  We study how the environment of photonic band gap (PBG) materials affects
entanglement dynamics of qubits. Entanglement between the single qubit and the
PBG environment is investigated through the von Neumann entropy while that for
two initially entangled qubits in this PBG reservoir is through concurrence.
Dynamics of these measurements are solved in use of the fractional calculus
which has been shown appropriate for the systems with non-Markovian dynamics.
Entropy dynamics of the single qubit system reveals that the coupling with the
PBG reservoir prevents decoherence of the qubit through the steady entropy with
non-zero value. The effect of PBG reservoir on the concurrence of the two-qubit
system leads to the long-time entanglement preservation. The concurrence
dynamics shows that unphysical entanglement trapping does not exist in the
system with the qubit frequency lying outside the PBG region. Long-time memory
effect of the PBG reservoir occurs only for the qubit frequency in the PBG
region. Entanglement mechanisms resulting from this long-time memory effect are
discussed.
