Geometric signature of non-Markovian dynamics

Non-Markovian effects in the dynamics of an open system are typically characterized by non-monotonic information flows from the system to its environment or by information backflows from the environment to the system. Using a two-level system (TLS) coupled to a dissipative single-mode cavity, we demonstrate that the geometric decoherence of the open quantum system can serve as a reliable indicator of non-Markovian dynamics. This geometric approach also reveals finer details of the dynamics, such as the specific time points when non-Markovian behavior emerges. In particular, we show that the divergence of the geometric decoherence factor of the TLS can serve as a sufficient condition for non-Markovian dynamics, and in certain cases, it can even be both a necessary and sufficient condition.