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arXiv:2009.12296

Coherent Dynamics of the Off-Diagonal Spin-Boson Model in the Ultra-Strong Coupling Regime

Nirmalendu Acharyya, Richter, Martin, Benjamin Philipp Fingerhut

Published Sep 25, 2020• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2009.12296

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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.
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.
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.
Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins, as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach for understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.
Within the lowest-order Born approximation, we present an exact calculation of the time dynamics of the spin-boson model in the Ohmic regime. We observe non-Markovian effects at zero temperature that scale with the system-bath coupling strength and cause qualitative changes in the evolution of coherence at intermediate times of order of the oscillation period. These changes could significantly affect the performance of these systems as qubits. In the biased case, we find a prompt loss of coherence at these intermediate times, whose decay rate is set by α\sqrtαα​, where ααα is the coupling strength to the environment. These calculations indicate precision experimental tests that could confirm or refute the validity of the spin-boson model in a variety of systems.