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arXiv:1903.01230 · The European Physical Journal C

Quantum speed limit time for the damped Jaynes-Cummings and Ohmic-like dephasing models in Schwarzschild space-time

S. Haseli

Published Jul 1, 2019• 7 citations
arXivHTMLPDF

Abstract

Quantum theory sets the bound on the minimal evolution time between initial and final states of the quantum system. This minimal evolution time can be used to specify the maximal speed of the evolution in open and closed quantum systems. Quantum speed limit is one of the interesting issue in the theory of open quantum systems. One may investigate the influence of the relativistic effect on the quantum speed limit time. When several observers are placed in different inertial or non-inertial frames, or in Schwarzschild space-time, the relativistic effect should be taken into account. In this work, the quantum speed limit time in Schwarzschild space-time will be studied for two various model consist of damped Jaynes-Cummings and Ohmic-like dephasing. First, it will be observed that how quantum coherence is affected by Hawking radiation. According to the dependence of quantum speed limit time on quantum coherence and the dependence of quantum coherence on relative distance of quantum system to event horizon $$R_{0}$$ , it will be represented that the quantum speed limit time in Schwarzschild space-time is decreased by increasing $$R_{0}$$ for damped Jaynes-Cummings model and conversely. It is increased by increasing $$R_{0}$$ for Ohmic-like dephasing model.

DOI
10.1140/epjc/s10052-019-7129-1

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Quantum theory sets the bound on the minimal evolution time between initial and final states of the quantum system. This minimal evolution time can be used to specify the maximal speed of the evolution in open and closed quantum systems. Quantum speed limit is one of the interesting issue in the theory of open quantum systems. One may investigate the influence of the relativistic effect on the quantum speed limit time. When several observers are placed in different inertial or non-inertial frames, or in Schwarzschild space-time, the relativistic effect should be taken into account. In this work, the quantum speed limit time in Schwarzschild space-time will be studied for two various model consist of damped Jaynes-Cummings and Ohmic-like dephasing. First, it will be observed that how quantum coherence is affected by Hawking radiation. According to the dependence of quantum speed limit time on quantum coherence and the dependence of quantum coherence on relative distance of quantum system to event horizon R0R_{0}R0​ , it will be represented that the quantum speed limit time in Schwarzschild space-time is decreased by increasing R0R_{0}R0​ for damped Jaynes-Cummings model and conversely. It is increased by increasing R0R_{0}R0​ for Ohmic-like dephasing model.
The minimal time a system needs to evolve from an initial state to its one orthogonal state is defined as the quantum speed limit time, which can be used to characterize the maximal speed of evolution of a quantum system. This is a fundamental question of quantum physics. We investigate the generic bound on the minimal evolution time of the open dynamical quantum system. This quantum speed limit time is applicable to both mixed and pure initial states. We then apply this result to the damped Jaynes-Cummings model and the Ohimc-like dephasing model starting from a general time-evolution state. The bound of this time-dependent state at any point in time can be found. For the damped Jaynes-Cummings model, when the system starts from the excited state, the corresponding bound first decreases and then increases in the Markovian dynamics. While in the non-Markovian regime, the speed limit time shows an interesting periodic oscillatory behavior. For the case of Ohimc-like dephasing model, this bound would be gradually trapped to a fixed value. In addition, the roles of the relativistic effects on the speed limit time for the observer in non-inertial frames are discussed.
In this paper, we investigate the unified bound of quantum speed limit time in open systems based on the modified Bures angle. This bound is applied to the damped Jaynes-Cummings model and the dephasing model, and the analytical quantum speed limit time is obtained for both models. As an example, the maximum coherent qubit state with white noise is chosen as the initial states for the damped Jaynes-Cummings model. It is found that the quantum speed limit time in both the non-Markovian and the Markovian regimes can be decreased by the white noise compared with the pure state. In addition, for the dephasing model, we find that the quantum speed limit time is not only related to the coherence of initial state and non-Markovianity, but also dependent on the population of initial excited state.
The quantum speed limit time for quantum system under squeezed environment is studied. We consider two typical models, the damped Jaynes–Cummings model and the dephasing model. For the damped Jaynes–Cummings model under squeezed environment, we find that the quantum speed limit time becomes larger with the squeezed parameter r increasing and indicates symmetry about the phase parameter value θ = π. Meanwhile, the quantum speed limit time can also be influenced by the coupling strength between the system and environment. However, the quantum speed limit time for the dephasing model is determined by the dephasing rate and the boundary of acceleration region that interacting with vacuum reservoir can be broken when the squeezed environment parameters are appropriately chosen.
A unified bound on the quantum speed limit is obtained for open quantum systems with a mixed initial state by utilizing the function of relative purity proposed by F. Campaioli et al. [Phys. Rev. Lett. 120, 060409 (2018)]. As applications, it is found that the quantum speed limit bound for the damped Jaynes-Cummings model is determined by the competition among the non-Markovianity, the population of the initial excited state, and the initial-state coherence, which shows that the population of the initial excited state and the coherence of the initial state can make the quantum speed limit bound tighter even though the non-Markovian effects can accelerate the evolution of open quantum system. For the dephasing model, a simple factorization law with the initial-state coherence shows that the quantum speed limit is governed by only the competition between the non-Markovianity and the coherence of the initial state.
Quantum theory sets a bound on the minimal time it takes for a system to evolve from initial state to target state. This bound is called the quantum speed limit (QSL) time. The quantum speed limit time is used to quantify the maximal speed of the quantum evolution. The quantum evolution will be faster if the quantum speed limit time decreases. In this work, we study the quantum speed limit time for an open quantum system in the presence of disturbance in an environment. We use the model which is provided by Ban [Phys. Rev. A 99, 012116 (2019)]. In this model, two quantum systems [Formula: see text] and [Formula: see text] interact with environment sequentially. At first, quantum system [Formula: see text] interacts with the environment [Formula: see text] as an auxiliary system, then quantum system [Formula: see text] starts its interaction with disturbed environment immediately. In this work, we consider the dephasing coupling with two types of environment that has different spectral density: Ohmic and Lorentzian. We observe that, non-Markovian effects will appear in the dynamics of the second quantum system [Formula: see text] due to the interaction of the first quantum system [Formula: see text] with the environment. Given the fact that the quantum speed limit time reduces due to the non-Markovian feature of quantum evolution, we show that disturbance effects will reduce the quantum speed limit time for the dynamics of the second quantum system [Formula: see text].
Quantum speed limit time (QSLT) can be used to characterize the intrinsic minimal time interval for a quantum system evolving from an initial state to a target state. We investigate the QSLT of the open system in Schwarzschild space-time. We show that, in some typical noisy channels,the Hawking effect can be beneficial to the evolution of the system. For an initial entangled state, the evolution speed of the system can be enhanced in the depolarizing, bit flip, and bit-phase flip channels as the Hawking temperature increases, which are in sharp contrast to the phase flip channel. Moreover, the optimal initial entanglement exists in other noise channels except the phase flip channel, which minimizes the QSLT of the system and thus leads to the maximum evolution speed of the system.