  Decoherence for a one-dimensional coupled-resonator waveguide with a
two-level system inside one of resonators, induced by their interaction with
corresponding environments, is investigated. Each environment is modeled as a
continuum of harmonic oscillators. By finding the eigenstates of the hybrid
system, which is the dressed state of the hybrid system, we calculate the
lifetime of one excitation, which characterizes the existence of quantum
coherence in such hybrid system and the basic quantum nature.
