Non-Markovian dynamics of a qubit coupled to a waveguide in photonic crystals with infinite cavity-array structure

We evaluate exactly the non-Markovian effect on the decoherence dynamics of a qubit coupling with a waveguide in photonic crystals. In our study, we extend the previous investigation that the waveguide is structured as a semi-infinite cavity array to the case that it is set as an infinite cavity array. For the infinite cavity array, we utilize the quantity of fidelity to characterize the ability of the system to preserve its initial quantum information. We make a discussion for different initial states of the qubit. Similar to the case of semi-infinite cavity array, we find that the quantum information of the qubit in the long-time scale could also be partially preserved when the qubit-waveguide coupling strength goes beyond a critical value. This is a strong non-Markovian memory effect induced by the strong qubit-waveguide coupling strength. Interestingly, the critical coupling strength for infinite cavity array happens to be zero, which means that in this real physical system, the quantum-to-classical transition behavior of the qubit never occurs. Therefore, by reasonably choosing the structure of the environment, the quantum information of the quantum systems could be more easily preserved. Moreover, we find that the higher probability of the qubit initially in its ground state, the more easily for it to preserve its initial information in the long-time scale, which proves that the quantum open system always tends to stay in its ground state.