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Bulletin of the American Physical Society

Analytical methods for design of surface-electrode ion traps

Janus H. Wesenberg, Jason Amini, R. B. Blakestad, J. Britton, Kenneth R. Brown, R. J. Epstein, Jonathan Home, Wayne M. Itano, John D. Jost, C. Langer, Dietrich G. Leibfried, Roee Ozeri, Signe Louise Seidelin, David J. Wineland

Published Jun 7, 2007• 1 citation
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The design of surface-electrode ion traps is studied analytically. The classical motion of a single ion in such a trap is described by coupled Mathieu equations. An analytic boundary-value solution for the Laplace equation in three dimensions with a piecewise-constant Dirichlet boundary condition is described. This solution is used to model the electrostatic potential field generated by a series of electrodes lying in a single plane. The model is applied to the problem of designing surface-electrode ion traps, including calculating important trap design parameters such as the center position of the trapped ion, trap depth, and stability parameters. The model is used to determine optimized dimensions for trap electrodes in various cases.
To realize scale quantum processors, the surface-electrode ion trap is an effective scaling approach, including single-layer, double-layer, and quasi-double-layer traps. To calculate critical trap parameters such as the trap center and trap depth, the finite element method (FEM) simulation was widely used, however, it is always time consuming. Moreover, the FEM simulation is also incapable of exhibiting the direct relationship between the geometry dimension and these parameters. To eliminate the problems above, House and Madsen et al. have respectively provided analytic models for single-layer traps and double-layer traps. In this paper, we propose a semi-analytical model for quasi-double-layer traps. This model can be applied to calculate the important parameters above of the ion trap in the trap design process. With this model, we can quickly and precisely find the optimum geometry design for trap electrodes in various cases.
We describe a new electrode design for a grooved surface-electrode ion trap, which is fabricated in printed-circuit-board technology with segmented electrodes. This design allows a laser beam to get through the central groove to avoid optical access blocking and laser scattering from the ion trap surface. The confining potentials are modeled both analytically and numerically. We optimize the radio frequency (rf) electrodes and dc electrodes to achieve the maximum trap depth for a given ion height above the trap electrodes. We also compare our design with the reality ion chip MI I for practical considerations. Comparison results show that our design is superior to MI I. This ion trap design may form the basis for large scale quantum computers or parallel quadrupole mass spectrometers.