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Journal of Modern Physics

Controlling Speedup Induced by a Hierarchical Environment

Jing Wang, Yunan Wu, Wenyu Ji

Published Jan 1, 2019• 3 citations
Publisher

Abstract

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.

DOI
10.4236/jmp.2019.1010078

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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.
Quantum evolution can be accelerated in a non-Markovian environment. Previous results show that the formation of a system-environment bound state governs the quantum speedup. Although a stronger bound state in the system-environment spectrum may seem like it should cause greater speed of evolution, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a classical-driven qubit interacting with a photonic crystal waveguide in the presence of a mirror, resulting in non-Markovian dynamics for the system. Within the considered model, we show the influence of the mirror and the classical field on the evolution speed of the system. In particular, we find that the formation of a bound state is not the essential reason for the acceleration of evolution. The quantum speedup is attributed to the flow of information, regardless of the direction in which the information flows. Our conclusion can also be used in other non-Markovian environments.
Non-Markovian evolution of an open quantum system can be induced by the memory effects of a reservoir. Although a reservoir with stronger memory effects may seem like it should cause stronger non-Markovian effects on the system of interest, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a qubit (a two-level atom) that is coupled to a hierarchical environment, which contains a single-mode cavity and a reservoir consisting of an infinite number of modes. We show how the non-Markovian character of the system is influenced by the coupling strength between the qubit and cavity and the correlation time of the reservoir. In particular, we found a phenomenon whereby the qubit Markovian and non-Markovian transition exhibits a anomalous pattern in a parameter space depicted by the coupling strength and the correlation time of the reservoir.
We investigate the dynamics of a two-level system in the presence of an overall environment composed of two layers. The first layer is just one single-mode cavity which decays to memoryless reservoir while the second layer is the two coupled single-mode cavities which decay to memoryless or memory-keeping reservoirs. In the weak-coupling regime between the qubit and the first-layer environment, our attention is focused on the effects of the coupling in the hierarchical environment on the non-Markovian speedup dynamics behavior of the system. We show that, by controlling the coupling in the second-layer environment, the multiple dynamics crossovers from Markovian to non-Markovian and from no-speedup to speedup can be realized. This results hold independently on the nature of the second-layer environment. Differently, we find that how the coupling between the two layers affects the non-Markovian speedup dynamics behavior depends on the nature of the second-layer environment.
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.
We investigate the qubit in the hierarchical environment where the first layer is just one lossy cavity while the second layer is the NNN-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.
Evolution speed of an open quantum system is vividly influenced by the structure of environments. The strong system‐environment coupling is found to be able to accelerate quantum evolution. In this work, we propose a different method of governing the quantum speedup via engineering multiple environments. It is shown that, with a judicious choice of the number of coupling environments, the quantum speedup of an open system can be achieved even under weak system‐environment coupling conditions. The mechanism for the speedup is due to the switch between Markovian and non‐Markovian regions by manipulating the number of the surrounding environments. In addition, we verify the above phenomena by using quantum dots embedded in a planar photonic crystal under current technologies. These results provide a new degree of freedoms to accelerate quantum evolution of open systems. The strong system‐environment coupling can speed up the quantum evolution process. This work shows that, via engineering multiple environments, one can speed up the evolution process even under weak coupling conditions.