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arXiv:2210.17091 · Physical Review A

Quantum nonstationary phenomena of spin systems in collision models

Yan Li, Xingli Li, Jiasen Jin

Published Apr 7, 2023• 18 citations
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Abstract

We investigate the nonstationary phenomenon in a tripartite spin-1/2 system in the collision model (CM) framework. After introducing the dissipation through the system-environment collision for both Markovian and non-Markovian cases, we find the emergence of long-time oscillation in the dynamics of the system and the synchronization among subsystems. We connect the CM description and the quantum master equation in the continuous-time limit and explain the existence of the stable oscillation by means of Liouvillian spectrum analysis. We investigate the thermodynamics of persistent oscillations in our CM in both Markovian and non-Markovian regimes. In addition, we find that the imperfection of collective dissipation can be compensated by the randomness of the interaction sequence in our CM.

DOI
10.1103/physreva.107.042205

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We investigate the nonstationary phenomenon in a tripartite spin-1/2 system in the collision model (CM) framework. After introducing the dissipation through the system-environment collision for both Markovian and non-Markovian cases, we find the emergence of long-time oscillation in the dynamics of the system and the synchronization among subsystems. We connect the CM description and the quantum master equation in the continuous-time limit and explain the existence of the stable oscillation by means of Liouvillian spectrum analysis. We investigate the thermodynamics of persistent oscillations in our CM in both Markovian and non-Markovian regimes. In addition, we find that the imperfection of collective dissipation can be compensated by the randomness of the interaction sequence in our CM.
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Detuned systems can spontaneously achieve a synchronous dynamics and display robust quantum correlations in different local and global dissipation regimes. Beyond the Markovian limit, information backflow from the environment becomes a crucial mechanism whose interplay with spontaneous synchronization is unknown. Considering a model of two coupled qubits, one of which interacts with a dissipative environment, we show that non-Markovianity is highly detrimental for the emergence of synchronization, for the latter can be delayed and hindered because of the presence of information backflow. The results are obtained considering both a master equation approach and a collision model based on repeated interactions, which represents a very versatile tool to tailor the desired kind of environment.
We explore the synchronization phenomenon in the quantum few-body system of spins with the nonlocal dissipation. Without the external driving, we find that the system can exhibit stable oscillatory behaviors in the long-time dynamics accompanied by the appearance of the purely imaginary eigenvalues of the Liouvillian. Moreover, the oscillations of the next-nearest-neighboring spins are completely synchronized, which is revealed by the quantum trajectory analysis within the stochastic Schr\"odinger equation. The possibility of the appearance of the long-time oscillations in an infinite-size lattice by means of cluster mean-field approximation is also discussed.
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.
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A sequence of controlled collisions between a quantum system and its environment (composed of a set of quantum objects) naturally simulates (with arbitrary precision) any Markovian quantum dynamics of the system under consideration. In this paper we propose and study the problem of simulation of an arbitrary quantum channel via collision models. We show that a correlated environment is capable to simulate non-Markovian evolutions leading to any indivisible qubit channel. In particular, we derive the corresponding master equation generating a continuous time non-Markovian dynamics implementing the universal NOT gate being an example of the most non-Markovian quantum channels.