I bet that isn't an alligator. It's a real crocodile (Crocodylus spec.) instead. I don't know what kind of crocodiles Nationalzoo Washington is keeping at the moment. Ref. coloration/pattern it MIGHT be a Cuban crocodile (Crocodylus rhombifer).
It is actually a Philippine Crocodile (Crocodylus mindorensis). The banding is an identifying feature (Cubans are usually more blotched than banded), but I also recognized this individual and enclosure from another photo taken around the same time:
