  Quantum chaos is usually characterized through its statistical implications
on the energy spectrum of a given system. In this work we propose a decoherent
mechanism for sensing quantum chaos. The chaotic nature of a many-body quantum
system is sensed by studying the implications that the system produces in the
long-time dynamics of a probe coupled to it under a dephasing interaction. By
introducing the notion of an effective averaged decoherence factor, we show
that the correction to the geometric phase acquired by the probe with respect
to its unitary evolution can be exploited as a robust tool for sensing the
integrable to chaos transition of the many-body quantum system to which it is
coupled. This sensing mechanism is verified for several systems with different
types of symmetries, disorder and even in the presence of long-range
interactions, evidencing its universality.
