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Hybrid quantum-classical systems constitute a promising architecture foruseful control strategies of quantum systems by means of a classical device.Here we provide a comprehensive study of the dynamics of various manifestationsof quantumness with memory effects, identified by non-Markovianity, for a qubitcontrolled by a classical field and embedded in a leaky cavity. We considerboth Leggett-Garg inequality and quantum witness as experimentally-friendlyindicators of quantumness, also studying the geometric phase of the evolved(noisy) quantum state. We show that, under resonant qubit-classical fieldinteraction, a stronger coupling to the classical control leads to enhancementof quantumness despite a disappearance of non-Markovianity. Differently,increasing the qubit-field detuning (out-of-resonance) reduces the nonclassicalbehavior of the qubit while recovering non-Markovian features. We then findthat the qubit geometric phase can be remarkably preserved irrespective of thecavity spectral width via strong coupling to the classical field. Thecontrollable interaction with the classical field inhibits the effectivetime-dependent decay rate of the open qubit. These results supply practicalinsights towards a classical harnessing of quantum properties in a quantuminformation scenario.

Quantumness and memory of one qubit in a dissipative cavity under classical control