  In the aftermath of a binary black hole merger event, the gravitational wave
signal emitted by the remnant black hole is modeled as a superposition of
damped sinusoids known as quasinormal modes. While the dominant quasinormal
modes originating from linear black hole perturbation theory have been studied
extensively in this post-merger "ringdown" phase, more accurate models of
ringdown radiation include the nonlinear modes arising from higher-order
perturbations of the remnant black hole spacetime. We explore the detectability
of quadratic quasinormal modes with both ground- and space-based
next-generation detectors. We quantify how predictions of the quadratic mode
detectability depend on the quasinormal mode starting times. We then calculate
the signal-to-noise ratio of quadratic modes for several detectors and binary
black hole populations, focusing on the ($220\times220$) mode - i.e., on the
quadratic term sourced by the square of the linear $(220)$ mode. For the events
with the loudest quadratic mode signal-to-noise ratios, we additionally compute
statistical errors on the mode parameters in order to further ascertain the
distinguishability of the quadratic mode from the linear quasinormal modes. The
astrophysical models used in this paper suggest that while the quadratic mode
may be detectable in at most a few events with ground-based detectors, the
prospects for detection with the Laser Interferometer Space Antenna (LISA) are
more optimistic.
