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International Journal of Modern Physics C

Steady-state coherence of spin-boson model in a general non-Markovian environment

Fangqin Jin, Wen‐Long You, Yue Dai, Tian-Cheng Yi, Yuli Dong, Chengjie Zhang

Published Sep 29, 2023• 1 citation
Publisher

Abstract

Based on the quantum coherence theory, we employ the [Formula: see text]-norm measure to explore the steady-state coherence (SSC) in the spin-boson model. In this model, the environment is a non-Markovian bosonic bath with Ohmic-like spectral density. More generally, the interaction coupling between the qubit and the environment is a linear superposition of pure dephasing and pure damping coupling. Governed by the non-Markovian dynamics, some compact expressions of the SSC have been obtained at both zero temperature and high temperature. It shows that the hybrid coupling significantly affects the SSC. Moreover, a comprehensive analysis has been conducted to investigate the effects of various crucial factors, including the temperature of the bosonic bath, the qubit’s tunneling and the Ohmicity parameter. This analysis provides an effective approach for maintaining a relatively high SSC by manipulating system parameters.

DOI
10.1142/s0129183124500542

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Based on the quantum coherence theory, we employ the [Formula: see text]-norm measure to explore the steady-state coherence (SSC) in the spin-boson model. In this model, the environment is a non-Markovian bosonic bath with Ohmic-like spectral density. More generally, the interaction coupling between the qubit and the environment is a linear superposition of pure dephasing and pure damping coupling. Governed by the non-Markovian dynamics, some compact expressions of the SSC have been obtained at both zero temperature and high temperature. It shows that the hybrid coupling significantly affects the SSC. Moreover, a comprehensive analysis has been conducted to investigate the effects of various crucial factors, including the temperature of the bosonic bath, the qubit’s tunneling and the Ohmicity parameter. This analysis provides an effective approach for maintaining a relatively high SSC by manipulating system parameters.
We investigate the dynamics of a two-qubit open quantum system, in particular the two-qubit spin-boson model in the strong coupling regime, coupled to two thermal bosonic baths under non-Markovian and non-equilibrium conditions. Two complementary approaches, the Hierarchical Equations of Motion (HEOM) and Reaction Coordinate Mapping (RCM), are employed to examine various coupling regimes between the qubits and their respective baths. The dynamical features of the model and the impact of the tunneling amplitude on quantum coherence of the system are probed using the l1l_1l1​-norm of coherence. The model is further shown to have non-Markovian evolution. The nontrivial task of calculating entropy production in the strong-coupling regime is performed using auxiliary density operators in HEOM. Motivated by the realization of a quantum thermal device in the strong-coupling regime, the non-equilibrium steady-state behavior of the system is investigated. Furthermore, the relationship between the heat and spin currents and the tunneling amplitude is probed.
The non-Markovian dynamics of the driven spin-boson model at zero and finite temperature is investigated theoretically. Based on a unitary transformation and convolution theorem, the analytical expression of population difference in Laplace space is obtained. This method provides a tool to help us to understand the interference between driving and dissipation within the non-Markovian frame. We study the transient and the steady-state non-Markovian dynamics of population difference P ( t ) in the case of different temperature, driving and spin–bath coupling (SBC) strength. It has been shown that it is necessary to use non-Markovian methods when SBC is strong. At zero temperature, the curve of steady-state amplitude P lt versus Rabi driving amplitude Ω is N-like shaped. While at finite temperature, the curve becomes Λ-like shaped. These curves come from the interference between driving and dissipation. Also, from the interference pattern above, we know that large coherent oscillations can be obtained by optimizing the parameters: Rabi driving amplitude, temperature and SBC strength.
We investigate memory effects in the spin-boson model using a recently proposed measure for non-Markovian behavior based on the information exchange between an open system and its environment. Employing the numerical exact multilayer multiconfiguration time-dependent Hartree approach, we simulate the dynamics of the spin-boson model at zero temperature for a broad range of parameters. For a fast bath, i.e., in the scaling limit, we find non-Markovian dynamics for a coherently decaying spin at weak system-bath coupling, whereas memory effects are absent for stronger coupling in the regimes of incoherent decay and localization. If the timescales of system and bath are comparable, a complex, nonmonotonic dependence of non-Markovianity on the system-bath coupling strength is observed.
Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment leading to an irreversible loss of coherence. The Spin-Boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains largely unexplored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteractive effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and non-equilibrium quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel opportunities to exploit coherence as a resource in quantum devices operating in the ultra-strong coupling regime.
Environment-induced steady-state quantum coherence (SSQC) is a captivating phenomenon that challenges conventional understandings of decoherence. In this article, we delve into the foundational aspects of environment-induced SSQC, shedding light on its emergence within the framework of system-bath interactions. Starting from a microscopic system-bath-coupled model, we investigate the dependence of SSQC on environmental memory effects, the bath temperature, the system-bath coupling strength, and squeezing parameters. Our findings reveal that the environment not only acts as a generator but also as a disruptor of SSQC. A peak will exist for a non-Markovian bath, which is a result of competition between these two mechanisms. Interestingly, the peak disappears in the Markovian case. Additionally, we observe that the generated SSQC can be further amplified through environment squeezing.
Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment, leading to an irreversible loss of coherence. The spin-boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath, but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains much less explored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteracting effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and transient quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel insight into the equilibration behavior of quantum devices operating in the ultra-strong coupling regime.