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The European Physical Journal C

Control of quantum dynamics: non-Markovianity and speedup of a massive particle evolution due to gravity

Qi Wang, Kai Dong Xu, Wei‐Bin Yan, Ying-Jie Zhang, Zhong‐Xiao Man, Yun‐Jie Xia, Heng Fan

Published Aug 21, 2022• 3 citations
Publisher

Abstract

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.

DOI
10.1140/epjc/s10052-022-10700-7

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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.
Abstract A two-dimensional ray model is introduced to realize the non-Markovian speedup evolution of a center massive particle gravitationally coupled to a controllable environment (multilayer arrangement of the massive particles). By controlling the environment, for instance by choosing a judicious 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 environmental particles. It is obvious 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 addition, it should be emphasized that the non-Markovian dynamics is the principal physical reason for the speedup evolution of the system massive particle. Particularly, the non-Markovianity of the dynamics process of the system massive particle in the even ray case has better correspondence with the quantum speed limit time than that in the singular ray case.
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.
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 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
Quantum speedup of an open quantum system can be induced by the non-Markovian effect of the environment. Although an environment with a higher degree of non-Markovianity may seem like it should cause a faster speed of quantum evolution, this seemingly intuitive thinking may not always be correct. To clarify this point, we give a mechanism for controlling speedup of a single qubit that is coupled to a hierarchical photonic-crystal (PC) environment, which contains a defect single-mode cavity and a semi-infinite one-dimensional (1D) waveguide. Via studying the dynamics of the qubit, we reveal that with a judicious choice of the qubit-cavity coupling strength and the memory time of the waveguide environment, a speed-up evolution can be achieved. In particular, we found that the quantum speedup is not entirely attributed to the non-Markovianity, but to the increase of the total amount of flow information. That is the intrinsic physical reason that the hierarchical environment may induce the speed-up process. Our results may open new perspectives for detecting quantum speedup in realistic environments.
We theoretically study the dynamical speedup of a quantum system in a nonequilibrium environment. Based on the trace distance, we derive the generalized Margolus-Levitin and Mandelstam-Tamm types of bounds on the quantum speed limit time of a quantum system evolving from an arbitrary initial state. We demonstrate that the mechanism for the speedup of dynamical evolution is closely associated with both the energy of the system and exchange of information between the system and its environment. It is shown that the nonequilibrium feature of the environment can speed up the quantum evolution in both Markovian and non-Markovian dynamics regions. We emphasize that the non-Markovian effect of the system dynamics is neither necessary nor sufficient to speed up the quantum evolution in a nonequilibrium environment.