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International Journal of Modern Physics C

Tunable steady-state coherence via composite system–environment interactions beyond weak tunnel coupling

Ming He, Yuyan Weng, Shijie Xu, Yuli Dong

Published May 2, 2025• 0 citations
Publisher

Abstract

We study a two-level system with an additional tunneling effect, where the general interaction with an Ohmic-class spectrum can be controlled by adjusting the coupling angle. We outline the derivation of the time-local microscopic non-Markovian master equation after renormalizing the eigenstates in the two-level system, hence removing the restriction of weak tunneling coupling. Further, two quantum coherence measures are exploited to analyze steady-state coherences (SSC). We identify that under strong tunneling effects, a specific coupling angle enables SSC generation that is both independent of the Ohmic-like spectral density and capable of reaching substantial magnitudes. Moreover, in the vicinity of this critical angle, SSC exhibits an opposite dependence on the Ohmic parameter in different regions. In addition, we examine the impact of Ohmic parameters and environmental temperature on SSC, demonstrating that optimizing these factors provides an effective strategy to maximize SSC.

DOI
10.1142/s0129183125501141

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Comment on "Steady-State Coherences by Composite System-Bath Interactions"

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In a recent Letter, Guarnieri et al. [1] reported on the possibility of generating steady-state coherence (SSC) in the energy basis of a two-level system by the sole action of a single thermal bath also for weak system-bath coupling and due to a composite form of this interaction. The results are based on a time-local Bloch-Redfield master equation without secular approximation and the associated set of Bloch equations, all derived in the Supplemental Material (SM) of Ref. [1]. We comment that the results reported by the authors present both technical flaws and conceptual limitations that substantially impact some of their main conclusions. Our objections mainly concern (a) technical errors in the calculation of SSC (Eqs.(2)-(4) in [1]) and (b) negativity issues associated with the weak-coupling master equation employed by the authors.

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Physica Scripta•Nov 23, 2021•1 citation
We study a two-level system with an additional tunneling effect, where the general interaction with an Ohmic-class spectrum can be controlled by adjusting the coupling angle. We outline the derivation of the time-local microscopic non-Markovian master equation after renormalizing the eigenstates in the two-level system, hence removing the restriction of weak tunneling coupling. Further, two quantum coherence measures are exploited to analyze steady-state coherences (SSC). We identify that under strong tunneling effects, a specific coupling angle enables SSC generation that is both independent of the Ohmic-like spectral density and capable of reaching substantial magnitudes. Moreover, in the vicinity of this critical angle, SSC exhibits an opposite dependence on the Ohmic parameter in different regions. In addition, we examine the impact of Ohmic parameters and environmental temperature on SSC, demonstrating that optimizing these factors provides an effective strategy to maximize SSC.
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 identify sufficient conditions on the structure of the interaction Hamiltonian between a two-level quantum system and a thermal bath that, without any external drive or coherent measurement, guarantee the generation of steady-state coherences (SSC). The SSC obtained this way, remarkably, turn out to be independent of the initial state of the system, which could therefore be taken as initially incoherent. We characterize in detail this phenomenon, first analytically in the weak coupling regime for two paradigmatic models, and then numerically in more complex systems without any assumption on the coupling strength. In all of these cases, we find that SSC become increasingly significant as the bath is cooled down. These results can be directly verified in many experimental platforms.
In a recent Letter, Guarnieri et al. [1] reported on the possibility of generating steady-state coherence (SSC) in the energy basis of a two-level system by the sole action of a single thermal bath also for weak system-bath coupling and due to a composite form of this interaction. The results are based on a time-local Bloch-Redfield master equation without secular approximation and the associated set of Bloch equations, all derived in the Supplemental Material (SM) of Ref. [1]. We comment that the results reported by the authors present both technical flaws and conceptual limitations that substantially impact some of their main conclusions. Our objections mainly concern (a) technical errors in the calculation of SSC (Eqs.(2)-(4) in [1]) and (b) negativity issues associated with the weak-coupling master equation employed by the authors.
The transient dynamics of quantum coherence of Gaussian states are investigated. The state is coupled to an external environment which can be described by a Fano-Anderson type Hamiltonian. Solving the quantum Langevin equation, we obtain the Greens functions which are used to compute the time evolved first and second moments of the quadrature operators. From the quadrature operator moments, we construct the covariance matrix which is used to measure the coherence in the system. The coherence is measured using the relative entropy of coherence measure. We consider three different classes of spectral densities in our analysis viz, the Ohmic, the sub-Ohmic, and the super-Ohmic densities. In our work, we study the dynamics of the coherent state, squeezed state, and displaced squeezed state. For all these states we observe that when the coupling with the system and the environment is weak, the coherence monotonically decreases and eventually vanishes in a long time. Thus all the states exhibit Markovian evolution in the weak coupling limit. In the strong coupling limit, the dynamics for the initial period is Markovian and after a certain period, it becomes non-Markovian where we observe an environmental backaction on the system. Thus in the strong coupling limit, we observe a dynamical crossover from Markovian nature to non-Markovian behavior. This crossover is very abrupt under some environmental conditions and for some parameters of the quantum state. Using a quantum master equation approach we verify the crossover from the dynamics of the dissipation and fluctuation parameters and the results endorse those obtained from coherence dynamics.
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.
Abstract In this work, we study the improvement of steady-state coherence (SSC) and steady-state entanglement (SSE) of two coupled qubits by means of composite system-reservoir interaction constructed by a linear combination of orthogonal and parallel ones. We show that in the non-equilibrium case, the SSC and SSE can be significantly enhanced by increasing the parallel components of the interaction Hamiltonian between the system of interest and the heat reservoirs. In addition, we find that in the non-equilibrium case, increasing the parallel components can enlarge the temperature (temperature difference) region where the SSC can maintain nonzero values. In the equilibrium situation, however, the SSC and SSE are not affected by the parallel components of the composite system-reservoir interactions.