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arXiv:1910.10567

Quantum speed-up based on classical-field and moving-qubit

Jianhe Yang, Rongfang Liu, Hong‐Mei Zou, Danping Lin, Ali Mortezapour

Published Oct 23, 2019• 1 citation
arXivHTMLPDF

Abstract

In this work, we provide a model of a moving-qubit interacting with the multimode cavity, where the qubit is driven by the classical field. We obtain the analytic solution of the density operator of the qubit, then investigate the quantum speed limit time(QSLT) and the non-Markovianity based on the classical field and the moving-velocity. The results show that the transition from Markovian to non-Markovian dynamics is the intrinsic physical reason of the quantum speed-up process, both of the driving field and the strong coupling can enhance the non-Markovianity in the dynamics process and speed up the evolution of the qubit, but the moving velocity of the qubit can decrease the non-Markovianity in dynamics process and delay the evolution of qubit. To some extent, the classical field can reduce the effect of the moving velocity of the qubit on the quantum evolution process.

DOI
10.48550/arxiv.1910.10567

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In this work, we provide a model of a moving-qubit interacting with the multimode cavity, where the qubit is driven by the classical field. We obtain the analytic solution of the density operator of the qubit, then investigate the quantum speed limit time(QSLT) and the non-Markovianity based on the classical field and the moving-velocity. The results show that the transition from Markovian to non-Markovian dynamics is the intrinsic physical reason of the quantum speed-up process, both of the driving field and the strong coupling can enhance the non-Markovianity in the dynamics process and speed up the evolution of the qubit, but the moving velocity of the qubit can decrease the non-Markovianity in dynamics process and delay the evolution of qubit. To some extent, the classical field can reduce the effect of the moving velocity of the qubit on the quantum evolution process.
Abstract In this work, we obtain an analytical representation of the density operator of an atom in a dissipative cavity when the reservoir is at zero temperature and the total number of excitations is N = 1. We also investigated the quantum speed limit time (QSLT) of the atom and the non-Markovianity in the dynamics process. The results show that the QSLT and the non-Markovianity can be effectively manipulated by the atom–cavity coupling and the reservoir parameters. Both of the atom–cavity coupling and the detuning can induce a sudden transition from Markovian to non-Markovian dynamics, and this transition is the main physical reason of the quantum speed-up process. The critical value of the sudden transition from no speed-up to speed-up the atom–cavity coupling and the reservoir parameters. The corresponding physical explanation is also provided for our results.
We propose a method of accelerating the speed of evolution of an open system by an external classical driving field for a qubit in a zero-temperature structured reservoir. It is shown that, with a judicious choice of the driving strength of the applied classical field, a speed-up evolution of an open system can be achieved in both the weak system-environment couplings and the strong system-environment couplings. By considering the relationship between non-Makovianity of environment and the classical field, we can drive the open system from the Markovian to the non-Markovian regime by manipulating the driving strength of the classical field. That is the intrinsic physical reason that the classical field may induce the speed-up process. In addition, the role of this classical field on the variation of quantum evolution speed in the whole decoherence process is discussed.
Abstract We study the non-Markovianity and quantum speedup of a two-level atom (quantum system of interest) in a dissipative Jaynes-Cumming model, where the atom is embedded in a single-mode cavity, which is leaky being coupled to an external reservoir with Ohmic spectral density. We obtain the non-Markovianity characterized by using the probability of the atomic excited state and the negative decoherence rate in the time-local master equation. We also calculate the quantum speed limit time (QSLT) of the evolution process of the atom. The results show that, the atom-cavity coupling is the main physical reasons of the transition from Markovian to non-Markovian dynamics and the transition from no speedup to speedup process, and the critical value of this sudden transition only depends on the Ohmicity parameter. The atom-cavity coupling and the appropriate reservoir parameters can effectively improve the non-Markovianity in the dynamics process and speed up the evolution of the atom. Moreover, the initial non-Markovian dynamics first turns into Markovian and then back to non-Markovian with increasing the atom-cavity coupling under certain condition. Finally, the physical interpretation is provided.
The quantum speed limit (QSL) is a theoretical lower bound of the time required for a quantum system to evolve from an arbitrary initial state to its orthogonal counterpart. This figure can be used to characterize the dynamics of open quantum systems, including non-Markovian maps. In this paper, we investigate the QSL time for a model that consists of a single qubit moving inside a leaky cavity. Notably, we show that for both weak and strong coupling regimes, the QSL time increases while we boost the velocity of the qubit inside the leaky cavity. Moreover, it is observed that by increasing the qubit velocity, the speed of the evolution tends to a constant value, and the system becomes more stable. The results provide a better understanding of the dynamics of atom-photon couplings and can be used to enhance the controllability of quantum systems.
Quantum evolution can be accelerated in a non-Markovian environment. Previous results show that the formation of a system-environment bound state governs the quantum speedup. Although a stronger bound state in the system-environment spectrum may seem like it should cause greater speed of evolution, this seemingly intuitive thinking may not always be correct. We illustrate this by investigating a classical-driven qubit interacting with a photonic crystal waveguide in the presence of a mirror, resulting in non-Markovian dynamics for the system. Within the considered model, we show the influence of the mirror and the classical field on the evolution speed of the system. In particular, we find that the formation of a bound state is not the essential reason for the acceleration of evolution. The quantum speedup is attributed to the flow of information, regardless of the direction in which the information flows. Our conclusion can also be used in other non-Markovian environments.
The non-Markovianity and the quantum speed limit time (QSLT) are investigated in Jaynes-Cummings model coupling with the Ohmic reservoir at zero temperature when when t=0t=0t=0 and N=1N=1N=1. We obtain the non-Markovianity expressed by using the decoherence rate in the time-local master equation. We find that the non-Markovianity in the dynamics process can be witnessed by both of the negative decoherence rate and the positive derivative of the trace distance. The atom-cavity coupling is the main physical reasons of the transition from Markovian to non-Markovian dynamics and the quantum speed-up process of the atom, which the critical value of this sudden transition only depends on the Ohmicity parameter. The atom-cavity coupling and the appropriate reservoir parameters can effectively improve the non-Markovianity in the dynamics process and speed up the evolution of the atom. Moreover, the initial non-Markovian dynamics first turns into Markovian and then back to non-Markovian with increasing the atom-cavity coupling under certain condition. We also provide the physical interpretation.