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Chinese Physics B

Quantum speed limit time of a two-level atom under different quantum feedback control

Min Yu, Mao-Fa Fang, Hong‐Mei Zou

Published Jan 1, 2018• 9 citations
Publisher

Abstract

We investigate the quantum speed limit time (QSLT) of a two-level atom under quantum-jump-based feedback control or homodyne-based feedback control. Our results show that the two different feedback control schemes have different influences on the evolutionary speed. By adjusting the feedback parameters, the quantum-jump-based feedback control can induce speedup of the atomic evolution from an excited state, but the homodyne-based feedback control cannot change the evolutionary speed. Additionally, the QSLT for the whole dynamical process is explored. Under the quantum-jump-based feedback control, the QSLT displays oscillatory behaviors, which implies multiple speed-up and speed-down processes during the evolution. While, the homodyne-based feedback control can accelerate the speed-up process and improve the uniform speed in the uniform evolution process.

DOI
10.1088/1674-1056/27/1/010303

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We investigate the quantum speed limit time (QSLT) of a two-level atom under quantum-jump-based feedback control or homodyne-based feedback control. Our results show that the two different feedback control schemes have different influences on the evolutionary speed. By adjusting the feedback parameters, the quantum-jump-based feedback control can induce speedup of the atomic evolution from an excited state, but the homodyne-based feedback control cannot change the evolutionary speed. Additionally, the QSLT for the whole dynamical process is explored. Under the quantum-jump-based feedback control, the QSLT displays oscillatory behaviors, which implies multiple speed-up and speed-down processes during the evolution. While, the homodyne-based feedback control can accelerate the speed-up process and improve the uniform speed in the uniform evolution process.
We consider a two-mode entangled coherent light field, in which one mode of the light field is injected into the cavity and interacts with a two-level atom. According to the theory of cavity electrodynamics, the evolution state of atomic system is deduced. Aiming at the dynamic process from the initial state of an atomic system to the target evolution state, the quantum speed limit time is used to characterize the maximum evolution rate of the quantum state of an atomic system. The maximum evolution rate of an atomic system can be controlled by adjusting the coherent parameters of the two-mode entangled coherent light field. But up to now, which kind of quantum speed limit time can be better, universal and strict applicable to the quantum dynamics process of any system is still an unresolved important issue. Based on different methods of measuring the distance between two quantum states and different dynamic evolution channels, many definitions of the quantum speed limit time have been given. The quantum speed limit time proposed by Deffner and Lutz (Deffner S, Lutz E 2013 Phys. Rev. Lett. 111 010402) and the other deduced by Campaioli et al. (Campaioli F, Pollock F A, Binder F C, Modi K 2018 Phys. Rev. Lett. 120 060409; Campaioli F, Pollock F A, Modi K 2018 arXiv:1806.08742) have attracted extensive attention. In this paper, we first compare the advantages of two quantum speed limit times to characterize the maximum evolution rate of quantum states. We find that the quantum speed limit time expression given by Campaioli et al. (Campaioli F, Pollock F A, Modi K 2018 arXiv:1806.08742) in 2018 is a tighter bound when describing the boundary of the shortest time required for the quantum state evolution of a two-level atomic system. Therefore, this paper is mainly based on the quantum speed limit time given by Campaioli et al. to analyze how to achieve the maximum evolution rate of the quantum state of the atomic system by manipulating the parameters of a two-level entangled coherent light field. The results show that the maximum evolution speed of the quantum state of the atomic system can be significantly affected by the coherent parameters of the light field interacting with the atom under certain conditions. Furthermore, when the interacting light field parameters cannot well control the maximum evolution speed of the quantum state, the quantum correlation with the two-mode entangled coherent light field can realize the remote control of the maximum evolution speed of quantum state of atomic system by the light field parameters that are not involved in the atom-light interaction.
Quantum state change cannot occur instantly, but the speed of quantum evolution is limited to an upper bound value, called quantum speed limit (QSL). Understanding the quantum speed limit time (QSLT) is fundamental to advancing the control and optimization of quantum systems under decoherence. While significant progress has been made for single-qubit systems, the dynamics of two-qubit systems remain less explored. Studying the effects of dynamical decoupling (DD), such as periodic dynamical decoupling (PDD), on QSLT in two-qubit systems provides an opportunity to explore how to approach coherence preservation, entanglement stabilization, and environmental noise suppression. This exploration can lead to optimized strategies for controlling the evolution of two-qubit systems, which serve as the foundation of quantum gates and scalable quantum architectures. By analyzing QSLT in two-qubit systems, this research seeks to find how DD techniques can be adapted to mitigate the adverse effects of decoherence and extend their coherence times. The insights from this work will also shed light on the role of non-Markovian effects in two-qubit systems, offering potential pathways for leveraging such phenomena to maintain quantum coherence. The results reveal that under special conditions when decoupling pulses are applied to both qubits, the PDD method can completely remove all undesirable effects of the pure dephasing process. Eventually, these findings try to bridge the gap between theoretical frameworks and practical applications in quantum technologies, aiming to develop high-performance quantum processors.
We study the behaviors of quantum speed limit time (QSLT) of a two-level atom and non-Markovianity of an atomic ensemble described by the Dicke model. Our results show that both quantities can accurately locate the critical point of quantum phase transition between normal and super-radiant phases of the model. The numerical simulations demonstrate a rapid increase in the non-Markovianity in the super-radiant phase with increasing size of the ensemble. The growing non-Markovianity, in turn, results in speeding up quantum evolution of the two-level atom.
In this paper, we investigate quantum speed limits (QSLs) of a two-level system in the colored environments which are described by stochastic processes. We present QSL can be affected by the correlation time, the partitions of the constituent elements of the two-level system in different colored environments: the Ornstein–Uhlenbeck environment, simple fluctuating bottleneck environment, and the Dichotomic (two-state) environment. The investigations provide us a potential way to manipulate the quantum speed limit time (QSLT) of the quantum system in the colored environments. Our results could provide different insights on quantum control technologies of QSL and decoherent dynamics for the quantum computation.
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.