  Efficient collection and analysis of trapped ion qubit fluorescence is
essential for robust qubit state detection in trapped ion quantum computing
schemes. We discuss simple techniques of improving photon collection efficiency
using high numerical aperture (N.A.) reflective optics. To test these
techniques we placed a spherical mirror with an effective N.A. of about 0.9
inside a vacuum chamber in the vicinity of a linear Paul trap. We demonstrate
stable and reliable trapping of single barium ions, in excellent agreement with
our simulations of the electric field in this setup. While a large N.A.
spherical mirror introduces significant spherical aberration, the ion image
quality can be greatly improved by a specially designed aspheric corrector lens
located outside the vacuum system. Our simulations show that the spherical
mirror/corrector design is an easy and cost-effective way to achieve high
photon collection rates when compared to a more sophisticated parabolic mirror
setup.
