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Chinese Physics B

Non-Markovian speedup dynamics control of the damped Jaynes–Cummings model with detuning

Kai Dong Xu, Wei Han, Ying-Jie Zhang, Heng Fan

Published Jan 1, 2018• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/27/1/010302

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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.
We investigate the qubit in the hierarchical environment where the first layer is just one lossy cavity while the second layer is the NNN-coupled lossy cavities. In the weak-coupling regime between the qubit and the first-layer environment, the dynamics crossovers from Markovian to non-Markovian and from no-speedup to speedup can be realized by controlling the hierarchical environment. We find that the coupling strength between two nearest-neighbor cavities and the number of cavities in the second-layer environment have the opposite effect on the non-Markovian dynamics and speedup evolution of the qubit. However, in the case of strong coupling between the qubit and the first-layer environment, we can be surprised to find that, compared with the original non-Markovian dynamics, the added second-layer environment cannot play a beneficial role on the speedup of the dynamics of the system. In addition, a phenomenon can be noticed that the complete opposite role of the coupling strength between two nearest-neighbor cavities (the number of cavities) in the second-layer environment in the above weak- and strong-coupling regimes.
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
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 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.
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.