  We present a detailed analysis of a high-bandwidth quantum memory protocol
for storing single photons in a rare-earth-ion doped crystal. The basic idea is
to benefit from a coherent free-induced decay type re-emission which occurs
naturally when a photon with a broadband spectrum is absorbed by a narrow
atomic transition in an optically dense ensemble. This allows for a
high-bandwidth memory for realistic material parameters. Long storage time and
on-demand readout are obtained by means of spins states in a lambda-type
configuration, through the transfer of the optical coherence to a spin
coherence (so-called spin-wave storage). We give explicit formulas and show
numerical results which make it possible to gain insight into the dependence of
the memory efficiency on the optical depth and on the width and the shape of
stored photons. We present a feasibility study in rare-earth doped crystals and
show that high efficiencies and high bandwidth can be obtained with realistic
parameters. High-bandwidth memories using spin-wave storage offers the
possibility of very high time-bandwidth products, which is important for
experiment where high repetition rates are needed.
