  The black-hole laser (BHL) effect is the self-amplification of Hawking
radiation between a pair of horizons which act as a resonant cavity. In a
flowing atomic condensate, the BHL effect arises in a finite supersonic region,
where Bogoliubov-Cherenkov-Landau (BCL) radiation is resonantly excited by any
static perturbation. Thus, experimental attempts to produce a BHL unavoidably
deal with the presence of a strong BCL background, making the observation of
the BHL effect still a major challenge in the analogue gravity field. Here, we
perform a theoretical study of the BHL-BCL crossover using an idealized model
where both phenomena can be unambiguously isolated. By drawing an analogy with
an unstable pendulum, we distinguish three main regimes according to the
interplay between quantum fluctuations and classical stimulation: quantum BHL,
classical BHL, and BCL. Based on quite general scaling arguments, the nonlinear
amplification of quantum fluctuations up to saturation is identified as the
most robust trait of a quantum BHL. A classical BHL behaves instead as a linear
quantum amplifier, where the output is proportional to the input. The BCL
regime also acts as a linear quantum amplifier, but its gain is exponentially
smaller as compared to a classical BHL. Complementary signatures of black-hole
lasing are a decrease in the amplification for increasing BCL amplitude or a
nonmonotonic dependence of the growth rate with respect to the background
parameters. We also identify interesting analogue phenomena such as
Hawking-stimulated white-hole radiation or quantum BCL-stimulated Hawking
radiation. The results of this work not only are of interest for analogue
gravity, where they help to distinguish each phenomenon and to design
experimental schemes for a clear observation of the BHL effect, but they also
open the prospect of finding applications of analogue concepts in quantum
technologies.
