nK. The sweep generates a low-density “cavity" of supersonic flow in the interior of the BEC, bounded by black-hole (BH) and white-hole (WH) horizons \[Figs. \[fig:exp\](a)-(c)\]. Steinhauer observed exponential growth of a standing wave between the horizons, and measured the density-density, two-point, connected correlation function, which displayed correlations between points within the cavity, as well as between a point in the cavity and a point outside the BH. He interpreted the latter as a signal of Hawking radiation phonons correlated with their partners behind the horizon, and he interpreted the growing standing wave and internal correlation function as evidence for self-amplifying Hawking radiation.

In a flow with a supersonic cavity bounded by BH and WH horizons, Hawking radiation can be self-amplifying if the phonon group velocity becomes supersonic at high wavenumbers[@jacobson1999]. The negative energy partner of a Hawking phonon is trapped in the cavity, so that the parent state for subsequent Hawking radiation is no longer the vacuum, but instead is an excited state. This produces stimulated emission of Hawking radiation, which amplifies the trapped negative energy mode. The repetition of this process leads to exponential growth of the negative energy mode and the associated Hawking emission. This is called 