pattern with periodicity very close to that of the standing wave. The growth of the checkerboard pattern was quantified in [@nphys3104] via the Fourier power spectrum of the correlation, and found to grow by a factor $\sim\exp(3.3)$. In [@correlations] we have shown, by introducing quantum and atom-number fluctuations into our simulations, that this checkerboard pattern results directly from the presence of the underlying BCR standing wave, modulated by the fluctuations.

### Spacetime portrait {#sec:BCRStim}

In this subsection we present a spacetime portrait for the evolving BEC. This portrait illustrates by visual inspection that the standing wave is generated from the WH, and has zero frequency in the WH reference frame. Its frequency in the step frame is nonzero, due to a Doppler shift arising because the WH recedes from the BH as the system evolves. The spacetime portrait also reveals a signal of Hawking radiation, which is stimulated by the BCR at the BH. We further verify this mechanism quantitatively through a windowed frequency spectrum evaluated inside the cavity, which reveals that the only frequencies present are those of the background condensate and the BCR.

![image](bhbec_evolution_072117){width="7in"}

The spacetime portrait for the simulated experiment, Fig. \[fig:stimulated\_HR\](b), displays $|\delta\Psi|=|\Psi-\bar\Psi|$. To resolve the 