Quantum beat of coherence induced by non-Markovian effect
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Quantum beat of coherence induced by non-Markovian effect Hao-Sheng Zenga and Ming-Jie Liao Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Department of Physics, Hunan Normal University, Changsha 410081, P.R. China Received 8 November 2019 / Received in final form 10 April 2020 Published online 9 June 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. The non-Markovianity of open quantum dynamics can give rise to the oscillation of quantum coherence in time, and the interference between oscillations leads to quantum beat of coherence. We design two dynamical models of open quantum systems for revealing this kind of phenomenon of quantum interference, analyze the forming process and the producing conditions of the quantum beats.
1 Introduction Quantum coherence is one of the key features of quantum world and responsible for quantum interference and the transition from quantum to classical [1]. It plays an important role in quantum biology [2,3], quantum thermodynamics [4,5], quantum optics [6,7] and quantum information science [8,9]. Though the research on quantum coherence has a long history [6,10], the problem of how to quantify the coherence of a quantum state has long been ignored. Until very recently, the problem has been placed on the agenda [11–17]. In reference [11], Baumgratz, Cramer and Plenio established a rigorous framework for the quantification of coherence from the point of resource theory. By introducing the set of incoherent states and the set of incoherent operations, as well as assuming that coherence is nonincreasing under incoherent operations, then the framework of resource for coherence is established, in which coherence is regarded as a resource relative to the set of incoherent operations. Any function that maps states to the nonnegative real numbers and satisfies the requirement of nonincreasing under incoherent operations constitutes a measure of coherence. Especially, the measure of l1 norm of coherence has been proposed: given some preferred basis {|ii}i=1,...,d of a d-dimensional quantum system, the l1 norm of coherence is defined as the sum of the absolute value of all the offdiagonal elements of the system density matrix, X Cl1 (ρ) = |ρi,j |. (1) i,j,i6=j
Realistic quantum systems cannot avoid interactions with their environments, leading to the loss of information of the open quantum systems. Based on the viewpoint of backflow of information, many definitions or a
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measures for non-Markovianity of open quantum processes have been proposed [18,19]. The method based on quantum coherence is one of them. Especially, the l1 norm of coherence is monotonic under incoherent completelypositive and trace-preserving maps, so it can be used as a witness for identifying a non-Markovian dynamics [20–22]. Markovian process is only an ideal one, which usually happens under the situation where
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