Physica Scripta

Sympathetic cooling of two trapped ions

В. А. Алексеев, D. D. Krylova, Vladilen S Letokhov

Published Mar 1, 1995• 9 citations

Abstract

The time-dependent distribution function of two different trapped ions when one of them is cooled by a laser field and the second one is cooled sympathetically is investigated using the Fokker-Planck equation. The limiting cooling temperatures of both ions are found to be equal to the limiting cooling temperature of single laser cooled ions.

DOI: 10.1088/0031-8949/51/3/015

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Physica Scripta

Sympathetic cooling of two trapped ions

В. А. Алексеев, D. D. Krylova, Vladilen S Letokhov

Published Mar 1, 1995• 9 citations

Publisher

Abstract

DOI: 10.1088/0031-8949/51/3/015

Related papers

Sympathetic cooling of trapped ions with resonant laser radiation

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Dec 31, 19940 citations

Temporal behavior of the velocity distribution function and the influence of collisions in laser cooling

В. А. Алексеев, D. D. Krylova

Journal of the Optical Society of America BSep 1, 19935 citations

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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.>

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Sympathetic cooling of mixed-species two-ion crystals for precision spectroscopy

Jannes B. Wübbena, Sana Amairi‐Pyka, Olaf Mandel +1 more

Sympathetic cooling of trapped ions has become an indispensable tool for quantum-information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al ${}^{+}$ with Be ${}^{+}$ , Mg ${}^{+}$ , and Ca ${}^{+}$ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalization dynamics after a background gas collision for the Al ${}^{+}$ -Ca ${}^{+}$ crystal for different cooling laser configurations.Sympathetic cooling of trapped ions has become an indispensable tool for quantum-information processing and precision spectroscopy. In the simplest situation a single Doppler-cooled ion sympathetically cools another ion which typically has a different mass. We analytically investigate the effect of the mass ratio of such an ion crystal on the achievable temperature limit in the presence of external heating. As an example, we show that cooling of a single Al${}^{+}$ with Be${}^{+}$, Mg${}^{+}$, and Ca${}^{+}$ ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalization dynamics after a background gas collision for the Al${}^{+}$-Ca${}^{+}$ crystal for different cooling laser configurations.

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We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a two-ion crystal of Ca + and Al + by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sympathethic cooling times before crystallization occurs. Our key result is a new technique for detecting the loading of an initially hot ion with energy in the eV range by monitoring the motional state of a Doppler-cooled ion already present in the trap. This technique not only detects the ion but also provides information about the dynamics of the sympathetic cooling process.We investigate the dynamics of an ion sympathetically cooled by another laser-cooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a two-ion crystal of Ca + and Al + by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sympathethic cooling times before crystallization occurs. Our key result is a new technique for detecting the loading of an initially hot ion with energy in the eV range by monitoring the motional state of a Doppler-cooled ion already present in the trap. This technique not only detects the ion but also provides information about the dynamics of the sympathetic cooling process.

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Daniel J. Larson, Jonas Bergquist, J. J. Bollinger +2 more

Sympathetic cooling of trapped ions has been demonstrated in an experiment where $^{198}\mathrm{Hg}^{+}$ ions were confined in a Penning ion trap with laser-cooled $^{9}\mathrm{Be}^{+}$ ions. $^{198}\mathrm{Hg}^{+}$ temperatures below 1 K were achieved. Ion plasma sizes, shapes, and rotation frequencies were measured. Dramatic changes in the $^{9}\mathrm{Be}^{+}$ plasma were observed when the $^{198}\mathrm{Hg}^{+}$ ions were introduced into the trap. These observations are consistent with the prediction of centrifugal separation for ions of different charge-to-mass ratios.Sympathetic cooling of trapped ions has been demonstrated in an experiment where $^{198}\mathrm{Hg}^{+}$ ions were confined in a Penning ion trap with laser-cooled $^{9}\mathrm{Be}^{+}$ ions. $^{198}\mathrm{Hg}^{+}$ temperatures below 1 K were achieved. Ion plasma sizes, shapes, and rotation frequencies were measured. Dramatic changes in the $^{9}\mathrm{Be}^{+}$ plasma were observed when the $^{198}\mathrm{Hg}^{+}$ ions were introduced into the trap. These observations are consistent with the prediction of centrifugal separation for ions of different charge-to-mass ratios.

Physical Review LettersJul 7, 1986375 citations

{}^{+}

with Be

{}^{+}

, Mg

{}^{+}

, and Ca

{}^{+}

ions provides similar results for heating rates typically observed in ion traps, whereas cooling ions with a larger mass perform worse. Furthermore, we present numerical simulation results of the rethermalization dynamics after a background gas collision for the Al

{}^{+}

-Ca

{}^{+}

crystal for different cooling laser configurations.

Sympathetic cooling of trapped ions has been demonstrated in an experiment where

^{198}\mathrm{Hg}^{+}

ions were confined in a Penning ion trap with laser-cooled

^{9}\mathrm{Be}^{+}

ions.

^{198}\mathrm{Hg}^{+}

temperatures below 1 K were achieved. Ion plasma sizes, shapes, and rotation frequencies were measured. Dramatic changes in the

^{9}\mathrm{Be}^{+}

plasma were observed when the

^{198}\mathrm{Hg}^{+}

ions were introduced into the trap. These observations are consistent with the prediction of centrifugal separation for ions of different charge-to-mass ratios.