  Under the Born--Markov approximation, a qubit system, such as a two-level
atom, is known to undergo a memoryless decay of quantum coherence or excitation
when weakly coupled to a featureless environment. Recently, it has been shown
that unavoidable disorder in the environment is responsible for non-Markovian
effects and information backflow from the environment into the system owing to
Anderson localization. This~turns disorder into a resource for enhancing
non-Markovianity in the system--environment dynamics, which could be of
relevance in cavity quantum electrodynamics. Here we consider the decoherence
dynamics of a qubit weakly coupled to a two-dimensional bath with a nontrivial
topological phase, such as a two-level atom embedded in a two-dimensional
coupled-cavity array with a synthetic gauge field realizing a quantum-Hall
bath, and~show that Markovianity is protected against moderate disorder owing
to the robustness of chiral edge modes in the quantum-Hall bath. Interestingly,
switching off the gauge field, i.e., flipping the bath into a topological
trivial phase, allows one to re-introduce non-Markovian effects. Such a result
indicates that changing the topological phase of a bath by a tunable synthetic
gauge field can be harnessed to control non-Markovian effects and quantum
information backflow in a qubit-environment system.
