Black-hole lasing in Bose–Einstein condensates: analysis of the role of the dynamical instabilities in a nonstationary setup

Abstract

We present a theoretical study on the origin of some findings of recent experiments on sonic analogs of gravitational black holes (BHs). We focus on the realization of a BH lasing configuration, where the conclusive identification of stimulated Hawking radiation (HR) requires dealing with the implications of the nonstationary character of the setup. To isolate the basic mechanisms responsible for the observed behavior, we use a toy model where nonstationarity can be described in terms of departures from adiabaticity. Our approach allows one to study which aspects of the characterization of BH lasing in static models are still present in a dynamical scenario. In particular, variations in the role of the dynamical instabilities can be traced. Arguments to conjecture the twofold origin of the detected amplification of sound are given: the differential effect of the instabilities on the mean field and on the quantum fluctuations gives some clues to separate a deterministic component from self-amplified HR. The role of classical noise, present in the experimental setup, is also tackled: we discuss the emergence of differences with the effect of quantum fluctuations when various unstable modes are relevant to the dynamics.