Dynamics of the Energy Relaxation and Decoherence of a Photon-Atom Bound State in an Anisotropic Photonic Crystal

An atom embedded inside photonic crystals can form a photon-atom bound state if the emission frequency of the excited atom is lying inside the photonic-band gap of photonic crystals. We studied the dynamics of the energy relaxation and decoherence of a QPAB, qubit made by a photon-atom bound state in photonic crystals. Dynamics of these measurements are solved analytically through the fractional calculus which has been shown to be appropriate mathematical method for the optical systems with non-Markovian dynamics. From these dynamics, we find that the losses of energy, coherence, and information of a QPAB are inhibited. As compared with those qubits without forming photon-atom bound states, the energy relaxation and decoherence rates of these QPABs are strongly suppressed. Other systems suitable for realizing these properties are discussed.