  Quantum networks consisting of quantum memories and photonic interconnects
can be used for entanglement distribution (L.-M.Duan and H. J. Kimble, PRL 90,
253601 (2003), H. J. Kimble, Nat. 453, 1023 EP (2008)), quantum teleportation
(S.Pirandola et.al, Nat. Photon. 9, 641 (2015)), and distributed quantum
computing (T.Spiller, et.al., New J. Phys. 8, 30 (2006). Remotely connected
two-node networks have been demonstrated using memories of the same type:
trapped ion systems (D.Hucul, et.al, Nat. Phys. 11, 37 (2014)), quantum dots
(W. B. Gao et. al, Nat. Photon. 9, 363 (2015)), and nitrogen vacancy centers
(W. B. Gao et. al, Nat. Photon. 9, 363 (2015), B. Hensen, et. al., Nat. 526,
682 (2015)). Hybrid systems constrained by the need to use photons with the
native emission wavelength of the memory, have been demonstrated between a
trapped ion and quantum dot (H.Meyer et.al PRL 114, 123001 (2015)) and between
a single neutral atom and a Bose-Einstein Condensate (M.Lettner et. al, PRL
106, 210503 (2011)). Most quantum systems operate at disparate and incompatible
wavelengths to each other so such two-node systems have never been
demonstrated. Here, we use a trapped 138Ba$^{+}$ ion and a periodically poled
lithium niobate (PPLN) waveguide, with a fiber coupled output, to demonstrate
19% end-to-end efficient quantum frequency conversion (QFC) of single photons
from 493 nm to 780 nm. At the optimal signal-to-noise operational parameter, we
use fluorescence of the ion to produce light resonant with the $^{87}$Rb $D_2$
transition. To demonstrate the quantum nature of both the unconverted 493 nm
photons and the converted photons near 780 nm, we observe strong quantum
statics in their respective second order intensity correlations. This work
extends the range of intra-lab networking between ions and networking and
communication between disparate quantum memories. A
