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arXiv:1802.01278 · Physical Review A

Hierarchical-environment-assisted non-Markovian speedup dynamics control

Kai Dong Xu, Ying-Jie Zhang, Yun‐Jie Xia, Zai-Kun Wang, Heng Fan

Published Aug 8, 2018• 34 citations
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Abstract

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

DOI
10.1103/physreva.98.022114

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Quantum speedup of an open quantum system can be induced by the non-Markovian effect of the environment. Although an environment with a higher degree of non-Markovianity may seem like it should cause a faster speed of quantum evolution, this seemingly intuitive thinking may not always be correct. To clarify this point, we give a mechanism for controlling speedup of a single qubit that is coupled to a hierarchical photonic-crystal (PC) environment, which contains a defect single-mode cavity and a semi-infinite one-dimensional (1D) waveguide. Via studying the dynamics of the qubit, we reveal that with a judicious choice of the qubit-cavity coupling strength and the memory time of the waveguide environment, a speed-up evolution can be achieved. In particular, we found that the quantum speedup is not entirely attributed to the non-Markovianity, but to the increase of the total amount of flow information. That is the intrinsic physical reason that the hierarchical environment may induce the speed-up process. Our results may open new perspectives for detecting quantum speedup in realistic environments.
Dynamics of an open system is vividly influenced by the structure of environments. This paper studies in detail the dynamics of a two-level atom in the presence of an overall environment composed of two hierarchies. The first hierarchy is just a single lossy cavity while the second hierarchy consists of a number of other lossy cavities. The atom is coupled directly to the first hierarchy but indirectly to the second one via the couplings between the two hierarchies. We show that even when the coupling between the atom and the first hierarchy is weak the atom's dynamics can become non-Markovian if the number of cavities in the second hierarchy or/and the coupling between the two hierarchies are large enough. We also analyze the case when the coupling between the atom and the first hierarchy is strong and show that the non-Markovian dynamics exhibits different patterns depending on both the number of cavities in the second hierarchy and the coupling between the two hierarchies.
We illustrate a scheme for implementing a non-Markovian speedup evolution of an open system weakly interacting with a controllable environment: the coupled qubit-array. By controlling the environment, for instance by choosing a judicious nearest-neighbor excitation quanta hopping strength among the qubit-array or by changing the number of qubits coupled to the quantum system, two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved in the weak system-environment coupling regime. For the weaker system-environment coupling, the larger hopping strength (or the larger qubits number) should be tuned to drive the non-Markovian speedup evolution. Particularly, the controllable non-Markovian dynamics is the intrinsic physical reason for the speedup evolution of a quantum system.
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For a two-level atom in a lossy cavity, a scheme to manipulate the non-Markovian speedup dynamics has been proposed in the controllable environment (the lossy cavity field). We mainly focus on the effects of the qubit–cavity detuning Δ and the qubit–cavity coupling strength κ on the non-Markovian speedup evolution of an open system. By controlling the environment, i.e., tuning Δ and κ , two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved. Furthermore, it is clearly found that increasing the coupling strength κ or detuning Δ in some cases can make the environmental non-Markovianity stronger and hence can lead to faster evolution of the open system.