Spin wave diffraction control and read-out with a quantum memory for light

A scheme for control and read-out of diffracted spins waves to propagating light fields is presented. Diffraction is obtained via sinusoidally varying lights shifts and ideal one-to-one mapping to light is realized using a gradient echo quantum memory. We also show that dynamical control of the diffracted spin waves spatial orders can be implemented to realize a quantum pulse sequencer for temporal modes that have high time-bandwidth products. Full numerical solutions suggest that both co-propagating and counter propagating light shift geometries can be used, making the proposal applicable to hot and cold atomic vapours as well as solid state systems with two-level atoms.