Environment spectrum and coherence behaviours in a rare-earth doped crystal for quantum memory

We theoretically investigate the dynamics of environment and coherence behaviours of the central ion in a quantum memory based on a rare-earth doped crystal. The interactions between the central ion and the bath spins suppress the flip-flop rate of the neighbour bath spins and yield a specific environment spectral density S(ω). Under dynamical decoupling pulses, this spectrum provides a general scaling for the coherence envelope and coherence time, which significantly extend over a range on an hour-long time scale. The characterized environment spectrum with ultra-long coherence time can be used to implement various quantum communication and information processing protocols.