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Physical Review Letters

Experimental Investigation of Spectra of Dynamical Maps and their Relation to non-Markovianity

Shang Yu, Yi‐Tao Wang, Zhi‐Jin Ke, Wei Liu, Yu Meng, Zhi-Peng Li, Wenhao Zhang, Geng Chen, Jian‐Shun Tang, Chuan‐Feng Li, Guang‐Can Guo

Published Feb 8, 2018• 29 citations
Publisher

Abstract

The spectral theorem of von Neumann has been widely applied in various areas, such as the characteristic spectral lines of atoms. It has been recently proposed that dynamical evolution also possesses spectral lines. As the most intrinsic property of evolution, the behavior of these spectra can, in principle, exhibit almost every feature of this evolution, among which the most attractive topic is non-Markovianity, i.e., the memory effects during evolution. Here, we develop a method to detect these spectra, and moreover, we experimentally examine the relation between the spectral behavior and non-Markovianity by engineering the environment to prepare dynamical maps with different non-Markovian properties and then detecting the dynamical behavior of the spectral values. These spectra will lead to a witness for essential non-Markovianity. We also experimentally verify another simplified witness method for essential non-Markovianity. Interestingly, in both cases, we observe the sudden transition from essential non-Markovianity to something else. Our work shows the role of the spectra of evolution in the studies of non-Makovianity and provides the alternative methods to characterize non-Markovian behavior.

DOI
10.1103/physrevlett.120.060406

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The spectral theorem of von Neumann has been widely applied in various areas, such as the characteristic spectral lines of atoms. It has been recently proposed that dynamical evolution also possesses spectral lines. As the most intrinsic property of evolution, the behavior of these spectra can, in principle, exhibit almost every feature of this evolution, among which the most attractive topic is non-Markovianity, i.e., the memory effects during evolution. Here, we develop a method to detect these spectra, and moreover, we experimentally examine the relation between the spectral behavior and non-Markovianity by engineering the environment to prepare dynamical maps with different non-Markovian properties and then detecting the dynamical behavior of the spectral values. These spectra will lead to a witness for essential non-Markovianity. We also experimentally verify another simplified witness method for essential non-Markovianity. Interestingly, in both cases, we observe the sudden transition from essential non-Markovianity to something else. Our work shows the role of the spectra of evolution in the studies of non-Makovianity and provides the alternative methods to characterize non-Markovian behavior.
A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of -- and interrelations between -- the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.
This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.
We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behavior in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behavior of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two-point correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.
Recent developments in practical quantum engineering and control techniques have allowed significant developments for experimental studies of open quantum systems and decoherence engineering. Indeed, it has become possible to test experimentally various theoretical, mathematical, and physical concepts related to non-Markovian quantum dynamics. This includes experimental characterization and quantification of non-Markovian memory effects and proof-of-principle demonstrations how to use them for certain quantum communication and information tasks. We describe here recent experimental advances for open system studies, focussing in particular to non-Markovian dynamics including the applications of memory effects, and discuss the possibilities for ultimate control of decoherence and open system dynamics.
The non-Markovian depolarizing channel is explored from the perspective of understanding its non-Markovian behavior as well as the occurrence of singularities. The study brings together the various ways to identify and quantify non-Markovianity. This includes dynamical techniques such as quantum information backflow witness, Breuer-Laine-Piilo, Rivas-Huelga-Plenio, and Hall-Cresser-Li-Andersson measures. In addition, geometrical visualization of non-Markovian effects is presented using the variation in the volume of accessible states during dynamical evolution. Further, a trajectory-based visualization of the dynamical map within the parameter space is presented. The trajectories traced during evolution demonstrate the loss of CP divisibility and the emergence of non-Markovianity under systematic variations of the system parameters. The effects of increasing system dimensions and qubit numbers on singularity and non-Markovianity are presented, with an extension of characterization techniques to higher-dimensional systems.