We study the process of decoherence in acoustic black holes. We focus on the ion trap model proposed by Horstmann et al. [Phys. Rev. Lett. 104, 250403 (2010)], but the formalism is general to any experimental implementation. For that particular setup, we compute the decoherence time for the experimental parameters that they proposed. We find that a quantum to classical transition occurs during the measurement, and we propose improved parameters to avoid such a feature. We also study the entanglement between the Hawking-pair phonons for an acoustic black hole while in contact with a reservoir, through the quantum correlations, showing that they remain strongly correlated for small enough times and temperatures.
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