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arxiv: 2507.16830 · v5 · pith:WZVTSGZJnew · submitted 2025-07-09 · ⚛️ physics.gen-ph

Non-Markovian Light-Matter Dynamics in the Time Fractional Jaynes-Cummings Model with Modulated Coupling

Enrique C. Gabrick , Thiago T. Tsutsui , Danilo Cius , Ervin K. Lenzi , Antonio S. M. de Castro , Fabiano M. Andrade This is my paper

Pith reviewed 2026-05-22 00:51 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords Jaynes-Cummings modeltime fractional Schrödinger equationnon-Markovian dynamicsmodulated couplingpopulation inversionquantum entanglementmemory effectsfractional order
0
0 comments X

The pith

Fractional order controls non-periodic evolution under sinusoidal coupling in the time fractional Jaynes-Cummings model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the impact of fractional time derivatives on a generalized Jaynes-Cummings light-matter system that includes constant, linear, exponential, and sinusoidal couplings. Fractional order introduces memory effects that produce damped oscillations and asymptotic decay in population inversion and entanglement. The central finding is that sinusoidal coupling keeps dynamics non-periodic for both formulations of the time fractional Schrödinger equation, while the fractional order itself serves as a tunable control parameter for that evolution within a defined range. This matters for modeling realistic non-Markovian behavior in quantum optical systems without resorting to full open-system master equations.

Core claim

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, with the time-dependent couplings and fractional formulations together determining whether entanglement remains high or low.

What carries the argument

Two formulations of the time fractional Schrödinger equation applied to the Jaynes-Cummings Hamiltonian with modulated couplings, which encode memory effects that damp oscillations and shape asymptotic population inversion and entanglement.

If this is right

  • Sinusoidal coupling preserves non-periodic dynamics across both TFSE formulations.
  • The fractional order tunes the character of the non-periodic evolution inside a specific interval.
  • Different couplings combined with each fractional formulation produce either high or low entanglement.
  • Memory effects from the fractional order lead to damped oscillations and asymptotic decay in observables.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The fractional-order control could be tested by comparing against cavity QED experiments that use modulated atom-field interactions.
  • This formulation supplies a simpler alternative to full non-Markovian master equations for simulating memory in light-matter systems.
  • The same approach may extend to related models such as the quantum Rabi or Dicke Hamiltonians with fractional time evolution.

Load-bearing premise

The two specific formulations of the time fractional Schrödinger equation correctly represent the non-Markovian memory effects present in the physical light-matter system under study.

What would settle it

Numerical comparison of the fractional model's population inversion and entanglement curves for sinusoidal coupling against the corresponding solution of the standard non-Markovian Lindblad master equation for the identical Jaynes-Cummings parameters.

Figures

Figures reproduced from arXiv: 2507.16830 by Antonio S. M. de Castro, Danilo Cius, Enrique C. Gabrick, Ervin K. Lenzi, Fabiano M. Andrade, Thiago T. Tsutsui.

Figure 1
Figure 1. Figure 1: Fractional probability Pα,β(t) as a function of time, setting a0 = 1, b0 = 0, n = 0, λ0 = 1 and ∆ = 0.5, for different values of α: α = 0.4 (solid blue line), α = 0.5 (finely dotted red line), α = 0.7 (dotted green line), α = 1.0 (dashed gray line). In (a), we study the scenario α = β, while in (b), β = 1.0. The inset in (a) displays the behavior of Pα,α(t) in the interval t ∈ [90, 100], while the inset in… view at source ↗
Figure 2
Figure 2. Figure 2: Fractional probability Pα,β(t) as a function of α in the interval α ∈ [0.4, 1.0], setting a0 = 1, b0 = 0, n = 0, λ0 = 1 and ∆ = 0.5, for different instants: t = 0 (dashed gray line), t = 1 (solid blue line), t = 5 (finely dotted red line), t = 10 (dotted green line), t = 20 (dot-dashed orange line). As an inset, we plot the same quantity but in the range α ∈ [0.025, 0.050]. In (a), we study the scenario α … view at source ↗
Figure 4
Figure 4. Figure 4: The normalized population inversion resulting [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The normalized VNE for a constant coupling [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: The normalized VNE resulting from a linear [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: The normalized VNE resulting from an expo [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Population inversion for sinusoidal coupling [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The normalized VNE resulting from an expo [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
read the original abstract

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 Schr\"odinger 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript investigates non-Markovian effects in a generalized Jaynes-Cummings model using two formulations of the time-fractional Schrödinger equation (TFSE) with various time-dependent couplings, including constant, linear, exponential, and sinusoidal. It analyzes the impact on population inversion and entanglement, concluding that fractional order introduces memory effects causing damped oscillations and asymptotic decay, and that sinusoidal coupling preserves non-periodic dynamics while the fractional order α serves as a control mechanism within a certain range.

