Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

Paul–Straubel–Kingdon trap for true zero-point confinement of an individual ion and reservoir

A modification of the Paul–Straubel trap previously described by us may profitably be operated in a Paul–Straubel–Kingdon (PSK) mode during the initial loading of an individual ion into the trap. Thereby the coating of the trap ring electrode by the atomic beam directed upon it in earlier experiments is eliminated, as is the ionization of an already trapped ion. Coating created serious problems as it spot-wise changed the work function of the ring electrode, which caused large, uncontrolled dc fields in the trap center that prevented zero-point confinement. Operating the Paul–Straubel trap with a small negative bias on the ring electrode wire is all that is required to realize the PSK mode. In this mode the tiny ring trap in the center of the long, straight wire section is surrounded by a second trapping well shaped like a long, thin-walled cylindrical shell and extending to the end-caps. There, ions may be conveniently created in this well without danger of coating the ring with barium. In addition, the long second well is useful as a multi-ion reservoir.

Excitation transfer spectroscopy with two metastable 138Ba+ ions in same trap.

In the absence of lasers approaching trapped ion clock transitions in sharpness we propose to replace the 12.49 m laser field exciting the D3/2-D5/2 transition of the single Ba+ ion A in D3/2 with the near-field of a close by identical ion B in the excited D5/2 state. We tune the frequency of the near-field by the differential Stark shift generated when the center of mass of the tuned ions is slightly moved out of the trap center by a small bias voltage. We demonstrate that the resultant resonant energy exchange can be made considerably faster than the natural lifetime of either metastable level and show how it might be detected.