  Long-range quantum communication requires the development of in-out
light-matter interfaces to achieve a quantum advantage in entanglement
distribution. Ideally, these quantum interconnections should be as fast as
possible to achieve high-rate entangled qubits distribution. Here, we
demonstrate the coherent quanta exchange between single photons generated
on-demand from a GaAs quantum dot and atomic ensemble in a $^{87}$Rb vapor
quantum memory. Through an open quantum system analysis, we demonstrate the
mapping between the quantized electric field of photons and the coherence of
the atomic ensemble. Our results play a pivotal role in understanding quantum
light-matter interactions at the short time scales required to build fast
hybrid quantum networks.
