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arXiv:1710.07142 · New Journal of Physics

Non-Markovianity in the collision model with environmental block

Jiasen Jin, Chang-shui Yu

Published Apr 27, 2018• 47 citations
arXivHTMLPDF

Abstract

We present an extended collision model to simulate the dynamics of an open quantum system. In our model, the unit to represent the environment is, instead of a single particle, a block which consists of a number of environment particles. The introduced blocks enable us to study the effects of different strategies of system–environment interactions and states of the blocks on the non-Markovianities. We demonstrate our idea in the Gaussian channels of an all-optical system and derive a necessary and sufficient condition of non-Markovianity for such channels. Moreover, we show the equivalence of our criterion to the non-Markovian quantum jump in the simulation of the pure damping process of a single-mode field. We also show that the non-Markovianity of the channel working in the strategy that the system collides with environmental particles in each block in a certain order will be affected by the size of the block and the embedded entanglement and the effects of heating and squeezing the vacuum environmental state will quantitatively enhance the non-Markovianity.

DOI
10.1088/1367-2630/aac0cb

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We present an extended collision model to simulate the dynamics of an open quantum system. In our model, the unit to represent the environment is, instead of a single particle, a block which consists of a number of environment particles. The introduced blocks enable us to study the effects of different strategies of system–environment interactions and states of the blocks on the non-Markovianities. We demonstrate our idea in the Gaussian channels of an all-optical system and derive a necessary and sufficient condition of non-Markovianity for such channels. Moreover, we show the equivalence of our criterion to the non-Markovian quantum jump in the simulation of the pure damping process of a single-mode field. We also show that the non-Markovianity of the channel working in the strategy that the system collides with environmental particles in each block in a certain order will be affected by the size of the block and the embedded entanglement and the effects of heating and squeezing the vacuum environmental state will quantitatively enhance the non-Markovianity.
Abstract By means of collision models (CMs) where the environment is simulated by a collection of ancillas consisting of two entangled qubits, we investigate the effects of entanglement in the environment on the non-Markovianity of an open quantum system. Two CMs are considered in this study, in the first one the open quantum system S directly collides with the environment, while in the second one the system interacts with two intermediate qubits which, in turn, are coupled to the environment. We show that it is possible to enhance the non-Markovianity by environment entanglement in both models. In particular, in the second model, we show that the initial state of the auxiliary qubits can also affect the non-Markovianity of the system and there exists the optimal combination of the initial environmental state and the initial state of auxiliary qubits. In this case, the non-Markovianity can be greatly enhanced.
We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-1/21/21/2 particles. In order to include non-Markovian features in our model, we introduce interactions among the environmental qubits and investigate the effect that different models of such interaction have on the degree of non-Markovianity of the system's dynamics. By extending that interaction beyond the nearest neighbor, we enhance the degree of non-Markovianity in the system's dynamics. A further significant increase can be observed if a collective interaction with the forthcoming environmental qubits is considered. However, the observed degree of non-Markovianity in this case is nonmonotonic with the increasing number of qubits included in the interaction. Moreover, one can establish a connection between the degree of non-Markovianity in the evolution of the system and the fading behavior of quantum coherence in its state as the number of collisions grows. We complement our study with an investigation of system-environment correlations and present an example of their importance on a physical upper bound on the trace distance derivative.
Abstract Collision models (CMs) describe an open system interacting in sequence with elements of an environment, termed ancillas. They have been established as a useful tool for analyzing non-Markovian open quantum dynamics based on the ability to control the environmental memory through simple feedback mechanisms. In this work, we investigate how ancilla–ancilla (AA) entanglement can serve as a mechanism for controlling the non-Markovianity of an open system, focusing on an operational approach to generating correlations within the environment. To this end, we first demonstrate that the open dynamics of CMs with sequentially generated correlations between groups of ancillas can be mapped onto a composite CM, where the memory part of the environment is incorporated into an enlarged Markovian system. We then apply this framework to an all-qubit CM, and show that non-Markovian behavior emerges only when the next incoming pair of ancillas are entangled prior to colliding with the system. On the other hand, when system-ancilla collisions precede AA entanglement, we find the open dynamics to always be Markovian. Our findings highlight how certain qualitative features of inter-ancilla correlations can strongly influence the onset of system non-Markovianity.
We study the applicability of collisional models for non-Markovian dynamics of open quantum systems. By allowing interactions between the separate environmental degrees of freedom in between collisions we are able to construct a collision model that allows us to study quantum memory effects in open system dynamics. We also discuss the possibility to embed non-Markovian collision model dynamics into Markovian collision model dynamics in an extended state space. As a concrete example we show how, using the proposed class of collision models, we can discretely model non-Markovian amplitude damping of a qubit. In the time-continuous limit, we obtain the well-known results for spontaneous decay of a two-level system into a structured zero-temperature reservoir.
Quantum non-Markovianity represents memory during system dynamics, which is typically weakened by temperature. We study here the effects of environmental temperature on the non-Markovianity of an open quantum system by virtue of collision models. The environment is simulated by a chain of ancillary qubits that are prepared in thermal states with a finite temperature TTT. Two distinct non-Markovian mechanisms are considered via two types of collision models, one where the system SSS consecutively interacts with ancillas and a second where SSS collides only with an intermediate system ${S}^{\ensuremath{'}}$, which in turn interacts with the ancillas. We show that in both models the relation between non-Markovianity and temperature is nonmonotonic. In particular, revivals of non-Markovianity may occur as temperature increases. We find that the physical reason behind this behavior can be revealed by examining a peculiar system-environment coherence exchange, leading to ancillary qubit coherence larger than system coherence, which triggers information backflow from the environment to the system. These results provide insights into the mechanisms underlying the counterintuitive phenomenon of temperature-enhanced quantum memory effects.
We study the dynamics of a quantum system whose interaction with an environment is described by a collision model, i.e., the open dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed ``ancillas,'' which are subsequently traced out. In this setting, non-Markovianity is introduced by allowing for additional unitary interactions between the ancillas. For this model, we identify the relevant system-environment correlations that lead to a non-Markovian evolution. Through an equivalent picture of the open dynamics, we introduce the notion of ``memory depth'' where these correlations are established between the system and a suitably sized memory rendering the overall system+memory evolution Markovian. We extend our analysis to show that while most system-environment correlations are irrelevant for the dynamical characterization of the process, they generally play an important role in the thermodynamic description. Finally, we show that under an energy-preserving system-environment interaction, a nonmonotonic time behavior of the heat flux serves as an indicator of non-Markovian behavior.