---
abstract: 'Hybrid quantum information protocols are based on local qubits, such as trapped atoms, NV centers, and quantum dots, coupled to photons. The coupling is achieved through optical cavities. Here we demonstrate far-field optimized H1 photonic crystal membrane cavities combined with an additional back reflection mirror below the membrane that meet the optical requirements for implementing hybrid quantum information protocols. Using numerical optimization we find that 80$\%$ of the light can be radiated within an objective numerical aperture of 0.8, and the coupling to a single-mode fiber can be as high as 92$\%$. We experimentally prove the unique external mode matching properties by resonant reflection spectroscopy with a cavity mode visibility above 50$\%$.'
address: |
    $^1$Physics Department, University of California Santa Barbara, Santa Barbara, California 93106, USA\
    $^2$Huygens Laboratory, Leiden University, PO Box 9504, 2300 RA Leiden, The Netherlands\
    $^3$Materials Department, University of California Santa Barbara, Santa Barbara, California 93106, USA\
    $^4$ECE Department, University of California Santa Barbara, Santa Barbara, California 93106, USA\
    $^a$These authors contributed equally to this work.\
    $^b$Present address: ECE Department, IREAP, University of Maryland, College Park, Maryland 20742, USA\
    $^c$Present address: Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 