  We theoretically explore coherent information transfer between ultra-slow
light pulses and Bose-Einstein condensates (BECs) and find that storing light
pulses in BECs, by switching off the coupling field, allows the coherent
condensate dynamics to process optical information. We develop a formalism,
applicable in both the weak and strong probe regimes, to analyze such
experiments and establish several new results. Investigating examples relevant
to Rb-87 experimental parameters we see a variety of novel two-component BEC
dynamics occur during the storage, including interference fringes, gentle
breathing excitations, and two-component solitons. We find the dynamics when
the levels |F=1, M_F=-1> and |F=2, M_F=+1> are well suited to designing
controlled processing of the information. By switching the coupling field back
on, the processed information is rewritten onto probe pulses which then
propagate out as slow light pulses. We calculate the fidelity of information
transfer between the atomic and light fields upon the switch-on and subsequent
output. The fidelity is affected both by absorption of small length scale
features and absorption of regions of the pulse stored near the condensate
edge. In the strong probe case, we find that when the oscillator strengths for
the two transitions are equal the fidelity is not strongly sensitive to the
probe strength, while when they are unequal the fidelity is worse for stronger
probes. Applications to distant communication between BECs, squeezed light
generation and quantum information are anticipated.
