Quantumness and speedup limit of a qubit under transition-frequency modulation

The control and maintenance of the quantum properties of an open quantum system along its evolution are 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 figure of merit ${\mathfrak{R}}_{\mathfrak{g}}$, we discover that the relation between quantum speed limit time 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.