  Quantum interfaces between photons and ensembles of atoms have emerged as
powerful tools for quantum technologies. A major objective for such interfaces
is high fidelity storage and retrieval of a photon in a collective quantum
state of many atoms. This requires long-lived collective superposition states,
which is typically achieved with immobilized atoms. Thermal atomic vapors,
which present a simple and scalable resource, have, so far, only been used for
continuous variable processing or for discrete variable processing on short
time scales where atomic motion is negligible. We develop a theory based on the
concept of motional averaging to enable room temperature discrete variable
quantum memories and coherent single photon sources. We show that by choosing
the interaction time so that atoms kept under spin protecting conditions can
cross the light beam several times during the interaction combined with
suitable spectral filtering, we erase the "which atom" information and obtain
an efficient and homogenous coupling between all atoms and the light. Heralded
single excitations can thus be created and stored as collective spinwaves,
which can later be read out to produce coherent single photons in a scalable
fashion. We demonstrate the feasibility of this approach to scalable quantum
memories with a proof-of-principle experiment with room temperature atoms
contained in microcells with spin protecting coating, placed inside an optical
cavity. The experiment is performed at conditions corresponding to a few
photons per pulse and clearly demonstrates a long coherence time of the forward
scattered photons, which is the essential feature of the motional averaging.
