The 3D resonance peaks of the 40Ca+–27Al+ pair obtained by using this method were in good agreement with the 3D in- and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%. The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the 40Ca+–27Al+ pair was primarily determined by its axial in-phase coupling. In addition, the frequencies and amplitudes of the ion pair’s resonance modes (in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the 40Ca+–27Al+ pair were slightly weaker than those of the 24Mg+–27Al+ pair, but significantly stronger than those of 9Be+–27Al+. However, the Doppler cooling limit temperature of 40Ca+ is comparable to that of 9Be+ but lower than approximately half of that of 24Mg+. Furthermore, laser cooling systems for 40Ca+ are more reliable than those for 24Mg+ and 9Be+. Therefore, 40Ca+ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of 27Al+ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable 27Al+ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.
Sympathetic cooling of Ca+,{\mathrm{Ca}}^{+},Ca+, Zn+,{\mathrm{Zn}}^{+},Zn+, Sr+,{\mathrm{Sr}}^{+},Sr+, Ba+,{\mathrm{Ba}}^{+},Ba+, and Yb+{\mathrm{Yb}}^{+}Yb+ as guest ions with laser-cooled 24Mg+{}^{24}{\mathrm{Mg}}^{+}24Mg+ as host ions in a rf ion trap is carried out, and resonant frequencies of their motion in the trap potential are measured. Various oscillation modes of the sympathetically cooled ions are observed. The resonant frequency of the oscillation mode is different from the frequency of either the collective oscillation frequency of the trapped ions or the oscillation frequency of each ion without host ions. This difference is well explained by a theoretical model in which coupled equations of motion of the host ion cloud with a single guest ion are considered.
Abstract Sympathetic cooling is an important technique for achieving low motional temperatures in trapped ion systems that cannot be directly laser cooled. In this paper, we report on the sympathetic cooling of large samples (5 × 10 4 ) of Ba + ions which have been optically pumped into a dark state, using laser cooled Ba + ions in a linear radiofrequency (RF) ion trap. The trap lifetime was evaluated with different dark ion fractions as a function of the RF amplitude, the DC trapping potentials, the power and frequency of the cooling lasers, the quality of the vacuum, and the total number of ions. We found that the RF amplitude was the dominant factor contributing to the loss of ions, and that under optimal conditions and with a dark ion fraction as high as 85%, no losses were observed over 100 s long measurement periods, and fewer than 10% of the ions were lost after 1000 s.
The barium ions are trapped with the laser-cooled magnesium ions simultaneously in an rf trap and cooled sympathetically. Sympathetically cooled ions are one of the candidates of accurate optical frequency standard. The barium ions are ionized by the charge transfer with the magnesium ions for avoiding the loss due to the shallow trapping potential. The temperature of the barium ions is measured and the effect of the sympathetic cooling is observed. It is also found that the application of the ionization by the charge transfer to other ion species is possible.