Photonic quantum memory in two-level ensembles based on modulating the refractive index in time: Equivalence to gradient echo memory

We present a quantum memory protocol that allows us to store light in ensembles of two-level atoms, e. g., rare-earth-metal ions doped into a crystal, by modulating the refractive index of the host medium of the atoms linearly in time. We show that under certain conditions the resulting dynamics is equivalent to that underlying the gradient echo memory protocol, which relies on a spatial gradient of the atomic resonance frequencies. We discuss the prospects for an experimental implementation.