  The realization of quantum networks and quantum repeaters remains an
outstanding challenge in quantum communication. These rely on entanglement of
remote matter systems, which in turn requires creation of quantum correlations
between a single photon and a matter system. A practical way to establish such
correlations is via spontaneous Raman scattering in atomic ensembles, known as
the DLCZ scheme. However, time multiplexing is inherently difficult using this
method, which leads to low communication rates even in theory. Moreover, it is
desirable to find solid-state ensembles where such matter-photon correlations
could be generated. Here we demonstrate quantum correlations between a single
photon and a spin excitation in up to 12 temporal modes, in a $^{151}$Eu$^{3+}$
doped Y$_2$SiO$_5$ crystal, using a novel DLCZ approach that is inherently
multimode. After a storage time of 1 ms, the spin excitation is converted into
a second photon. The quantum correlation of the generated photon pair is
verified by violating a Cauchy - Schwarz inequality. Our results show that
solid-state rare-earth crystals could be used to generate remote multi-mode
entanglement, an important resource for future quantum networks.
