Abstract Our work explores the time evolution of entanglement, local quantum uncertainty, and correlated coherence within a system modeled by two coupled double quantum dots. The dynamics is described using a time-fractional Schrödinger equation, which is treated here as a phenomenological effective framework introducing temporal nonlocality and memory-like effects, rather than as a first-principles open-system reduction. We vary the fractional parameter τ , the tunneling amplitudes δ A and δ B , and the inter-dot Coulomb interaction strength V , in order to investigate how these key parameters govern the generation, stabilization, and decay of quantum resources within the system. The obtained results reveal that, for both initial states (separable and partially entangled), fractional dynamics with a small τ rapidly generates entanglement reaching maximal values LN ≈ 1 together with strong non-classical correlations quantified by the local quantum uncertainty. Conversely, when τ is closer to unity, entanglement builds up more slowly but the memory-like effects allow quantum resources to remain significant for a longer time, with the negativity remaining above ≈ 0.6 . We also find that higher Coulomb-interaction frequencies V accelerate the build-up of correlations and stabilize coherence, while a strong tunneling asymmetry degrades entanglement and coherence despite the initial benefits of increasing quantum resources. We find that the standard unitary Schrödinger evolution is recovered analytically at τ = 1 , where the Mittag–Leffler functions reduce to ordinary exponentials, while decreasing τ progressively introduces fractional-time nonlocal (memory-like) effects.
Abstract Our work explores the time evolution of entanglement, local quantum uncertainty, and correlated coherence within a system modeled by two coupled double quantum dots. The dynamics is described using a time-fractional Schrödinger equation, which is treated here as a phenomenological effective framework introducing temporal nonlocality and memory-like effects, rather than as a first-principles open-system reduction. We vary the fractional parameter τ , the tunneling amplitudes δ A and δ B , and the inter-dot Coulomb interaction strength V , in order to investigate how these key parameters govern the generation, stabilization, and decay of quantum resources within the system. The obtained results reveal that, for both initial states (separable and partially entangled), fractional dynamics with a small τ rapidly generates entanglement reaching maximal values LN ≈ 1 together with strong non-classical correlations quantified by the local quantum uncertainty. Conversely, when τ is closer to unity, entanglement builds up more slowly but the memory-like effects allow quantum resources to remain significant for a longer time, with the negativity remaining above ≈ 0.6 . We also find that higher Coulomb-interaction frequencies V accelerate the build-up of correlations and stabilize coherence, while a strong tunneling asymmetry degrades entanglement and coherence despite the initial benefits of increasing quantum resources. We find that the standard unitary Schrödinger evolution is recovered analytically at τ = 1 , where the Mittag–Leffler functions reduce to ordinary exponentials, while decreasing τ progressively introduces fractional-time nonlocal (memory-like) effects.
Our work explore the time evolution of entanglement, local quantum uncertainty, and correlated coherence, within a system modeled by two double quantum dots. The dynamics is represented using a time-fractional Schrödinger equation, which includes memory effects in a non-Markovian regime. We vary the fractional parameter τ, the tunneling amplitudes δA and δB, as well as the inter-dot interaction strength V, to investigate how these key parameters govern the generation, stabilization, and decay of quantum resources within the system. The obtained results reveal that, for both initial states, fractional dynamics with a low τ rapidly generates entanglement expecting maximal values LN≈1 and non-classical correlations quantified by local quantum uncertainty. Conversely, higher values of τ lead to slower entanglement but memory effects allow quantum resources to remain significant for a longer time, with the negativity remaining above (≈0.6). We also find that higher interaction frequencies V accelerate correlations and stabilize coherence, while a strong tunneling asymmetry degrades entanglement and coherence despite the initial benefits of increasing quantum resources.
