1. PROPERTIES OF TRAPPED Ca+ IONS
James Oldham, University of Oxford
63rd Molecular Spectroscopy Symposium
17th June 2008

2. Introduction Motivation and Experimental Apparatus Simulation Model
Findings from Simulations
Motions of Trapped Ions
Ion Temperature Dependencies
Bi-component Crystals
Conclusions

3. Motivation
Provide theoretical data about Coulomb crystals in context of current experiments.
Determine thermal properties of ions in a crystal which will affect collision energies:
Dependence on trap parameters.
Dependence on ion positions.
Determine extent that time-dependent potential changes ion energies.
Investigate positions of reactant and product ions in bi-component crystals seen during a reaction.

4. Experimental Apparatus
Photo-ionised Ca+ trapped with linear RF (Paul) trap.
Primarily cooled with 397nm diode laser.
866nm diode laser used to repump ion population from metastable 2D3/2.

5. Coulomb Crystals ‘Condensed’ state of a one-component plasma
Arises from equilibrium between trapping and repulsive Coulomb forces.
Molecular dynamics (MD) simulations provide details such as ion energies, positions of non-fluorescing ions.

6. Modelling Trapped Ca+ Ions

7. Simulation of a Coulomb Crystal
Simulated image of 1080 Ca+ Coulomb crystal

8. Types of Ion Motion Ion motion comprised of :
secular motion, random thermal motion of ions;
micromotion, high frequency ordered motion induced by RF field.
In adiabatic regime, types of motion are independent of one another.

9. How hot are the ions?
Two different kinetic energies can be attributed to ions:
Secular energy
Effective energy
Secular distributions match Boltzmann distributions at equal Tsec.
No match between effective energy and Boltzmann distributions.
Secular velocity distribution of a 2685Ca+ Coulomb crystal with mean secular temperature of 15mK, and corresponding Boltzmann distribution.

10. Ion Secular Temperatures
Varying magnitude of heating force alters Tsec in simulations.
Tsec of experimental crystals obtained by comparing experimental and simulated images.
Micromotion has negligible impact on images.

11. Effective Energies of Ions
Experimental images of an ion string and prolate and oblate crystals.
For a trapped ion,
Average radial ion displacement increases for larger or more oblate crystals.
Greater range of energies expected for large/oblate crystals.

12. Effective Energy Distributions
Distributions formed by taking ion effective energies over many timesteps in simulation.
Distributions dependent on number of ions and shape of crystal
Clear shell structures of crystals seen.
Changing secular temperature of ions has little effect on distribution.

13. Reaction Progression
Simulated images of bi-component crystals replicate experimental images.
Imply product ions formed and trapped experimentally.
CaF+ reside at greater radial distances than Ca+.

14. Conclusions
Experimental crystals accurately reproduced by use of time-dependent MD simulation, allowing greater knowledge of crystals, including kinetic energy profiles including and excluding micromotion.
Trap parameters and shape/size of crystal strongly affect effective energies of ions, although secular temperatures not significantly dependent.
Micromotion generally dominates kinetic energy of a radially displaced ion.
Simulations of bi-component crystals indicate that product ions are formed when CH3F is present in chamber.

15. Acknowledgements Alex Gingell Martin Bell Dr. Stefan Willitsch
Prof. Tim Softley
EPSRC