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Physical Review A

Quantum decoherence of a two-level system in colored environments

Longli Zheng, Yonggang Peng

Published May 31, 2022• 7 citations
Publisher

Abstract

In this paper, we investigate quantum decoherence dynamics of a two-level system in colored environments described by stochastic processes. We present the extension of the theoretical framework of the stochastic Liouville approach, and we employ the approach in studying the decoherence dynamics of the two-level system in typical colored environments: the Ornstein-Uhlenbeck environment, a simple fluctuating bottleneck environment, and the dichotomic (two-state) environment. The analytical expressions of the decoherence factor of a two-level system in colored environments are obtained by introducing the marginal average operator, whose eigenvalues and eigenfunctions provide different viewpoints from which to understand the behavior of the decoherence factor. In addition, the investigations provide us a potential way to manipulate the decoherence of the quantum system in colored environments.

DOI
10.1103/physreva.105.052443

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In this paper, we investigate quantum decoherence dynamics of a two-level system in colored environments described by stochastic processes. We present the extension of the theoretical framework of the stochastic Liouville approach, and we employ the approach in studying the decoherence dynamics of the two-level system in typical colored environments: the Ornstein-Uhlenbeck environment, a simple fluctuating bottleneck environment, and the dichotomic (two-state) environment. The analytical expressions of the decoherence factor of a two-level system in colored environments are obtained by introducing the marginal average operator, whose eigenvalues and eigenfunctions provide different viewpoints from which to understand the behavior of the decoherence factor. In addition, the investigations provide us a potential way to manipulate the decoherence of the quantum system in colored environments.
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.
We theoretically study the decoherence of a two-level quantum system coupled to noisy environments exhibiting linear and quadratic fluctuations within the framework of a stochastic Liouville equation. It is shown that the intrinsic energy levels of the quantum system renormalize under either the linear or quadratic influence of the environmental noise. In the case of quadratic dependence, the renormalization of the energy levels of the system emerges even if the environmental noise exhibits stationary statistical properties. This is in contrast to the case under linear influence, where the intrinsic energy levels of the system renormalize only if the environmental noise displays nonstationary statistics. We derive the analytical expressions of the decoherence function in the cases where the fluctuation of the frequency difference depends linearly and quadratically on the nonstationary Ornstein-Uhlenbeck noise (OUN) and random telegraph noise (RTN) processes, respectively. In the case of the linear dependence of the OUN, the environmental nonstationary statistical property can enhance the dynamical decoherence. However, the nonstationary statistics of the environmental noise can suppress the quantum decoherence in this case under the quadratic influence of the OUN. In the presence of the RTN, the quadratic influence of the environmental noise does not give rise to decoherence but only causes a determinate frequency renormalization in dynamical evolution. The environmental nonstationary statistical property can suppress the quantum decoherence of the case under the linear influence of the RTN.
We theoretically investigate the dynamics of a quantum system which is coupled to a fluctuating environment based on the framework of Kubo-Anderson spectral diffusion. By employing the projection operator technique, we derive two types of dynamical equations, namely, time-convolution and time-convolutionless quantum master equations, respectively. We derive the exact quantum master equations of a qubit system with both diagonal splitting and tunneling coupling when the environmental noise is subject to a random telegraph process and a Ornstein-Uhlenbeck process, respectively. For the pure decoherence case with no tunneling coupling, the expressions of the decoherence factor we obtained are consistent with the well-known existing ones. The results are significant to quantum information processing and helpful for further understanding the quantum dynamics of open quantum systems.
In this paper we investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical fluctuating environment. The interaction with the bath has the Lorentzian spectral density, and the fluctuating environment (stochastic field) is represented by a set of Ornstein-Uhlenbeck processes. Each of the subenvironments of the composite environment is able to induce non-Markovian dynamics of the two-level system. By means of the numerically exact method of hierarchical equations of motion, we study dependence of the steady states of the two-level system, the reduced density matrix evolution and the equilibrium emission spectrums on frequency cutoffs and coupling strengths of the subenvironments. Additionally we investigate the impact of the rotation-wave approximation (RWA) used for the interaction with the bath on accuracy of the results.
In this paper we investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical fluctuating environment. The interaction with the bath has the Lorentzian spectral density, and the fluctuating environment (stochastic field) is represented by a set of Ornstein-Uhlenbeck processes. Each of the subenvironments of the composite environment is able to induce non-Markovian dynamics of the two-level system. By means of the numerically exact method of hierarchical equations of motion, we study steady states of the two-level system, evolution of the reduced density matrix and the equilibrium emission spectra in dependence on the frequency cutoffs and the coupling strengths of the subenvironments. Additionally, we investigate the impact of the rotating wave approximation (RWA) for the interaction with the bath on accuracy of the results.
Detailed studies are carried out for the problem of decoherence control by a successive application of ?-pulses when a relevant spin-1/2 (qubit) system is surrounded by a stochastically fluctuating environment. Specifically, considerations are given to two representative stochastic processes: a two-state-jump Markov process and a Gauss?Markov process. Exact analytical solutions are obtained for the decoherence control by the ?-pulse application even for non-stationary stochastic processes as well as for stationary processes. In view of recent advances in dynamical decoupling experiments with artificial (engineered) stochastic noise, the results are useful in analysing qubit systems under the influence of a fluctuating environment.