  A nonlinear stimulated Raman adiabatic passage (STIRAP) is a fascinating
physical process that dynamically explores chaotic and non-chaotic phases. In a
recent paper Phys. Rev. Res. 2, 042004 (R) (2020), such a phenomenon is
realized in a cavity-QED platform. There, the emergence of chaos and its impact
on STIRAP efficiency are mainly demonstrated in the semiclassical limit. In the
present paper I treat the problem in a fully quantum many-body framework. With
the aim of extracting quantum signatures of a classically chaotic system, it is
shown that an out-of-time-ordered correlator (OTOC) measure precisely captures
chaotic/non-chaotic features of the system. The prediction by OTOC is in
precise matching with classical chaos quantified by Lyapunov exponent (LE).
Furthermore, it is shown that the quantum route corresponding to the
semiclassical followed state encounters a dip in single-particle purity within
the chaotic phase, depicting a consequence of chaos. A dynamics through the
chaotic phase is associated with spreading of many-body quantum state and an
irreversible increase in the number of participating adiabatic eigenstates.
