Analytical methods for design of surface-electrode ion traps

Surface-electrode ion traps\footnote{J. Chiaverini et al., Quantum Inf. Comput. 5, 419 (2005).}$^,$\footnote{S. Seidelin et al., Phys. Rev. Lett. 96, 253003 (2006).} are promising candidates for the large scale multi-zone ion traps which are required for large scale quantum information processing. Electrode design for surface-electrode traps is complicated by the low symmetry and the large exposed electrode area. We apply a simple method\footnote{M. H. Oliveira et al., Eur. J. Phys. 22, 31 (2001).} to obtain analytical expressions for the field of arbitrarily shaped surface-electrodes. The efficiency of this method compared to traditional boundary (BEM) or finite (FEM) element methods has allowed us to use numerical optimization techniques to help in the design of advanced trap structures, such as intersections and ion separation zones. Work supported by DTO and NIST. J.H.W. acknowledges support from the Danish Research Agency.