# Hierarchical environment-assisted dynamical speedup control. (arXiv:1802.01278v1 [quant-ph])

We investigate the qubit in the hierarchical environment where the first
level is just one lossy cavity while the second level is the N-coupled lossy
cavities. In the weak coupling regime between the qubit and the first level
environment, the dynamics crossovers from the original Markovian to the new
non-Markovian and from no-speedup to speedup can be realized by controlling the
hierarchical environment, i.e., manipulating the number of cavities or the
coupling strength between two nearest-neighbor cavities in the second level
environment. And we find that the coupling strength between two
nearest-neighbor cavities and the number of cavities in the second level
environment have the opposite effect on the non-Markovian dynamics and speedup
evolution of the qubit. In addition, in the case of strong coupling between the
qubit and the first level environment, we can be surprised to find that,
compared with the original non-Markovian dynamics, the added second level
environment cannot play a beneficial role on the speedup of the dynamics of the
system.