  We reexamine the well-known Duan-Kimble entanglement scheme, wherein the
state of a single-photon qubit is entangled with a quantum memory consisting of
a single-atom qubit in a strongly coupled optical cavity, providing the
capability to load the photon's state into the memory. We correct a common
error appearing in some subsequent papers regarding the validity of the
single-photon reflectivity function that characterizes the essential phase
shift at the heart of the protocol. Using the validated analytical solution, we
introduce an improved scheme-the push-pull configuration-where the photon and
cavity are tuned at the midpoint between atomic resonances and show that it can
outperform the original on-off configuration in which the photon and cavity are
tuned exactly to one of the atomic resonances. The performance metric used is
the final memory-state fidelity versus the heralding probability, which
determines the memory loading rate. The results should play a role in
optimizing future quantum repeater schemes based on the Duan-Kimble protocol.
