Scalable, efficient ion-photon coupling with phase Fresnel lenses for   large-scale quantum computing
  Efficient ion-photon coupling is an important component for large-scale ion-trap quantum computing. We propose that arrays of phase Fresnel lenses (PFLs) are a favorable optical coupling technology to match with multi-zone ion traps. Both are scalable technologies based on conventional micro-fabrication techniques. The large numerical apertures (NAs) possible with PFLs can reduce the readout time for ion qubits. PFLs also provide good coherent ion-photon coupling by matching a large fraction of an ion's emission pattern to a single optical propagation mode (TEM00). To this end we have optically characterized a large numerical aperture phase Fresnel lens (NA=0.64) designed for use at 369.5 nm, the principal fluorescence detection transition for Yb+ ions. A diffraction-limited spot w0=350+/-15 nm (1/e^2 waist) with mode quality M^2= 1.08+/-0.05 was measured with this PFL. From this we estimate the minimum expected free space coherent ion-photon coupling to be 0.64%, which is twice the best previous experimental measurement using a conventional multi-element lens. We also evaluate two techniques for improving the entanglement fidelity between the ion state and photon polarization with large numerical aperture lenses. 
E.W. Streed, B.G. Norton, J.J. Chapman, and D. Kielpinski