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

Temperature and heating rate of ion crystals in Penning traps

M. J. Jensen, Taro Hasegawa, John Bollinger

Published Sep 3, 2004• 32 citations
Publisher

Abstract

We have determined the temperature and heating rate of laser-cooled ions in a Penning trap using Doppler laser spectroscopy. Between and ions are trapped in a Penning trap and Doppler laser cooled to temperatures of a few millikelvin, where they form ion crystals. This system is an example of a strongly coupled one-component plasma. The ion temperature was measured as a function of time after turning off the laser-cooling. In the solid phase, we measured a heating rate of . Information about possible heating mechanisms was obtained directly from temperature measurements, and also from measurements of the rate of radial expansion of the ion plasma. We determined that the observed heating is due to collisions with the residual gas of our vacuum system.

DOI
10.1103/physreva.70.033401

Related papers

Temperature Measurements of Laser-Cooled Ions in a Penning Trap

M. J. Jensen

Between 104 and 106 9Be+ ions are trapped in a Penning trap. The ions are laser‐cooled to ∼millikelvin temperatures, where they form ion crystals. This system is an example of a strongly coupled one‐component plasma. By means of Doppler laser spectroscopy we have measured the temperature and heating rate of the plasma. Initially the heating rate is low, 60 ± 40 mK/s, but after about 100 ms the plasma heats up rapidly to a few kelvin. The onset of the rapid heating coincides with the solid‐liquid phase transition.

AIP conference proceedings•Jan 1, 2003•2 citations

Preparation and cooling of magnesium ion crystals for sympathetic cooling of highly charged ions in a Penning trap

T. Murböck

In this work, laser-cooled ion crystals containing 1000 to 100000 singly charged magnesium ions (Mg+) were prepared in a Penning trap. The properties of the ion crystals and their structure displaying long-range ordering were analyzed by various non-destructive techniques. After creation of the Mg + ions in the form of ion bunches in an external source, the ions were injected into the Penning trap where their temperature was reduced by eight orders of magnitude within seconds using a combination of buffer gas cooling and Doppler laser cooling. The achieved temperatures in the millikelvin-regime were close to the theoretical Doppler-cooling limit and sufficiently low to induce the transition to a crystal phase exhibiting long-range ordering. The structure of these mesoscopic ion crystals is in agreement with a model describing the crystal as a set of planar shells. This allows for a derivation of properties such as the charge density or the temperature of the observed crystals. For the process of combined buffer-gas and Doppler laser cooling an analytical model has been developed, which explains the time development of the temperature and the fluorescence signal in agreement with the experimental results.

•Jan 1, 2017•2 citations

First principles simulation of ultracold ion crystals in a Penning trap with Doppler cooling and a rotating wall potential

Chen Tang, Dominic Meiser, John J. Bollinger +1 more

A direct numerical simulation of many interacting ions in a Penning trap with a rotating wall is presented. The ion dynamics is modeled classically. Both axial and planar Doppler laser cooling processes are modeled using stochastic momentum impulses based on two-level atomic scattering rates. The plasmas being modeled are ultracold two-dimensional crystals made up of hundreds of ions. We compare Doppler cooled results directly to a previous linear eigenmodes analysis. Agreement in both frequency and mode structure is obtained. Additionally, when Doppler laser cooling is applied, the laser cooled steady state plasma axial temperature agrees with the Doppler cooling limit. Numerical simulations using the approach described and benchmarked here will provide insights into the dynamics of large trapped-ion crystals, improving their performance as a platform for quantum simulation and sensing.

arXiv:1903.10600•Physics of Plasmas•Jul 1, 2019•10 citations

Perpendicular laser cooling of a rotating ion plasma in a Penning trap

Wayne M. Itano, Laurence R. Brewer, D. J. Larson +1 more

The steady-state temperature of an ion plasma in a Penning trap, cooled by a laser beam perpendicular to the trap axis, has been calculated and measured. The rotation of the plasma, due to crossed E and B fields, strongly affects the minimum attainable temperature. This is because the velocity distribution of the ions, as seen by a laser beam intersecting the plasma at some distance from the axis of rotation, is skewed, and this leads to a change in the velocity distribution (and hence temperature) at which a steady state is attained. The calculated temperature is a function of the intensity, frequency, and position of the laser beam, and of the rotation frequency of the plasma. Temperatures of $^{9}\mathrm{Be}^{+}$ plasmas were measured for a wide range of experimental parameters. The lowest and highest temperatures were approximately 40 mK and 2 K. The measured and calculated temperatures are in agreement.

