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arXiv:2408.01865 · Physical review. B./Physical review. B

Open quantum systems with noncommuting coupling operators: An analytic approach

Jakub Garwoła, Dvira Segal

Published Nov 12, 2024• 13 citations
arXivHTMLPDF

Abstract

We present an analytic approach to treat open quantum systems strongly coupled to multiple environments via noncommuting system operators: a prime example is a qubit concurrently coupled to both decohering and dissipative baths. Our approach, which accommodates strong system-bath couplings, generalizes the recently developed reaction-coordinate polaron transform method [N. Anto-Sztrikacs et al., PRX Quantum 4, 020307 (2023)] to handle couplings to baths via noncommuting system operators. Our approach creates an effective Hamiltonian that reveals the cooperative effect of the baths on the system. For a spin impurity coupled to both dissipative and decohering environments, the effective Hamiltonian predicts the suppression of relaxation by decoherence, a phenomenon previously observed in simulations but lacking so far a theoretical foundation. We also apply the method to an ensemble of spins coupled to local baths through noncommuting operators, demonstrating the engineering of the Kitaev XY spin chain interaction. Noncommutativity is a feature of quantum systems; future prospects of our approach include the study of thermal machines that leverage such genuine quantum effects.

DOI
10.1103/physrevb.110.174304

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We present an analytic approach to treat open quantum systems strongly coupled to multiple environments via noncommuting system operators: a prime example is a qubit concurrently coupled to both decohering and dissipative baths. Our approach, which accommodates strong system-bath couplings, generalizes the recently developed reaction-coordinate polaron transform method [N. Anto-Sztrikacs et al., PRX Quantum 4, 020307 (2023)] to handle couplings to baths via noncommuting system operators. Our approach creates an effective Hamiltonian that reveals the cooperative effect of the baths on the system. For a spin impurity coupled to both dissipative and decohering environments, the effective Hamiltonian predicts the suppression of relaxation by decoherence, a phenomenon previously observed in simulations but lacking so far a theoretical foundation. We also apply the method to an ensemble of spins coupled to local baths through noncommuting operators, demonstrating the engineering of the Kitaev XY spin chain interaction. Noncommutativity is a feature of quantum systems; future prospects of our approach include the study of thermal machines that leverage such genuine quantum effects.
Control of decoherence in open quantum systems has become a topic of great interest due to the emergence of quantum technologies that depend on quantum coherent effects. In this work, we investigate the decoherence dynamics of systems coupled to multiple baths through noncommuting systems' operators, and beyond the weak system-bath coupling limit. By building on cooperative effects between baths, we propose a novel strategy to mitigate rapid decoherence. Concretely, we study the dynamics of a qubit coupled to multiple environments with arbitrary interaction strengths, and along different coordinates. Based on insights gained on the decoherence dynamics from the analytical Effective Hamiltonian method, we carry out numerical simulations using the Reaction Coordinate quantum master equation method. In contrast to standard expectations, we show that when the system strongly interacts with a decohering bath, increasing its coupling to a second, dissipative bath slows down the decoherence dynamics. Our work offers insights into the preservation of quantum coherences in open quantum systems based on frustration effects, by utilizing cooperative effects between different heat baths.
We present the reaction-coordinate polaron-transform (RCPT) framework for generating effective Hamiltonian models to treat nonequilibrium open quantum systems at strong coupling with their surroundings. Our approach, which is based on two exact transformations of the Hamiltonian followed by its controlled truncation, ends with a new Hamiltonian with a weakened coupling to the environment. This new effective Hamiltonian mirrors the initial one, except that its parameters are dressed by the system-bath couplings. The power and elegance of the RCPT approach lie in its generality and in its mathematical simplicity, allowing for analytic work and thus profound understanding of the impact of strong system-bath coupling effects on open quantum system phenomena. Examples interrogated in this work include canonical models for quantum thermalization, charge and energy transport at the nanoscale, performance bounds of quantum thermodynamical machines such as absorption refrigerators and thermoelectric generators, as well as the equilibrium and nonequilibrium behavior of many-body dissipative spin chains.
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.
We focus on a dissipative three-level system as a case study to analytically demonstrate that strong system-bath coupling separates the relaxation dynamics of this dissipative quantum system into two distinct regimes: a short-time dynamics that, as expected, accelerates with increasing coupling to the environment, and a slow dynamics that, counterintuitively, becomes prolonged at sufficiently strong coupling. Using the reaction-coordinate polaron-transform mapping, we uncover the general mechanism behind this effect and derive accurate expressions for both relaxation timescales. Numerical simulations confirm our analytical predictions. From a practical perspective, our results suggest that strong coupling to a dissipative bath can autonomously generate and sustain long-lived quantum coherences, offering a promising strategy for bath-engineered quantum state preparation.
We present a general and practical theoretical framework to investigate how energy is dissipated in open quantum system dynamics. This is performed by quantifying the contributions of individual bath components to the overall dissipation of the system. The framework is based on the Nakajima-Zwanzig projection operator technique, which allows us to express the rate of energy dissipation into a specific bath degree of freedom by using traces of operator products. The approach captures system-bath interactions to all orders, but is based on second-order perturbation theory on the off-diagonal subsystem's couplings and a Markovian description of the bath. The usefulness of our theory is demonstrated by applying it to various models of open quantum systems involving harmonic oscillators or spin baths and connecting the outcomes to existing results such as our previously reported formula derived for locally coupled harmonic baths [Kim and Franco, J. Chem. Phys. 154, 084109 (2021)]. We also prove that the dissipation calculated by our theory rigorously satisfies thermodynamic principles such as energy conservation and detailed balance. Overall, the strategy can be used to develop the theory and simulation of dissipation pathways to interpret and engineer the dynamics of open quantum systems.