© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical Review A

Characterization of ion Coulomb crystals in a linear Paul trap

K. Okada, M. Wada, Toshiyuki Takayanagi, S. Ohtani, Hans A. Schuessler

Published Jan 28, 2010• 52 citations

Abstract

We describe a simple and fast method for simulating observed images of ion Coulomb crystals. In doing so, cold elastic collisions between Coulomb crystals and virtual very light atoms are implemented in a molecular dynamics (MD) simulation code. Such an approach reproduces the observed images of Coulomb crystals by obtaining density plots of the statistics of existence of each ion. The simple method has the advantage of short computing time in comparison with previous calculation methods. As a demonstration of the simulation, the formation of a planar Coulomb crystal with a small number of ions has been investigated in detail in a linear ion trap both experimentally and by simulation. However, also large Coulomb crystals including up to 1400 ions have been photographed and simulated to extract the secular temperature and the number of ions. For medium-sized crystals, a comparison between experiments and calculations has been performed. Moreover, an MD simulation of the sympathetic cooling of small molecular ions was performed in order to test the possibility of extracting the temperature and the number of refrigerated molecular ions from crystal images of laser-cooled ions. Such information is basic to studying ultracold ion-molecule reactions using ion Coulomb crystals including sympathetically cooled molecular ions.

DOI: 10.1103/physreva.81.013420

Related papers

Improving Molecular Dynamics Simulations of Ion Coulomb Crystals in Linear Paul Traps

Kevin M Loeffler

Molecular dynamics simulations of ion Coulomb crystals in linear Paul traps allow for the extraction of properties such as ion temperature and ion counts enabling the investigation of ion chemistry in the ultra-cold regime. These simulations reproduce experimental CCD images using density plots of simulated ions allowing for comparisons to be drawn between simulated and experimental results and providing information inaccessible to the researcher, such as the locations of clouds of non- uorescing species. In this thesis, a method for creating these simulated CCD images is presented, as well as the demonstration of a fourth order integrator for producing more accurate calculations of the ion energy. The simulation of a single frequency Paul trap is presented and the ability to match simulations with experimental parameters as inputs to experimental results is demonstrated in order to show that the simulations that have been constructed can be used to analyze experimental data and work as a predictive lab tool for future explorations of ultra-cold chemistry.

•Jan 1, 2017•0 citations

Sympathetic cooling and crystallization of ions in a linear Paul trap

Michael Drewsen, Paul David Bowe, Liv Hornekær +3 more

Coulomb crystals, containing up to a few hundred ions of which more than 50% were cooled sympathetically by the Coulomb interaction with laser cooled Mg+ ions, have been produced in a linear Paul trap. By controlling the balance of the radiation pressure from the two cooling lasers, the Coulomb crystals could be segregated according to ion species. Previous studies of ion crystals and molecular dynamics simulations suggest that the temperature may be around 10 mK or lower. The obtained results indicate that a wide range of atomic and molecular ions, which due to their internal structures are not amenable to direct laser cooling, can be effectively cooled and localized (crystallized) in linear Paul traps. For high resolution spectroscopy of such ions this may turn out to be very useful.

AIP conference proceedings•Jan 1, 1999•0 citations

Sympathetic Crystallization of Trapped Ions

Paul David Bowe, Liv Hornekær, Christina Brodersen +3 more

We have created multispecies Coulomb crystals in a linear Paul trap containing up to a few hundred ions of which more than $50%$ were cooled only sympathetically through the Coulomb interaction with laser-cooled ${\mathrm{Mg}}^{+}$ ions. In an extreme case, one laser-cooled ion maintained order in a 15 ion string. Ion species segregation was obtained by radiation pressure. Previous experiments and molecular dynamics simulations suggest the temperature is 10 mK or lower. These results indicate that a wide range of atomic and molecular ions can be cooled and localized in linear Paul traps which is important for improvements in spectroscopic studies of such ions.

Physical Review Letters•Mar 8, 1999•83 citations

Molecular-dynamics simulations of cold single-species and multispecies ion ensembles in a linear Paul trap

C. B. Zhang, David Offenberg, Bernhard Roth +2 more

The properties of cold ion plasmas with large numbers $(>200)$ of laser- and sympathetically cooled species are modeled in detail using molecular dynamics simulations. We describe how to extract temperatures and ion numbers from CCD images. The identification of the ion species by excitation of their oscillation modes is discussed. The sympathetic cooling efficiency, effects of the rf micromotion and of collision heating by a neutral background gas are analyzed, in part experimentally.

Physical Review A•Jul 30, 2007•105 citations

Ultra-cold molecules in Coulomb crystals

Bernhard Roth, U. Fröhlich, Andreas Ostendorf +2 more

Ultracold molecular hydrogen (D/sub 2//sup +/) is produced by sympathetic cooling in a linear Paul trap. With this method the translational degrees of freedom of the molecules are cooled by Coulomb interaction with laser-cooled /sup 9/Be/sup +/. This work shows that sympathetic cooling and crystallization is possible down to mass ratios of 0.45. Using molecular dynamics simulations, the mass range for sympathetic cooliing is predicted. By employin a light and a heavy species of laser-cooled ions (/sup 9/Be/sup +/ and e.g. /sup 137/Ba/sup +/) the mass range from 2 to 20 000 amu, i.e. from the simplest molecule to complex proteins, can be sympathetically cooled.

