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arXiv:2004.08974

Coherent dynamics in a dual-coupling spin-boson model

Leonard Ruocco

Published Apr 19, 2020• 0 citations
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Abstract

We study the dynamics of a particle tunneling between the ground states of a symmetric double potential well system, in the presence of simultaneous diagonal and non-diagonal couplings to an Ohmic oscillator bath. We use the noninteracting-blip approximation to investigate coherence effects across a wide range of system-environment coupling strengths at physiological temperatures. We show how the presence of a non-diagonal coupling mechanism significantly alters the dynamics of the tunneling particle, producing coherent oscillations despite strong thermal fluctuations in the environment. Fluctuations in both the particle's polarization, as well as tunneling energies, lead to competing influences on the coherent nature of tunneling particle dynamics, with non-diagonal couplings introducing a relatively long-lived oscillatory mode in an otherwise incoherent setting.

DOI
10.48550/arxiv.2004.08974

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We study the dynamics of a particle tunneling between the ground states of a symmetric double potential well system, in the presence of simultaneous diagonal and non-diagonal couplings to an Ohmic oscillator bath. We use the noninteracting-blip approximation to investigate coherence effects across a wide range of system-environment coupling strengths at physiological temperatures. We show how the presence of a non-diagonal coupling mechanism significantly alters the dynamics of the tunneling particle, producing coherent oscillations despite strong thermal fluctuations in the environment. Fluctuations in both the particle's polarization, as well as tunneling energies, lead to competing influences on the coherent nature of tunneling particle dynamics, with non-diagonal couplings introducing a relatively long-lived oscillatory mode in an otherwise incoherent setting.
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.
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.
The dynamical behavior of a two-level system coupled linearly to a dissipative bath of two-level systems whose tunneling splittings and coupling parameters are distributed according to an Ohmic spectrum is studied using numerical path integral methods as well as the noninteracting blip approximation for an equivalent harmonic environment characterized by a scaled spectral density. Comparisons with the behaviors of the conventional spin-boson model of similar coupling strength reveal a weaker quenching of coherence in the present case. Finally, the boundary in parameter space between coherent and incoherent dynamics is mapped.
We study the spin-boson model with a sub-Ohmic bath using a variational method. The transition from coherent dynamics to incoherent tunneling is found to be abrupt as a function of the coupling strength $\ensuremath{\alpha}$ and to exist for any power 0<s<10<s<10<s<1, where the bath coupling is described by $J(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\alpha}{\ensuremath{\omega}}^{s}$. We find nonmonotonic temperature dependence of the two-level gap $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K}$ and a reentrance regime close to the transition due to nonadiabatic low-frequency bath modes. Differences between thermodynamic and dynamic conditions for the transition as well as the limitations of the simplified bath description are discussed.
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.
A master equation approach based on an optimized polaron transformation is adopted for dynamics simulation with simultaneous diagonal and off-diagonal spin-boson coupling. Two types of bath spectral density functions are considered, the Ohmic and the sub-Ohmic. The off-diagonal coupling leads asymptotically to a thermal equilibrium with a nonzero population difference Pz(t → ∞) ≠ 0, which implies localization of the system, and it also plays a role in restraining coherent dynamics for the sub-Ohmic case. Since the new method can extend to the stronger coupling regime, we can investigate the coherent-incoherent transition in the sub-Ohmic environment. Relevant phase diagrams are obtained for different temperatures. It is found that the sub-Ohmic environment allows coherent dynamics at a higher temperature than the Ohmic environment.