Significance. If the chosen TFSE formulations validly represent non-Markovian memory in light-matter systems, this work could offer a novel approach to controlling quantum dynamics and entanglement via fractional parameters. The exploration of multiple coupling types provides a comparative view, but the lack of microscopic derivation limits the physical interpretability of the results.

major comments (1)
  1. [§2] §2: The Caputo and Riemann-Liouville time-fractional Schrödinger equations are introduced directly without derivation from a system-bath Hamiltonian or explicit validation that their memory kernels reproduce established non-Markovian signatures (e.g., those obtained from a Lorentzian spectral density or Nakajima-Zwanzig projection). This is load-bearing for the central claim that the observed damping, asymptotic decay, and α-dependent control correspond to physical non-Markovian light-matter dynamics.
minor comments (2)
  1. The abstract states that 'within a certain range' the fractional order acts as a control mechanism but does not specify the numerical interval for α; this should be stated explicitly with reference to the relevant figures or tables.
  2. Notation for the two TFSE formulations should be introduced with a brief reminder of the integral kernels in the first appearance to aid readability for readers unfamiliar with fractional calculus.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the importance of physical interpretability. We address the single major comment below and outline targeted revisions to improve context without altering the core phenomenological approach of the work.

read point-by-point responses

  1. Referee: §2: The Caputo and Riemann-Liouville time-fractional Schrödinger equations are introduced directly without derivation from a system-bath Hamiltonian or explicit validation that their memory kernels reproduce established non-Markovian signatures (e.g., those obtained from a Lorentzian spectral density or Nakajima-Zwanzig projection). This is load-bearing for the central claim that the observed damping, asymptotic decay, and α-dependent control correspond to physical non-Markovian light-matter dynamics.

    Authors: We acknowledge that the TFSE formulations are introduced in §2 on a phenomenological basis rather than derived from a microscopic system-bath Hamiltonian. This choice follows the standard practice in the fractional quantum mechanics literature, where the Caputo and Riemann-Liouville operators are employed precisely because their non-local kernels encode memory effects that produce damping and asymptotic decay—features widely associated with non-Markovian evolution. While we do not claim equivalence to a specific spectral density such as Lorentzian, the fractional order α directly modulates the strength and range of the memory kernel, providing the control mechanism reported in our results. In the revised manuscript we will expand the opening of §2 with a concise paragraph that (i) cites representative works applying TFSE to quantum optics and light-matter systems, (ii) explicitly states the phenomenological nature of the model, and (iii) notes that the observed dynamical signatures are consistent with known non-Markovian phenomenology even if a full Nakajima-Zwanzig projection is not performed here. These additions will clarify the scope and limitations of our claims while preserving the comparative study of coupling types. revision: partial

Circularity Check

0 steps flagged

No circularity: numerical exploration of posited TFSE models

full rationale

The paper introduces the Caputo and Riemann-Liouville time-fractional Schrödinger equations as modeling frameworks for non-Markovian memory in the Jaynes-Cummings system and then numerically solves the resulting integro-differential equations for constant, linear, exponential, and sinusoidal couplings. All reported behaviors—damped oscillations, asymptotic decay, preservation of non-periodic dynamics under sinusoidal modulation, and α acting as a control parameter—are direct outputs of these simulations rather than quantities fitted to data or redefined by construction. No equations equate a derived observable to an input parameter, no self-citation supplies a uniqueness theorem that forces the central claim, and no ansatz is smuggled through prior work. The derivation chain is therefore self-contained as an exploratory numerical study whose validity rests on the external plausibility of the chosen fractional operators, not on internal tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to list concrete free parameters or axioms; the fractional order itself functions as a tunable parameter whose physical justification is assumed rather than derived.

free parameters (1)
  • fractional order alpha
    Varied to explore memory effects; value range not specified in abstract but acts as control parameter for dynamics.

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