  Superradiant instabilities can trigger the formation of bosonic clouds around
rotating black holes. If the bosonic field growth is sufficiently fast, these
clouds could form shortly after a binary black hole merger. Such clouds are
continuous sources of gravitational waves whose detection (or lack thereof) can
probe the existence of ultralight bosons (such as axion-like particles) and
their properties. Motivated by the binary black hole mergers seen by Advanced
LIGO so far, we investigate in detail the parameter space that can be probed
with continuous gravitational wave signals from ultralight scalar field clouds
around black hole merger remnants with particular focus on future ground-based
detectors (A+, Voyager and Cosmic Explorer). We also study the impact that the
confusion noise from a putative stochastic gravitational-wave background from
unresolved sources would have on such searches and we estimate, under different
astrophysical priors, the number of binary black-hole merger events that could
lead to an observable post-merger signal. Under our most optimistic
assumptions, Cosmic Explorer could detect dozens of post-merger signals.
