  We study the bandwidth and multiplexing capacity of an erbium-doped optical
memory for quantum storage purposes. We concentrate on the protocol ROSE
(Revival of a Silenced Echo) because it has the largest potential multiplexing
capacity. Our analysis is applicable to other protocols that involve strong
optical excitation. We show that the memory performance is limited by
instantaneous spectral diffusion and we describe how this effect can be
minimised to achieve optimal performance.
