Role of chiral symmetry in a kicked Jaynes-Cummings model

We have studied the role of chiral symmetry in a periodically kicked Jaynes--Cummings (KJC) model by freezing an initial phase. We show that commensurate kicks ($2\ensuremath{\pi}k$ periodicity with integer $k$) conserve the chiral symmetry in the KJC model under the resonant condition, while incommensurate kicks break the symmetry. The chiral symmetry preserves the phase of an initial state against phase fluctuations during the dynamical evolution, but broken chiral symmetry erases the initial phase. The frozen phase is preserved within a finite evolution time for slight deviations of the kick period from an integer multiple of $2\ensuremath{\pi}$ and small variations of detuning from the resonant condition. The chiral symmetry-protected phase information is noteworthy as it provides various uses in quantum computation and information.