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New Journal of Physics

Non-Markovian dynamics of the driven spin-boson model

Xiufeng Cao, Cheng Jiang, Peihao Huang

Published Sep 1, 2021• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/ac2593

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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.
The dynamics of a driven spin-boson model is studied by means of the perturbation approach based on a unitary transformation. Analytical expressions for the population difference and the coherence of the two state system are obtained. The results show that for weak driving, the population difference displays damping coherent oscillation and/or damping quantum beat, depending on the initial preparation. The coherence exhibits damped oscillation with Rabi frequency. When driving is strong enough, the population difference exhibits undamped large-amplitude coherent oscillation. In addition, our theory leads to correct results in two limiting cases: without dissipation and without driving field.
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.
The quantum dynamics of the dissipative two-level system in the Ohmic bath with Rabi driving is studied by means of a modified Bloch-Redfield approach based on a unitary transformation. The main purpose is to understand the effect of counter-rotating terms of the system-environment interaction on the dynamics of the two-level system and, in particular, if it is possible to control the effective system-environment coupling by their effect on the interference between driving and dissipation. By calculating the nonequilibrium correlation P(t)P(t)P(t) for a finite driving it is shown that the counter-rotating terms of the system-environment interaction play an important role in the dynamic evolution with a longer coherent time and a weaker amplitude of the long-time driven oscillation.
A new analytical approach, beyond the rotating wave approximation, based on unitary transformations and the non-markovian master equation for the density operator, is applied to treat the biased spin-boson model with a Lorentzian structured bath for arbitrary detunings at zero temperature. Compared to zero bias, we find that the non-equilibrium dynamics demonstrates two more damping oscillation frequencies and one additional relaxation frequency for non-zero bias. Analytical expressions for the non-markovian dynamics and the corresponding spectrum, the localized-delocalized transition point, the coherent-incoherent transition point, the analytical ground energy, the renormalized tunneling factor and the susceptibility are determined. The sum rule and the Shiba relation are checked in the coherent regime.
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.
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.