  It has been proposed that a black hole horizon should generate Hawking
radiation. In order to test this theory, we have created a narrow, low density,
very low temperature atomic Bose-Einstein condensate, containing an analog
black hole horizon and an inner horizon, as in a charged black hole. We observe
Hawking radiation emitted by the black hole. This is the output of the black
hole laser. We also observe the exponential growth of a standing wave between
the horizons. The latter results from interference between the negative energy
partners of the Hawking radiation and the negative energy particles reflected
from the inner horizon. We thus observe self-amplifying Hawking radiation.
