  We propose a quantum optical interface between an atomic and solid state
system. We show that quantum states in a single trapped atom can be entangled
with the states of a semiconductor quantum dot through their common interaction
with a classical laser field. The interference and detection of the resulting
scattered photons can then herald the entanglement of the disparate atomic and
solid-state quantum bits. We develop a protocol that can succeed despite a
significant mismatch in the radiative characteristics of the two matter-based
qubits. We study in detail a particular case of this interface applied to a
single trapped \Yb ion and a cavity-coupled InGaAs semiconductor quantum dot.
Entanglement fidelity and success rates are found to be robust to a broad range
of experimental nonideal effects such as dispersion mismatch, atom recoil, and
multi-photon scattering. We conclude that it should be possible to produce
highly entangled states of these complementary qubit systems under realistic
experimental conditions.
