  Controlling and maintaining quantum properties of an open quantum system
along its evolution is essential for both fundamental and technological aims.
We assess the capability of a frequency-modulated qubit embedded in a leaky
cavity to exhibit enhancement of its dynamical quantum features. The qubit
transition frequency is sinusoidally modulated by an external driving field. We
show that a properly optimized quantum witness effectively identifies quantum
coherence protection due to frequency modulation while a standard quantum
witness fails. We also find an evolution speedup of the qubit through proper
manipulation of the modulation parameters of the driving field. Importantly, by
introducing a new figure of merit Rg, we discover that the relation between
Quantum Speed Limit Time (QSLT) and non-Markovianity depends on the system
initial state, which generalizes previous connections between these two
dynamical features. The frequency-modulated qubit model thus manifests
insightful dynamical properties with potential utilization against decoherence.
