Dynamics of an acoustic black hole as an open quantum system

Abstract

We study the process of decoherence induced by the presence of an environment in acoustic black holes, using the open quantum system approach, thus extending previous work. We focus on the ion trap model but the formalism is general to any experimental implementation. We compute the decoherence time for that setup. We find that a quantum-to-classical transition occurs during the measurement and we propose improved parameters to avoid such a feature. We provide analytic estimations for both zero and finite temperature. 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. We use the stochastic formalism and the method of characteristic to solve the field wave equation.