Dependence of the decoherence of polarization states in phase-damping channels on the frequency spectrum envelope of photons

We consider the decoherence of photons suffering in phase-damping channels. By exploring the evolutions of single-photon polarization states and two-photon polarization-entangled states, we find that different frequency spectrum envelopes of photons induce different decoherence processes. A white frequency spectrum can lead the decoherence to an ideal Markovian process. Some color frequency spectrums can induce asymptotical decoherence, while, some other color frequency spectrums can make coherence vanish periodically with variable revival amplitudes. These behaviors result from the non-Markovian effects on the decoherence process, which may give rise to a revival of coherence after complete decoherence.