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arXiv:2409.14661 · APL Quantum

Spectral signatures of the Markovian to non-Markovian transition in open quantum systems

Zeng-Zhao Li, Chi‐Hang Lam, Cho‐Tung Yip, Bo Li

Published Apr 10, 2025• 3 citations
arXivHTMLPDF

Abstract

We present a new approach for investigating the Markovian to non-Markovian transition in quantum aggregates strongly coupled to a vibrational bath through the analysis of linear absorption spectra. Utilizing hierarchical algebraic equations in the frequency domain, we elucidate how these spectra can effectively reveal transitions between Markovian and non-Markovian regimes, driven by the complex interplay of dissipation, aggregate–bath coupling, and intra-aggregate dipole–dipole interactions. Our results demonstrate that reduced dissipation induces spectral peak splitting, signaling the emergence of bath-induced non-Markovian effects. The spectral peak splitting can also be driven by enhanced dipole–dipole interactions, although the underlying mechanism differs from that of dissipation-induced splitting. In addition, with an increase in aggregate–bath coupling strength, initially symmetric or asymmetric peaks with varying spectral amplitudes may merge under weak dipole–dipole interactions, whereas strong dipole–dipole interactions are more likely to cause peak splitting. Moreover, we find that spectral features serve as highly sensitive indicators for distinguishing the geometric structures of aggregates while also unveiling the critical role that geometry plays in shaping non-Markovian behavior. This study not only deepens our understanding of the Markovian to non-Markovian transition but also provides a robust framework for optimizing and controlling quantum systems.

