Abstract
In this paper, we investigate the relationship between the quantum speedup, non-Markovianity and formation of a system-environment bound state. Previous results show a monotonic relation between these three such that providing bound states with more negative energy can lead to a higher degree of non-Markovianity, and hence to a greater speed of quantum evolution. By studying dynamics of a dissipative two-level system or a V-type three-level system, when similar and additional systems are present, we reveal that the quantum speedup is exclusively related to the formation of the system-environment bound state, while the non-Markovian effect of the system dynamics is neither necessary nor sufficient to speed up the quantum evolution. On the other hand, it is shown that only the formation of the system-environment bound state plays a decisive role in the acceleration of the quantum evolution.
Highlights
The quantum speed limit (QSL) time[1,2] is defined as the minimal time a quantum system needs to evolve from an initial state to a target state, which can be used to characterize the maximal speed of evolution of a quantum system
Www.nature.com/scientificreports neither necessary nor sufficient to speed up the quantum evolution when the environment becomes more complex in the presence of additional systems
The mechanism of quantum speedup for a two-level system and a V-type three-level system has been studied in the presence of additional systems from two perspectives: non-Markovianity and formation of a system-environment bound state
Summary
The quantum speed limit (QSL) time[1,2] is defined as the minimal time a quantum system needs to evolve from an initial state to a target state, which can be used to characterize the maximal speed of evolution of a quantum system. Since any real system is coupled to its environment in the practical scenarios, a considerable effort has been devoted to study controlling speedup in open quantum systems[12,13,14] In this regard, Deffner and Lutz showed that the dynamical acceleration in the damped Jaynes-Cummings model for a two-level system can be induced by the non-Markovian effect, and results in a smaller QSL time[14]. It was demonstrated that if the bound state in a two-level system coupled to an environment with Ohmic spectrum is established, the evolution of the system becomes non-Markovian, and this results in quantum speedup. The aim of the present study is to investigate the relationship between the quantum speedup, non-Markovianity and formation of a system-environment bound state in the more complex settings. Our results suggest that only the formation of the system-environment bound state is the essential reason for the quantum speedup
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