  The coherent coupling of flying photonic qubits to stationary matter-based
qubits is an essential building block for quantum communication networks. We
show how such a quantum interface can be realized between a traveling-wave
optical field and the polarized nuclear spins in a singly charged quantum dot
strongly coupled to a high-finesse optical cavity. By adiabatically eliminating
the electron a direct effective coupling is achieved. Depending on the laser
field applied, interactions that enable either write-in or read-out are
obtained.
