Colloquium: Non-Markovian dynamics in open quantum systems

Abstract

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry and quantum information. In close analogy to a classical Markovian stochastic process, the interaction of an open quantum system with a noisy environment is often modeled phenomenologically by means of a dynamical semigroup with a corresponding time-independent generator in Lindblad form, which describes a memoryless dynamics of the open system typically leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence, correlations and entanglement. Here, recent theoretical results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of quantum memory effects. The general theory is illustrated by a series of physical examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This article further explores the various physical sources of non-Markovian quantum dynamics, such as structured environmental spectral densities, nonlocal correlations between environmental degrees of freedom and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments addressing the detection, quantification and control of non-Markovian quantum dynamics are also briefly discussed.

Non-Markovianity-assisted high-fidelity Deutsch–Jozsa algorithm in diamond

“…39,40,42 However, a recent study revealed that the memory effects of a non-Markovian environment can be regarded as important physical resources 28,33 to improve QIP in an open quantum system. To further enhance the POS of the RDJA, we utilized the memory effects of the non-Markovian environment, which can be extracted by the DD method 26,39 to mitigate imperfect operations and decoherence.…”

“…Non-Markovian effect of noise environment on RDJA These nontrivial phenomena deviate mainly from the quantum Born-Markovian process [28][29][30][31] and reflect the occurrence of nonMarkovian dynamics. To confirm this supposition and study how the memory effects of the environment affect the RDJA, we measured the non-Markovianity of the quantum system by employing the trace distance method, 29,31,44 which is given by…”

“…28 However, because of strong system-environment couplings, structured or finite reservoirs, low temperatures, or large initial system-environment correlations, the dynamics of an open quantum system may deviate substantially from the Born-Markov approximation and follow a non-Markovian process. [28][29][30][31][32] In such a process, the pronounced memory effect, which is the primary feature of a non-Markovian environment, can be used to revive the genuine quantum properties, [28][29][30][31][32][33][34] such as quantum coherence and correlations. Consequently, improving the performance of QIP by utilizing memory effects as important physical resources in the nonMarkovian environment is crucial.…”

“…Here, we investigated the memory effects of non-Markovian environments using the quantum Deutsch-Jozsa algorithm 37 with a solid spin in a diamond nitrogen-vacancy (NV) center. The memory effects were further applied as important physical resources 28 to substantially improve the performance of the quantum algorithm with the assistance of the DD protection method. 26 The Deutsch-Jozsa algorithm, [38][39][40] which can be used to determine whether a coin is fair or fake in a single examination step, 40,41 is one of the seminal algorithms used to demonstrate the advantages of quantum computations.…”

Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction

“…In order to understand the relation between the structure of the environment and the nonMarkovianity and to quantity these effects, several measures have been proposed recently. A review can be found in references [31][32][33][34]. The measure used by Breuer [35] is based on the quantum trace distance measuring the distinguishability between two quantum states.…”