# 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.