Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening

We present a detailed analysis of a quantum memory for photons based on controlled and reversible inhomogeneous broadening (CRIB). The explicit solution of the equations of motion is obtained in the weak excitation regime, making it possible to gain insight into the dependence of the memory efficiency on the optical depth, and on the width and shape of the atomic spectral distributions. We also study a simplified memory protocol which does not require any optical control fields.