Hierarchical environment-assisted dynamical speedup control

TL;DR

This paper explores how hierarchical environments influence the dynamical speedup of a qubit, demonstrating control over non-Markovian behavior and speedup through environmental parameters, with different effects observed in weak and strong coupling regimes.

Contribution

It introduces a model of hierarchical environments affecting qubit dynamics and reveals how environmental parameters can control speedup and non-Markovian effects, a novel insight in quantum control.

Findings

Control of non-Markovian dynamics via environmental parameters.

Opposite effects of cavity coupling strength and number on speedup.

Second level environment's limited role in strong coupling regime.

Abstract

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.