DOI
10.1063/5.0262783

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We present a new approach for investigating the Markovian to non-Markovian transition in quantum aggregates strongly coupled to a vibrational bath through the analysis of linear absorption spectra. Utilizing hierarchical algebraic equations in the frequency domain, we elucidate how these spectra can effectively reveal transitions between Markovian and non-Markovian regimes, driven by the complex interplay of dissipation, aggregate–bath coupling, and intra-aggregate dipole–dipole interactions. Our results demonstrate that reduced dissipation induces spectral peak splitting, signaling the emergence of bath-induced non-Markovian effects. The spectral peak splitting can also be driven by enhanced dipole–dipole interactions, although the underlying mechanism differs from that of dissipation-induced splitting. In addition, with an increase in aggregate–bath coupling strength, initially symmetric or asymmetric peaks with varying spectral amplitudes may merge under weak dipole–dipole interactions, whereas strong dipole–dipole interactions are more likely to cause peak splitting. Moreover, we find that spectral features serve as highly sensitive indicators for distinguishing the geometric structures of aggregates while also unveiling the critical role that geometry plays in shaping non-Markovian behavior. This study not only deepens our understanding of the Markovian to non-Markovian transition but also provides a robust framework for optimizing and controlling quantum systems.
Abstract Fractional-order extensions of quantum dynamical equations provide an effective framework for incorporating memory and non-Markovian effects into the description of open quantum systems. In this work we investigate a laser-driven two-level system governed by a fractional generalization of the optical Bloch equations based on Caputo derivatives. The resulting evolution is analyzed in phase space, where temporal memory manifests itself through systematic geometric modifications of the relaxation trajectories. In particular, decreasing the fractional order produces a rotation and contraction of the phase-space spirals, together with a displacement of their effective centers, revealing a consistent reorganization of the dissipative oscillatory dynamics. We further connect this time-domain behavior to experimentally accessible frequency-domain signatures by constructing the incoherent resonance-fluorescence power spectrum from the stationary dipole correlation function. The fractional spectra recover the classical three-peak (Mollow-type) structure in the limit α → 1 , while for α < 1 they exhibit a redistribution of spectral weight accompanied by modified peak localization, sideband separation, and intensity ratios. These results demonstrate how fractional dynamics links the geometry of relaxation to measurable spectral morphology in non-Markovian quantum systems.
Non-Markovian effects in open quantum systems are central to understanding spectral lineshape. Here, we quantify the non-Markovianity associated with both overdamped and underdamped vibrations in terms of information flow between the bath and the system and compare this with the broadening and ellipticity of two-dimensional spectra. Using the Breuer Laine Piilo (BLP) measure, we link the well-known stochastic models for spectral lineshape with modern quantum information theory. Specifically, we study the effect of non-Markovianity in a system in contact with underdamped vibrations and examine the differences observed on increasing the damping to the overdamped limit. The open quantum system dynamics are evolved using the hierarchical equations of motion, efficiently terminated with a Markovian cutoff, where separate hierarchies are derived for the underdamped and overdamped environments. It is shown that the BLP measure is quantitatively correlated with the ellipticity of two-dimensional spectra and memory effects are more pronounced in underdamped environments, due to the long-lived feedback of information between the system and its bath, compared to overdamped environments. Environmental signatures in spectral lineshapes emerge as a result of information flow from the bath back into the system.
We investigate signatures of non-Markovianity in the dynamics of a periodically driven qubit coupled to a dissipative bosonic environment. We propagate the dynamics of the reduced density matrix of the qubit by integrating the numerically exact hierarchical equations of motion. Non-Markovian features are quantified by comparing on an equal footing the predictions from diverse and complementary approaches to quantum dissipation. In particular, we analyze the distinguishability of quantum states, the decay of the volume accessible to the qubit on the Hilbert space, the negativity of the canonical rates in the generalized Lindblad equation, and the relaxation of the memory kernels in the Nakajima-Zwanzig generalized quantum master equation. We study the effects of controlled driving on the coherent dynamics of the system. We show that a suitable external field can offset the ergodic relaxation of time-correlation functions, increase distinguishability over time, and strengthen non-Markovian effects witnessed by the canonical dissipation channels. We furthermore observe the phenomenon of eternal non-Markovianity for sufficiently small system-bath coupling and we discuss how this can be enhanced by modulating the frequency of the external drive. This work provides a broad theoretical analysis of quantum dissipation in the framework of open quantum dynamics and quantum information.
Markovian (memoryless) system-bath interactions play a fundamental role across physics, chemistry, and biological systems. Typically, such memoryless behavior arises from the bath’s properties. Here, we reveal a distinct mechanism: when a system interacts with both a Markovian and a non-Markovian bath, losses induced by the former suppress memory effects from the latter, making the interaction appear more Markovian. This effect leads to a direct interplay between independent baths, where Markovianity becomes “contagious,” transferring between them via their common system. To describe this phenomenon, we introduce a Bloch-Redfield-inspired approach that accurately captures how a lossy system, governed by a Lindblad master equation, interacts with a non-Markovian bath. Beyond offering new insights into dissipative dynamics, this framework provides a computationally efficient alternative for modeling complex system-bath interactions across a broad range of scientific disciplines. Markovianity, where system-bath interactions have no memory, is central for describing many physical processes and serves as a useful approximation that reduces complexity. Here, the authors show that Markovianity can arise not only from the bath’s properties, but also from dissipation induced in a system coupled to a non-Markovian bath by its coupling to an additional Markovian bath.
We analyze the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The model is amenable to an analytical solution when the initial state of the chain is Gaussian. We study the dynamics of the qubits' concurrence starting from a separable state and assuming that the chain spectrum is gapped and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak-coupling regime, where the qubits are entangled at the asymptotics, (ii) the strong-coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude, and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits' distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows one to identify the key resources for realizing quantum coherent dynamics of open systems.
In interacting quantum many-body systems, relaxation toward equilibrium reflects a competition between internal chaotic dynamics and environmental dissipation. While conventional Markovian baths typically produce exponential decay, non-Markovian dissipation can give rise to more intricate behavior, including algebraic relaxation. We study an open Sachdev-Ye-Kitaev (SYK) model coupled to a pseudogapped fermionic bath, using the Keldysh formalism to compute steady-state correlations in the large-NNN limit. Our results uncover a rich dynamical phase diagram, with regimes of bath-driven power-law relaxation, chaos-driven exponential decay, and an intermediate pre-relaxation phase where exponential decay crosses over to algebraic decay. These findings demonstrate that non-Markovian environments can qualitatively reshape relaxation mechanisms in strongly correlated quantum many-body systems.