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.
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.
Dissipation caused by nonhomogeneous bosonic finite chain environments (implementable in, e.g., segmented ion traps) is investigated through an exact diagonalization approach, avoiding common approximations used to describe open systems. Different spectral densities, including band gaps, can be engineered to separately assess different factors leading to memory effects, namely, the environment's size, temperature, proximity of the cutoff frequency, the spectral density's shape (sub-Ohmic, Ohmic, super-Ohmic), and the strength of its coupling to the system. Non-Markovianity is quantified with two recently introduced measures related to information backflow and nondivisibility of the system dynamical map. By sweeping the bath spectrum via tuning of the system frequency we show strongest memory effects at band-gap edges and provide an interpretation based on energy flow between system and environment. A system weakly coupled to a stiff chain ensures a Markovian dynamics, while the size of the environment as well as the local density of modes are not substantial factors. We show an opposite effect when increasing the temperature inside or outside the spectral band gap. Further, non-Markovianity arises for larger (negative and positive) powers of algebraic spectral densities, being the Ohmic case not always the most Markovian one.
Abstract Non-Markovian dynamics is central to quantum information processing, as memory effects strongly influence coherence preservation, metrology, and communication. In this work, we investigate the role of stochastic system–bath couplings in shaping non-Markovian behavior of open quantum systems, using the central spin model within a time-convolutionless master equation framework. We show that the character of the reduced dynamics depends jointly on the intrinsic memory of the environment and on the structure of the system–environment interaction. In certain regimes, the dynamics simplify to pure dephasing, while in general both amplitude damping and dephasing contribute to the evolution. By employing two complementary measures: the Quantum Fisher Information (QFI) flow and the Breuer–Laine–Piilo (BLP) measure, we demonstrate that QFI flow may fail to witness memory effects in weak-coupling and near-resonant regimes, whereas the BLP measure still detects information backflow. Furthermore, external modulation of the interaction kernel produces qualitatively richer behavior, including irregular and frequency-dependent revivals of non-Markovianity. These results clarify the physical origin of memory effects, highlight the limitations of single-witness approaches, and suggest that stochasticity and modulation can be harnessed to engineer robust, noise-resilient quantum technologies.
We study non-Markovian effects present in a driven qubit coupled to a finite environment using a recently proposed model developed in the context of calorimetric measurements of open quantum systems. To quantify the degree of non-Markovianity we use the Breuer-Laine-Piilo (BLP) measure [H.-P. Breuer, Phys. Rev. Lett. 103, 210401 (2009)]. We show that information backflow only occurs in the case of driving, in which case we investigate the dependence of memory effects on the environment size, driving amplitude, and coupling to the environment. We show that the degree of non-Markovianity strongly depends on the ratio between the driving amplitude and the coupling strength. We also show that the degree of non-Markovianity does not decrease monotonically as a function of the environment size.
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.
The exchange of information between an open quantum system and its environment allows us to discriminate among different kinds of dynamics, in particular detecting memory effects to characterize non-Markovianity. Here, we investigate the role played by the system-environment correlations and the environmental evolution in the flow of information. First, we derive general conditions ensuring that two generalized dephasing microscopic models of the global system-environment evolution result exactly in the same open-system dynamics, for any initial state of the system. Then, we use the trace distance to quantify the distinct contributions to the information inside and outside the open system in the two models. Our analysis clarifies how the interplay between system-environment correlations and environmental-state distinguishability can lead to the same information flow from and toward the open system, despite significant qualitative and quantitative differences at the level of the global evolution.
Abstract We explore in a rigorous manner the intuitive connection between the non-Markovianity of the evolution of an open quantum system and the performance of the system as a quantum memory. Using the paradigmatic case of a two-level open quantum system coupled to a bosonic bath, we compute the recovery fidelity, which measures the best possible performance of the system to store a qubit of information. We deduce that this quantity is connected, but not uniquely determined, by the non-Markovianity, for which we adopt the Breuer–Laine–Piilo measure proposed in Breuer et al (2009 Phys. Rev. Lett . 103 210401). We illustrate our findings with explicit calculations for the case of a structured environment.