  We demonstrate the storage and retrieval of an on-demand single photon
generated by a collective Rydberg excitation in an ultra-low noise Raman
quantum memory located in a different cold atomic ensemble. We generate single
photons on demand by exciting a cold cloud of Rubidium atoms off resonantly to
a Rydberg state, with a generation probability up to 15 $\%$ per trial. We then
show that the single photons can be stored and retrieved with an efficiency of
21 $\%$ and a noise floor of $p_n= 2.3(3) \times 10^{-4}$ per trial in the
Raman quantum memory. This leads to a signal-to-noise ratio ranging from 11 to
26 for the retrieved single photon depending on the input photon generation
probability, which allows us to observe significant antibunching. We also
evaluate the performances of the Raman memory as built-in unbalanced temporal
beam splitter, tunable by varying the write-in control pulse intensity. In
addition, we demonstrate that the Raman memory can be used to control the
single-photon waveshape. These results are a step forward in the implementation
of efficient quantum-repeater links using single-photon sources.
