  A classical logic gate connecting input and output light pulses is
demonstrated. The gate operation is based on three steps: First, two incoming
light pulses are stored in a Bose-Einstein condensate, second, atomic four-wave
mixing generates a new matter wave, and third, the light pulses are retrieved.
In the presence of the new matter wave, the retrieval generates a new optical
wave. The latter will only be generated if both input light pulses are applied,
thus realizing an AND gate. Finally, we show that the gate operation is phase
coherent, an essential prerequisite for a quantum logic gate.
