---
abstract: 'We model a sonic black hole analog in a quasi one-dimensional Bose-Einstein condensate, using a Gross-Pitaevskii equation matching the configuration of a recent experiment by Steinhauer \[Nat. Phys. [**10**]{}, 864 (2014)\]. The model agrees well with important features of the experimental observations, demonstrating their hydrodynamic nature. We find that a zero-frequency bow wave is generated at the inner (white hole) horizon, which grows in proportion to the square of the background condensate density. The relative motion of the black and white hole horizons produces a Doppler shift of the bow wave at the black hole, where it stimulates the emission of monochromatic Hawking radiation. The mechanism is confirmed using temporal and spatial windowed Fourier spectra of the condensate. Mean field behavior similar to that in the experiment can thus be fully explained without the presence of self-amplifying Hawking radiation.'
author:
- 'Yi-Hsieh Wang$^{1,2}$'
- 'Ted Jacobson$^{3}$'
- 'Mark Edwards$^{1,4}$'
- 'Charles W. Clark$^{1,2}$'
bibliography:
- 'HawkingCondensateFinal.bib'
title: 'Mechanism of stimulated Hawking radiation in a laboratory Bose-Einstein condensate'
---

Introduction and Summary {#sec:intro}
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Hawking radiation [@hawking1; @hawking2] is a pair creation process, resulting from a vacuum instability of quantum fields at a black hole horizon. The radiation is 