Physical Review A•Dec 1, 1988•38 citations

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.

arXiv:1202.2730•Physical Review A•Apr 13, 2012•99 citations

Determining temperature and Rabi frequency regarding trapped ions in Doppler cooling: An analytic investigation

L.-L. Yan, Shi‐Lei Su, Feng, Mang

Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler cooling. Here we analytically explore the Doppler cooling process of trapped ions, exemplified by $^{40}$Ca$^{+}$, by solving the friction coefficient in the Doppler cooling with respect to a thermal bath, particularly, to a bath with large heating rate. We show four regions for cooling and heating induced by the three-level electromagnetically induced transparency and propose a practical method for measuring the Rabi frequency by the Doppler cooling window. In addition, the final temperature of the laser-cooled ions can be obtained analytically in the case of a weak thermal bath, whereas for the strong thermal bath this requires numerical treatment due to involvement of the Doppler shift and large Lamb-Dicke parameter. Our analytic results would help for understanding many experimental observations, such as configuration phase transition, phonon laser and thermodynamics regarding hot trapped ions.

arXiv:1902.00302•Feb 1, 2019•0 citations
We have determined the temperature and heating rate of laser-cooled ions in a Penning trap using Doppler laser spectroscopy. Between and ions are trapped in a Penning trap and Doppler laser cooled to temperatures of a few millikelvin, where they form ion crystals. This system is an example of a strongly coupled one-component plasma. The ion temperature was measured as a function of time after turning off the laser-cooling. In the solid phase, we measured a heating rate of . Information about possible heating mechanisms was obtained directly from temperature measurements, and also from measurements of the rate of radial expansion of the ion plasma. We determined that the observed heating is due to collisions with the residual gas of our vacuum system.
Between 104 and 106 9Be+ ions are trapped in a Penning trap. The ions are laser‐cooled to ∼millikelvin temperatures, where they form ion crystals. This system is an example of a strongly coupled one‐component plasma. By means of Doppler laser spectroscopy we have measured the temperature and heating rate of the plasma. Initially the heating rate is low, 60 ± 40 mK/s, but after about 100 ms the plasma heats up rapidly to a few kelvin. The onset of the rapid heating coincides with the solid‐liquid phase transition.
In this work, laser-cooled ion crystals containing 1000 to 100000 singly charged magnesium ions (Mg+) were prepared in a Penning trap. The properties of the ion crystals and their structure displaying long-range ordering were analyzed by various non-destructive techniques. After creation of the Mg + ions in the form of ion bunches in an external source, the ions were injected into the Penning trap where their temperature was reduced by eight orders of magnitude within seconds using a combination of buffer gas cooling and Doppler laser cooling. The achieved temperatures in the millikelvin-regime were close to the theoretical Doppler-cooling limit and sufficiently low to induce the transition to a crystal phase exhibiting long-range ordering. The structure of these mesoscopic ion crystals is in agreement with a model describing the crystal as a set of planar shells. This allows for a derivation of properties such as the charge density or the temperature of the observed crystals. For the process of combined buffer-gas and Doppler laser cooling an analytical model has been developed, which explains the time development of the temperature and the fluorescence signal in agreement with the experimental results.
A direct numerical simulation of many interacting ions in a Penning trap with a rotating wall is presented. The ion dynamics is modeled classically. Both axial and planar Doppler laser cooling processes are modeled using stochastic momentum impulses based on two-level atomic scattering rates. The plasmas being modeled are ultracold two-dimensional crystals made up of hundreds of ions. We compare Doppler cooled results directly to a previous linear eigenmodes analysis. Agreement in both frequency and mode structure is obtained. Additionally, when Doppler laser cooling is applied, the laser cooled steady state plasma axial temperature agrees with the Doppler cooling limit. Numerical simulations using the approach described and benchmarked here will provide insights into the dynamics of large trapped-ion crystals, improving their performance as a platform for quantum simulation and sensing.
The steady-state temperature of an ion plasma in a Penning trap, cooled by a laser beam perpendicular to the trap axis, has been calculated and measured. The rotation of the plasma, due to crossed E and B fields, strongly affects the minimum attainable temperature. This is because the velocity distribution of the ions, as seen by a laser beam intersecting the plasma at some distance from the axis of rotation, is skewed, and this leads to a change in the velocity distribution (and hence temperature) at which a steady state is attained. The calculated temperature is a function of the intensity, frequency, and position of the laser beam, and of the rotation frequency of the plasma. Temperatures of 9Be+^{9}\mathrm{Be}^{+}9Be+ plasmas were measured for a wide range of experimental parameters. The lowest and highest temperatures were approximately 40 mK and 2 K. The measured and calculated temperatures are in agreement.
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.
Doppler cooling with lasers is essential to ions' trapping and also a preliminary step towards achievement of ultracold ions. Due to lack of effective tools, experimentally monitoring the ions' temperature and the laser-ion coupling is difficult in Doppler cooling. Here we analytically explore the Doppler cooling process of trapped ions, exemplified by 40^{40}40Ca+^{+}+, by solving the friction coefficient in the Doppler cooling with respect to a thermal bath, particularly, to a bath with large heating rate. We show four regions for cooling and heating induced by the three-level electromagnetically induced transparency and propose a practical method for measuring the Rabi frequency by the Doppler cooling window. In addition, the final temperature of the laser-cooled ions can be obtained analytically in the case of a weak thermal bath, whereas for the strong thermal bath this requires numerical treatment due to involvement of the Doppler shift and large Lamb-Dicke parameter. Our analytic results would help for understanding many experimental observations, such as configuration phase transition, phonon laser and thermodynamics regarding hot trapped ions.