Abstract This research explores the progression of fractional time dynamics of quantum entanglement, nonclassical correlations, and quantum coherence C l 1 in a qubit-qutrit XXZ system through an in-depth analysis of the effects of the fractional parameter τ , the exchange interaction J , the XXZ exchange anisotropy δ , and the Dzyaloshinskii-Moriya interaction (DMI) D z , and the initial state. The results reveal that lower values of τ lead to a rapid and stable increase in quantum correlations (measured by logarithmic negativity, LN, and local quantum uncertainty (LQU) but cause a faster decay in coherence C l 1 , indicating a quick loss of quantum superposition. Conversely, higher values of τ slow the dynamics of correlations, allowing coherence to persist longer. The exchange strength J similarly influences stability: low J values promote fast correlation formation but reduce coherence stability, while high J values stabilize coherence at the expense of slower correlation growth. As for the XXZ anisotropy δ and DMI strength D z , lower values promote rapid quantum correlation development but compromise coherence. In contrast, higher values help sustain C l 1 over time, limiting the intensity of correlations. The initial state is also critical: an initially partially entangled state is more resilient to perturbations. It preserves correlations over time compared to a separable state, which exhibits cycles of entanglement creation and destruction. Thus, by tuning system parameters, it is possible to control the stability and duration of correlations and coherence, providing a framework for optimizing quantum systems in applications that require both strong entanglement and durable coherence, such as quantum computing and secure communication.
This work explores the generation and robustness dynamics of coupled double quantum dots using uncertainty-induced (UI) nonlocality, maximum Bell-CHSH inequality, and log-negativity with intrinsic-decoherence. This study examines the generation of Bell-CHSH nonlocality, UI-nonlocality, and log-negativity entanglement using a separable two-double-quantum-dots state. Enhancing these features is achieved by tuning intrinsic decoherence and dot interaction strengths, highlighting their potential for creating robust quantum correlations. The two-double-quantum-dots correlated states can be produced and enhanced by increasing the pair-dots tunneling couplings and Coulomb-two-electrons interactions. The decoherence effect acceleration depends on Coulomb-two-electrons interactions and the pair-dots tunneling coupling. For a maximally entangled state, the robustness dynamics of the initial maximal Bell-CHSH-nonlocality, UI-nonlocality, and log-negativity’s entanglement, is explored against the two-double-quantum-dots interactions and the decoherence effects.
• A generalized time-dependent Jaynes–Cummings model is investigated within the framework of the time fractional Schr¨odinger equation. • Two distinct fractional formulations are compared, encompassing oscillatory and dissipative non- Markovian dynamics. • Our results shows that fractional order introduces memory effects leading to damped oscillations and asymptotic decay in population inversion and entanglement. • Time-dependent couplings (linear, exponential, and sinusoidal) strongly modulate entanglement generation and decay. • Fractional order acts as a control parameter, preserving non-periodic dynamics under sinusoidal coupling within specific regimes. We investigate the fractional time description of a generalized quantum light-matter system modeled by a time-dependent Jaynes-Cummings (JC) interaction, with different coupling types: constant, linear, exponential, and sinusoidal. Two formulations of the time fractional Schrödinger equation (TFSE) are examined, with a focus on their impact on population inversion and entanglement. Our findings highlight that the introduction of fractional order introduces memory effects, associated with damped oscillations and asymptotic decay. Furthermore, we find that the time-dependent couplings, combined with distinct fractional formulations, influence how these effects occur, ultimately resulting in high or low entanglement. A key finding of our work is that, under sinusoidal coupling, non-periodic dynamics is preserved for both formulations of the TFSE; however, within a certain range, the fractional order can act as a control mechanism for the non-periodic evolution.
We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schrödinger equation. We examine how the fractional derivative order α influences non-classical features under different initial conditions. For an initial Fock state, fractional evolution introduces transient dynamics and heightened sensitivity to coupling strength. Through an inverse problem approach, we interpret these effects as arising from an effective time-dependent coupling with a strong initial pulse. For an initial coherent state, the fractional order tunes the system between dynamical regimes, with a transition at $α= 0.50 $ where standard collapse-and-revival is replaced by stable, periodic evolution. This regime enhances non-classical field properties, including stronger sub-Poissonian statistics, periodic quadrature squeezing, and the formation of Schrödinger cat states.
The memory fractional effects of a one-axis twisting model on the dynamics of two-qubit entanglement and non-locality are discussed. It consists of solving the time-dependent fractional Schrödinger equation by extending any integration into non-integer orders using Riemann–Liouville integration. The obtained results present the possibility of controlling the fractional order of memory, varying the parameters to significantly generate concurrency and Bell’s non-locality. Under the current investigation setup, it is noticeable that the behaviors of the proposed quantifiers are similar to each other, but with a small difference in the amplitude of non-locality with respect to entanglement. Importantly, we show that the most intriguing aspect of this paper is to detect that pair-qubit entanglement and non-locality can be preserved for an indefinite time, which still holds significance in quantum information processing.