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New Journal of Physics

Non-Markovian dynamics control of spin-1/2 system interacting with magnets

Ying-Jie Zhang, Wei Han, Wei‐Bin Yan, Zhong‐Xiao Man, Yun‐Jie Xia, Heng Fan

Published Oct 1, 2021• 3 citations
Publisher

Abstract

The unavoidable interaction of an open quantum system with its surrounding environment may follow non-Markovian dynamics behavior, which causes its memory effects to play a key role in many quantum technologies. In this work, we first consider the dynamics control of a spin-1/2 system that simultaneously interacts with two magnets. Subsequently, we study in detail the evolution of a classically driven spin-1/2 system that is coupled with a magnet. Two dynamical crossovers of the spin system, namely, from Markovian dynamics to non-Markovian dynamics and from no-speedup evolution to speedup evolution, can be controlled in these two models. Slightly different from the previous quantum speedup scenarios with controllable non-Markovianity, the stronger non-Markovianity does not necessarily lead to the quantum speedup dynamics process of the spin system in our spin-magnet schemes.

DOI
10.1088/1367-2630/ac2c2a

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The unavoidable interaction of an open quantum system with its surrounding environment may follow non-Markovian dynamics behavior, which causes its memory effects to play a key role in many quantum technologies. In this work, we first consider the dynamics control of a spin-1/2 system that simultaneously interacts with two magnets. Subsequently, we study in detail the evolution of a classically driven spin-1/2 system that is coupled with a magnet. Two dynamical crossovers of the spin system, namely, from Markovian dynamics to non-Markovian dynamics and from no-speedup evolution to speedup evolution, can be controlled in these two models. Slightly different from the previous quantum speedup scenarios with controllable non-Markovianity, the stronger non-Markovianity does not necessarily lead to the quantum speedup dynamics process of the spin system in our spin-magnet schemes.
We illustrate a scheme for implementing a non-Markovian speedup evolution of an open system weakly interacting with a controllable environment: the coupled qubit-array. By controlling the environment, for instance by choosing a judicious nearest-neighbor excitation quanta hopping strength among the qubit-array or by changing the number of qubits coupled to the quantum system, two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved in the weak system-environment coupling regime. For the weaker system-environment coupling, the larger hopping strength (or the larger qubits number) should be tuned to drive the non-Markovian speedup evolution. Particularly, the controllable non-Markovian dynamics is the intrinsic physical reason for the speedup evolution of a quantum system.
We investigate the dynamics of an N -qubit interacting system coupled to a common reservoir. In the weak system-environment coupling regime, the crossovers from Markovian to non-Markovian and from no speedup to speedup can be realized by adjusting the controllable parameters (i.e., the coupling strength between qubits and the number of the qubits). However, in the case of strong coupling, the multiple transitions from non-Markovian regime to Markovian regime and from speedup to no speedup can be induced by manipulating controllable parameters. In addition, a phenomenon can be noticed that the number of qubits and the coupling strength between the qubits have the different effect on the non-Markovian dynamics and speedup evolution of the system in the above weak- and strong-coupling regimes. Our results provide an effective theoretical scheme for the realization of non-Markovian speedup dynamic processes. Published by the American Physical Society 2024
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.
Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in the absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for the zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.
For a two-level atom in a lossy cavity, a scheme to manipulate the non-Markovian speedup dynamics has been proposed in the controllable environment (the lossy cavity field). We mainly focus on the effects of the qubit–cavity detuning Δ and the qubit–cavity coupling strength κ on the non-Markovian speedup evolution of an open system. By controlling the environment, i.e., tuning Δ and κ , two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved. Furthermore, it is clearly found that increasing the coupling strength κ or detuning Δ in some cases can make the environmental non-Markovianity stronger and hence can lead to faster evolution of the open system.
Abstract We illustrate two linear configurations (one-side model and two-side model) for implementing a non-Markovian speedup evolution of a massive particle gravitationally coupled with a controllable environment: multiple massive particles. By controlling the environment, for instance by choosing a judicious the mass of the environmental particles or by changing the separation distance of each massive particle, two dynamical crossover behaviors from Markovian to non-Markovian and from no-speedup to speedup are achieved due to the gravitational interactions between the system particle and each environmental particle. Numerical calculation also shows that the critical mass of the environmental particles or the critical separation distance for these two dynamical crossover behaviors restrict each other directly. The larger the value of the mass of the environmental particles is, the smaller the value of the critical separation distance should be requested. In this work, the non-Markovian dynamics is the principal physical reason for the speedup evolution of a quantum system. Particularly, the non-Markovianity of the system mass particle in the two-side model has better correspondence with the quantum speed limit time than that in the one-side model.