Multi-Modal Properties and Dynamics of the Gradient Echo Quantum Memory

We investigate the properties of a recently proposed Gradient Echo Memory (GEM) scheme for information mapping between optical and atomic systems. We show that GEM can be described by the dynamic formation of polaritons in k-space. This picture highlights the flexibility and robustness with regards to the external control of the storage process. Our results also show that, as GEM is a frequency-encoding memory, it can accurately preserve the shape of signals that have large time-bandwidth products, even at moderate optical depths. At higher optical depths, we show that GEM is a high fidelity multi-mode quantum memory.