European Quantum Electronics Conference (EQEC)•Jan 1, 2003•1 citation

Structural and energetic properties of molecular Coulomb crystals in a surface-electrode ion trap

Arezoo Mokhberi, Stefan Willitsch

Cold molecular ions are of great interest for applications in cold collision studies, chemistry, precision spectroscopy and quantum technologies. In this context, sympathetic cooling of molecular ions by the interaction with laser-cooled atomic ions is a powerful method to cool their translational motion and achieve translational temperatures in the millikelvin range. Recently, we implemented this method in a surface-electrode ion trap. The flexibility in shaping the trapping potentials offered by the surface-electrode structure enabled us to generate planar bicomponent Coulomb crystals and spatially separate the molecular from the atomic ions. Here, we present a detailed description of the fabrication and simulation of the trap as well as a theoretical and experimental investigation of the structural and energetic properties of the Coulomb crystals obtained in the device. We discuss in more detail the separation of different ion species using static electric fields and explore the effects of trap anharmoncities on the shape of bicomponent crystals.

New Journal of Physics•Apr 16, 2015•8 citations

We describe a simple and fast method for simulating observed images of ion Coulomb crystals. In doing so, cold elastic collisions between Coulomb crystals and virtual very light atoms are implemented in a molecular dynamics (MD) simulation code. Such an approach reproduces the observed images of Coulomb crystals by obtaining density plots of the statistics of existence of each ion. The simple method has the advantage of short computing time in comparison with previous calculation methods. As a demonstration of the simulation, the formation of a planar Coulomb crystal with a small number of ions has been investigated in detail in a linear ion trap both experimentally and by simulation. However, also large Coulomb crystals including up to 1400 ions have been photographed and simulated to extract the secular temperature and the number of ions. For medium-sized crystals, a comparison between experiments and calculations has been performed. Moreover, an MD simulation of the sympathetic cooling of small molecular ions was performed in order to test the possibility of extracting the temperature and the number of refrigerated molecular ions from crystal images of laser-cooled ions. Such information is basic to studying ultracold ion-molecule reactions using ion Coulomb crystals including sympathetically cooled molecular ions.

Molecular dynamics simulations of ion Coulomb crystals in linear Paul traps allow for the extraction of properties such as ion temperature and ion counts enabling the investigation of ion chemistry in the ultra-cold regime. These simulations reproduce experimental CCD images using density plots of simulated ions allowing for comparisons to be drawn between simulated and experimental results and providing information inaccessible to the researcher, such as the locations of clouds of non- uorescing species. In this thesis, a method for creating these simulated CCD images is presented, as well as the demonstration of a fourth order integrator for producing more accurate calculations of the ion energy. The simulation of a single frequency Paul trap is presented and the ability to match simulations with experimental parameters as inputs to experimental results is demonstrated in order to show that the simulations that have been constructed can be used to analyze experimental data and work as a predictive lab tool for future explorations of ultra-cold chemistry.

Coulomb crystals, containing up to a few hundred ions of which more than 50% were cooled sympathetically by the Coulomb interaction with laser cooled Mg+ ions, have been produced in a linear Paul trap. By controlling the balance of the radiation pressure from the two cooling lasers, the Coulomb crystals could be segregated according to ion species. Previous studies of ion crystals and molecular dynamics simulations suggest that the temperature may be around 10 mK or lower. The obtained results indicate that a wide range of atomic and molecular ions, which due to their internal structures are not amenable to direct laser cooling, can be effectively cooled and localized (crystallized) in linear Paul traps. For high resolution spectroscopy of such ions this may turn out to be very useful.

We have created multispecies Coulomb crystals in a linear Paul trap containing up to a few hundred ions of which more than

50%

were cooled only sympathetically through the Coulomb interaction with laser-cooled

{\mathrm{Mg}}^{+}

ions. In an extreme case, one laser-cooled ion maintained order in a 15 ion string. Ion species segregation was obtained by radiation pressure. Previous experiments and molecular dynamics simulations suggest the temperature is 10 mK or lower. These results indicate that a wide range of atomic and molecular ions can be cooled and localized in linear Paul traps which is important for improvements in spectroscopic studies of such ions.

The properties of cold ion plasmas with large numbers

(>200)

of laser- and sympathetically cooled species are modeled in detail using molecular dynamics simulations. We describe how to extract temperatures and ion numbers from CCD images. The identification of the ion species by excitation of their oscillation modes is discussed. The sympathetic cooling efficiency, effects of the rf micromotion and of collision heating by a neutral background gas are analyzed, in part experimentally.

Ultracold molecular hydrogen (D/sub 2//sup +/) is produced by sympathetic cooling in a linear Paul trap. With this method the translational degrees of freedom of the molecules are cooled by Coulomb interaction with laser-cooled /sup 9/Be/sup +/. This work shows that sympathetic cooling and crystallization is possible down to mass ratios of 0.45. Using molecular dynamics simulations, the mass range for sympathetic cooliing is predicted. By employin a light and a heavy species of laser-cooled ions (/sup 9/Be/sup +/ and e.g. /sup 137/Ba/sup +/) the mass range from 2 to 20 000 amu, i.e. from the simplest molecule to complex proteins, can be sympathetically cooled.

Cold molecular ions are of great interest for applications in cold collision studies, chemistry, precision spectroscopy and quantum technologies. In this context, sympathetic cooling of molecular ions by the interaction with laser-cooled atomic ions is a powerful method to cool their translational motion and achieve translational temperatures in the millikelvin range. Recently, we implemented this method in a surface-electrode ion trap. The flexibility in shaping the trapping potentials offered by the surface-electrode structure enabled us to generate planar bicomponent Coulomb crystals and spatially separate the molecular from the atomic ions. Here, we present a detailed description of the fabrication and simulation of the trap as well as a theoretical and experimental investigation of the structural and energetic properties of the Coulomb crystals obtained in the device. We discuss in more detail the separation of different ion species using static electric fields and explore the effects of trap anharmoncities on the shape of bicomponent crystals.