  Gravitational wave (GW) detection has enabled us to test General Relativity
in an entirely new regime. A prominent role in tests of General Relativity
takes the detection of the Quasi-normal modes (QNMs) that arise as the highly
distorted remnant formed after the merger emits GWs until it becomes a regular
Kerr BH. According to the no-hair theorem, the frequencies and damping times of
these QNMs are determined solely by the mass and spin of the remnant BH.
Therefore, detecting the QNMs offers a unique way to probe the nature of the
remnant BH and to test General Relativity. We study the detection of a merging
binary black hole (BBH) in the intermediate mass range, where the
inspiral-merger phase is detected by space-based laser interferometer detectors
TianQin and LISA while the ringdown is detected by the ground-based atom
interferometer (AI) observatory AION. The analysis of the ringdown is done
using the regular broadband mode of AI detectors as well as using the resonant
mode where the detection band is optimized to the frequencies of the QNMs
predicted from the inspiral-merger phase. We find that using the regular
broadband mode allows constraining the parameters of the BBH with relative
errors of at most $10^{-6}$ from the ringdown while the frequencies and the
damping times of the QNMs can be determined with total errors below $0.2\,{\rm
Hz}$ and $115\,{\rm \mu s}$, respectively. Furthermore, we find that using the
resonant mode can improve the parameter estimation for the BBH from the
ringdown by up to one order of magnitude. Utilizing the resonant mode
significantly limits the detection of the frequency of the QNMs but improves
the detection error of the damping times by one to four orders of magnitude.
